./S50-v2writeHTML.pl Mon Oct  9 16:30:34 1995

HTML generation from source for Mathematics:Sci

Subjects sourced by Mathematics:Sci in page sequence as they appear in the handbook.

Source for 618-111 v4, p206

618-111 Mathematics 1A(Advanced)

Note: Students may not gain credit for both 618-111 and any of 618-101 (1995 Handbook), 618-121, 618-142, nor for any of 618-141, 618-161, 618-162 if 618-111 has already been passed.

Credit points: 12.5

Coordinator: Dr J R J Groves

Prerequisite: Invitation by the Head of Department.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
the theoretical treatment of systems of simultaneous linear equations.

Have developed:

an ability to construct simple proofs;
an ability to manipulate complex numbers and to use them to solve problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute areas, arc lengths and volumes;
an ability to solve arbitrary systems of simultaneous linear equations.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers;
the role of limits in both the differential and integral calculus;
the practical uses of calculus;
the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.

Content:

Foundations: integers, mathematical induction; topics in elementary number theory; real numbers. Complex numbers including the complex exponential. Topics in elementary geometry. Calculus: functions of one real variable, limits, continuity, derivatives; introduction to Riemann integration, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc lengths, volumes and surface areas of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products; geometrical applications; linear dependence, bases and coordinates, dimension. Solution of simultaneous linear equations, row-reduction, rank, computation of inverses, determinants.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

Source for 618-112 v4, p206

618-112 Mathematics 1B (Advanced)

Note: Students may gain credit for only one of 618-102 (1995 Handbook), 618-112, 618-122, 618-200 or 618-211.

Credit points: 12.5

Coordinator: Professor J H Rubinstein

Prerequisite: Mathematics 618-111 or by invitation by the Head of Department.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Second semester

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra in finding invariants and bringing out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimension, Rⁿ and Cⁿ; inner products in real and complex spaces; linear transformations, matrix of a linear transformation, change of basis; eigenvectors and eigenvalues, diagonalisation of real symmetric matrices, applications -- including applications to geometry; symmetry groups of matrices of R² and R³. Multivariable calculus: functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

Source for 618-121 v4, p206 (Differences)

618-121 "Mathematics 1A" appears differently in several places - choose the one you want:


618-121 Mathematics, Faculty of Science.
618-121 Math. & Stats., Faculty of Educ(Parkville).
618-121 First Year Engineering, Faculty of Engineering.
618-121 Mathematical Sciences, Faculty of Eco & Comm.

1. Mathematics, Faculty of Science (v4, p206) : Next:618-122 | Prev:618-112
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-122 | Prev:610-172

618-121 Mathematics 1A

Note: Credit cannot be obtained for both 618-121 and any of 618-101 (1995 Handbook), 618-111 or 618-142, nor for both of 618-121 and any of 618-141, 618-161 or 618-162 if 618-121 has already been passed.

Credit points: 12.5

Coordinator: Dr J J Cross

Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Semester 1

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the intuitive notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
the theoretical treatment of systems of simultaneous linear equations.

Have developed:

an ability to manipulate complex numbers and to use them to solve problems;
an ability to use differential calculus to solve extremal problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute area, length and volume;
an ability to solve arbitrary systems of simultaneous linear equations.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers; the role of limits in both the differential and integral calculus;
the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.

Content:

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row-reduction, rank, inverse, solution of linear equations, geometrical interpretation.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

1. Mathematics, Faculty of Science (v4, p206) : Next:618-122 | Prev:618-112
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-122 | Prev:610-172

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p144) : Next:618-122

618-121 Mathematics 1A

Credit points: 12.5

Coordinator: Dr J J Cross.

Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.

Contact: 39 lectures (three a week), 13 1-hour tutorials and 39 hours problem solving

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the intuitive notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
the theoretical treatment of systems of simultaneous linear equations.

Have developed:

an ability to manipulate complex numbers and to use them to solve problems;
an ability to use differential calculus to solve extremal problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute area, length and volume;
an ability to solve arbitrary systems of simultaneous linear equations.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers; the role of limits in both the differential and integral calculus;
the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.

Content:

Foundations Sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus Functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations Vectors in three- dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row- reduction, rank, inverse, solution of linear equations, geometrical interpretation.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p144) : Next:618-122

4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-122 | Prev:617-141

618-121 Mathematics 1A

Credit points: 12.5

Coordinator: Dr J J Cross

Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Semester 1

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the intuitive notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
the theoretical treatment of systems of simultaneous linear equations.

Have developed:

an ability to manipulate complex numbers and to use them to solve problems;
an ability to use differential calculus to solve extremal problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute area, length and volume;
an ability to solve arbitrary systems of simultaneous linear equations.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers; the role of limits in both the differential and integral calculus;
the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.

Content:

Foundations Sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus Functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations Vectors in threedimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; rowreduction, rank, inverse, solution of linear equations, geometrical interpretation.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written exam-ination and class tests totalling not more than 1.5 hours.

* Note that ASSESSMENT, CONTENT, OBJECTIVES differs from the maintainer's version above. A log of variations is available.

4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-122 | Prev:617-141

Source for 618-122 v4, p207 (Differences)

618-122 "Mathematics 1B" appears differently in several places - choose the one you want:


618-122 Mathematics, Faculty of Science.
618-122 Math. & Stats., Faculty of Educ(Parkville).
618-122 First Year Engineering, Faculty of Engineering.
618-122 Mathematical Sciences, Faculty of Eco & Comm.

1. Mathematics, Faculty of Science (v4, p207) : Next:618-130 | Prev:618-121
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-130 | Prev:618-121

618-122 Mathematics 1B

Note: Students may gain credit for only one of 618-122, 618-102 (1995 Handbook), 618-112, 618-200 and 618-211.

Credit points: 12.5

Coordinator: Professor J H Rubinstein

Prerequisite: Mathematics 618-101 (1995 Handbook) or 618-111 or 618-121

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Second semester; available in first semester of the following year as 618-200

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra to find invariants and bring out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real-symmetric and orthogonal matrices. Multivariable calculus: functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p207) : Next:618-130 | Prev:618-121
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-130 | Prev:618-121

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-130 | Prev:618-121

618-122 Mathematics 1B

Note: Students may gain credit for only one of 618-122, 618-102 (1995 Handbook), 618-112, 618-200 and 618-211.

Credit points: 12.5

Coordinator: Professor J H Rubinstein.

Prerequisite: Mathematics 618-101 (1995 Handbook) or 618-111 or 618-121.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: Second semester; available in first semester of the following year as 618-200.

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra to find invariants and bring out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series Convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra Vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real- symmetric and orthogonal matrices. Multivariable calculus Functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-130 | Prev:618-121

4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-151 | Prev:618-121

618-122 Mathematics 1B

Note: Students may gain credit for only one of 618-122, 618-102 (1995 Handbook), 618-112, 618-200 and 618-211.

Availability: Available in first semester of the following year as 618-200

Credit points: 12.5

Coordinator: Professor J H Rubinstein

Prerequisite: Mathematics 618-101 (1995 Handbook) or 618-111 or 618-121

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Second semester

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra to find invariants and bring out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series Convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra Vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rn and Cn; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, realsymmetric and orthogonal matrices. Multivariable calculus Functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that AVAILABILITY, CONTENT, OBJECTIVES, SEMESTER differs from the maintainer's version above. A log of variations is available.

4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-151 | Prev:618-121

Source for 618-130 v4, p207 (Differences)

618-130 "Applied Mathematics" appears differently in several places - choose the one you want:


618-130 Mathematics, Faculty of Science.
618-130 Math. & Stats., Faculty of Educ(Parkville).
618-130 First Year Engineering, Faculty of Engineering.

1. Mathematics, Faculty of Science (v4, p207) : Next:618-131 | Prev:618-122
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-132 | Prev:618-122

618-130 Applied Mathematics

Note: Students may not gain credit for both 618-130 and 618-132.

Credit points: 12.5

Coordinator: Dr S L Carnie

Prerequisite: 618-101 (1995 Handbook) or 111 or 121 or 142; or 618-100 (1995 Handbook), with 618-142 as corequisite; or 618-141, with 618-142 as corequisite; or 618-162, with 618-142 as corequisite.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Second semester, repeated in first semester of the following year

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of ordinary differential equations;
the principles and essential information regarding first and second ordinary differential equations; eigenvalues and eigenvectors; linear systems of first and second order ordinary differential equations and their application primarily in the field of mechanics.

Have developed:

the ability to solve analytically: first order ordinary differential equations (ODEs) of linear, separable or homogeneous type; second order linear ODEs, including the method of reduction of order, with special emphasis on constant coefficient equations; systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques;
the ability to apply the above techniques to simple problems in particle dynamics, including projectile motion and orbital motion under central forces.

Appreciate:

the role of differential equations in applied mathematics and their use in modelling the dynamics of single particles and small systems of particles.

Content:

Differential equations: first-order differential equations (linear via integrating factors, separable and homogeneous) and applications; linear differential equations with constant coefficients, particular integrals and complementary functions. Mechanics: Newton's laws, conservation of energy, projectiles, central forces and orbital motion. Systems of differential equations: systems of linear differential equations with constant coefficients, eigenvalues and eigenvectors; systems of oscillators, an introduction to the phase plane

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p207) : Next:618-131 | Prev:618-122
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-132 | Prev:618-122

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-141 | Prev:618-122

618-130 Applied Mathematics

Note: Students may not gain credit for both 618-130 and 618-132.

Credit points: 12.5

Coordinator: Dr S L Carnie.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: Second semester, repeated in first semester of the following year.

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of ordinary differential equations;
the principles and essential information regarding first and second ordinary differential equations; eigenvalues and eigenvectors; linear systems of first and second order ordinary differential equations and their application primarily in the field of mechanics.

Have developed:

the ability to solve analytically: first order ordinary differential equations (ODEs) of linear, separable or homogeneous type; second order linear ODEs, including the method of reduction of order, with special emphasis on constant coefficient equations; systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques;
the ability to apply the above techniques to simple problems in particle dynamics, including projectile motion and orbital motion under central forces.

Appreciate:

the role of differential equations in applied mathematics and their use in modelling the dynamics of single particles and small systems of particles.

Content:

Differential equations First- order differential equations (linear via integrating factors, separable and homogeneous) and applications; linear differential equations with constant coefficients, particular integrals and complementary functions. Mechanics Newton's laws, conservation of energy, projectiles, central forces and orbital motion Systems of differential equations Systems of linear differential equations with constant coefficients, eigenvalues and eigenvectors; systems of oscillators, an introduction to the phase plane

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-141 | Prev:618-122

Source for 618-131 v4, p207

618-131 Discrete Mathematics (Advanced)

Note: Students may not gain credit for both 618-131 and any of 618-141 (1995 Handbook), 618-251, or the Mathematical Sciences subject 617-170 Discrete Mathematics and Statistics (1994 Handbook).

Credit points: 12.5

Coordinator: Professor C F Miller.

Prerequisite: Invitation by the Head of Department.

Contact: 39 lectures (three a week) 13 x 1-hour tutorials and 39 hours problem solving.

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the notion of validity of a mathematical formula
the concept of a mathematical proof
the principle of mathematical induction
the use of logical notation
countability and uncountability

Have developed:

skills and experience in using the language of sets, functions and relations
skills in counting and combinatorics
elementary skills in analysing graphs
the ability to prove simple theorems properly
skills in proving results by mathematical induction.

Appreciate:

the need for mathematical rigour
the variety of applications of discrete mathematical techniques

Content:

The natural numbers: well-ordering, forms of mathematical induction, division algorithm, greatest common divisor, prime factorization, recursion. Combinatorics: graphs and trees, paths, cycles, counting principles. Logic: logical notation, propositional connectives, quantifiers, truth tables, logical validity, counter-examples, methods of proof. Set theory: sets and set operations, functions, relations, orderings, equivalence relations and partitions, cardinality, countable and uncountable sets. Additional topics selected from: difference equations, generating functions, graph theory.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-132 v4, p207

618-132 Applied Mathematics (Advanced)

Note:

Students may not gain credit for both 618-132 and 618-130.
Students who have obtained a result of H3 or better in 618-101 (1995 Handbook) or 618-121 may ask for permission to enter 618-132.

Credit points: 12.5

Coordinator: Professor L R White

Prerequisite: 618-111 or by invitation by the Head of Department (See Note 2 below).

Corequisite: 618-112 or 618-122.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving.

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the classification and principles governing the solution of the basic first and second order differential equations;
the range of calculus skills and techniques necessary for the solution of these differential equations, and the solution methods applicable to each type;
the mathematical formulation of physical problems and their solution via the above techniques;
the principles of Newtonian mechanics and its application in single particle and simple rigid body motions and in coupled vibrating systems.

Have developed:

the ability to classify and solve the basic differential equations of first and second order; the integral and differential calculus skills to achieve these solutions with accuracy and confidence;
a sound understanding of the action of forces in mechanical systems and the translation of that understanding into mathematical formulation of physical problems.

Appreciate:

the power of differential equation modelling in advancing an understanding of complex physical processes from a wide variety of real world phenomena.

Content:

Differential equations: first-order differential equations (linear via integrating factors, separable and homogeneous) and applications; linear differential equations with constant coefficients, particular integrals and complementary functions. Mechanics: kinematics; Newton's laws, projectiles, constrained motion of a particle; systems of particles; motion of a rigid body; impulse problems. Systems of differential equations: systems of linear differential equations with constant coefficients, applications of matrix methods, stability; equilibrium and stability of conservative systems, small oscillations; first-order autonomous nonlinear systems and the phase plane.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-141 v4, p207 (Differences)

618-141 "Intermediate Mathematics A" appears differently in several places - choose the one you want:


618-141 Mathematics, Faculty of Science.
618-141 First Year Engineering, Faculty of Engineering.
618-141 Geomatics, Faculty of Engineering.
618-141 Math. & Stats., Faculty of Educ(Parkville).
618-141 Agriculture, Faculty of Agric, For & Hort.

1. Mathematics, Faculty of Science (v4, p207) : Next:618-142 | Prev:618-132
2. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-142 | Prev:618-132
3. Geomatics, Faculty of Engineering (v4, p123) : Next:618-142 | Prev:600-202

618-141 Intermediate Mathematics A

Note: Students may not gain credit for both Mathematics 618-141 and any of 618-100 (1995 Handbook), 618-151 or 618-162. Furthermore, credit cannot be obtained for 618-141 if any of 618-101 (1995 Handbook), 618-111 or 618-121 has already been passed.

Credit points: 12.5

Coordinator: Dr I R Aitchison

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Semester 1

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of vectors, matrices, and systems of linear equations;
the concepts of solid geometry;
the properties of basic functions of calculus.

Have developed:

the skills required to solve systems of linear equations;
the skills required to differentiate and integrate the basic functions of calculus;
the skills to work with functions of two variables;
the skills to solve simple first order differential equations;

Appreciate:

the fundamental concepts in linear algebra and calculus necessary for further serious studies in mathematics.

Content:

Vectors and matrices: vectors in three-dimensional space, dot and cross products, triple products, determinants; equations of lines and planes, geometrical applications; matrices, row operations, inverses; solution of linear equations, row-reduction, rank. Calculus: functions of one real variable, differentiation and integration, maxima and minima; approximate integration; functions of several variables, contours, partial differentiation. Differential equations: gradient fields, simple first order; applications; numerical solutions.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

4. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-142 | Prev:618-130

618-141 Intermediate Mathematics A

Credit points: 12.5

Coordinator: Dr I R Aitchison.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of vectors, matrices, and systems of linear equations;
the concepts of solid geometry;
the properties of basic functions of calculus.

Have developed:

the skills required to solve systems of linear equations;
the skills required to differentiate and integrate the basic functions of calculus;
the skills to work with functions of two variables;
the skills to solve simple first order differential equations;

Appreciate:

the fundamental concepts in linear algebra and calculus necessary for further serious studies in mathematics.

Content:

Vectors and matrices Vectors in three- dimensional space, dot and cross products, triple products, determinants; equations of lines and planes, geometrical applications; matrices, row operations, inverses; solution of linear equations, row- reduction, rank. Calculus Functions of one real variable, differentiation and integration, maxima and minima; approximate integration; functions of several variables, contours, partial differentiation. Differential equations Gradient fields, simple first order; applications; numerical solutions.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.

4. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-142 | Prev:618-130

5. Agriculture, Faculty of Agric, For & Hort (v4, p15) : Next:618-161 | Prev:610-142

618-141 Intermediate Mathematics A

Year 1 Agriculture.

Credit points: 12.5

Timetable: First semester

See additional details under the Mathematics subject above.

* Note that SEMESTER differs from the maintainer's version above. A log of variations is available.

5. Agriculture, Faculty of Agric, For & Hort (v4, p15) : Next:618-161 | Prev:610-142

Source for 618-142 v4, p208 (Differences)

618-142 "Intermediate Mathematics B" appears differently in several places - choose the one you want:


618-142 Mathematics, Faculty of Science.
618-142 Geomatics, Faculty of Engineering.
618-142 Math. & Stats., Faculty of Educ(Parkville).
618-142 First Year Engineering, Faculty of Engineering.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-151 | Prev:618-141
2. Geomatics, Faculty of Engineering (v4, p123) : Next:618-200 | Prev:618-141
4. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-171 | Prev:618-141

618-142 Intermediate Mathematics B

Note: Credit cannot be obtained for both 618-142 and any of 618-101 (1995 Handbook), 618-111 or 618-121, nor for both 618-142 and any of 618-141, 618-161 or 618-162 if 618-142 has already been passed.

Credit points: 12.5

Coordinator: Prof A J Guttmann

Prerequisite: 618-100 (1995 Handbook), or 618-141, or both of 618-161, 618-162, or satisfactory performance on the Exemption Test.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Offered in both semesters

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the intuitive notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions.

Have developed:

an ability to manipulate complex numbers and to use them to solve problems;
an ability to use differential calculus to solve extremal problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute area, length and volume;
an ability to determine the linear dependence or independence of sets of vectors, and to recognize where this is significant.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers; the role of limits in both the differential and integral calculus;
the practical uses of calculus; the importance of the general concept of a vector.

Content:

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; Taylor polynomials; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vector spaces: the space Rⁿ; linear dependence; spanning sets; bases and coordinates, applications.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

3. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-161 | Prev:618-141

618-142 Intermediate Mathematics B

Credit points: 12.5

Coordinator: Prof A J Guttmann.

Prerequisite: 618-100 (1995 Handbook), or 618-141, or both of 618-161, 618-162, or satisfactory performance on the Exemption Test.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: First or second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

some of the nature of the different types of numbers they use;
the intuitive notion of limits as used in continuity, differentiation and integration;
the notion of integral as area;
the extension of the notion of vectors in two or three dimensions to any finite number of dimensions.

Have developed:

an ability to manipulate complex numbers and to use them to solve problems;
an ability to use differential calculus to solve extremal problems;
an ability to compute a wide range of integrals;
an ability to use integration to compute area, length and volume;
an ability to determine the linear dependence or independence of sets of vectors, and to recognize where this is significant.

Appreciate:

the role of proof and logical reasoning in mathematics;
the use of complex numbers; the role of limits in both the differential and integral calculus;
the practical uses of calculus; the importance of the general concept of a vector.

Content:

Foundations Sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus Functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; Taylor polynomials; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vector spaces The space Rⁿ; linear dependence; spanning sets; bases and coordinates, applications.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.

3. Math. & Stats., Faculty of Educ(Parkville) (v5, p145) : Next:618-161 | Prev:618-141

Source for 618-151 v4, p208 (Differences)

618-151 "Mathematics for Economics" appears differently in several places - choose the one you want:


618-151 Mathematics, Faculty of Science.
618-151 Mathematical Sciences, Faculty of Eco & Comm.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-161 | Prev:618-142

618-151 Mathematics for Economics

Note: Students may not gain credit for both Mathematics 618-151 and 618-100 (1995 Handbook) or 141 or 162; furthermore, credit cannot be obtained for 618-151 if any of 618-101 (1995 Handbook), 111, 112, 211, 121, 122, 200 or 211 has already been passed. Students who desire a more extensive introduction to tertiary mathematics should consider taking the sequential subject 618-142.

Credit points: 12.5

Coordinator: Prof C J Thompson

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic properties and representation of vectors;
fundamental concepts in linear algebra, particularly those associated with solution of linear equations;
fundamental aspects of calculus of one and two variables.

Have developed:

skills in manipulating vectors;
skills in systematically solving systems of linear equations;
skills in differentiating and integrating the basic functions of calculus.

Appreciate:

the relationship between various branches of mathematics;
the application of mathematics to solving problems in economics and the social sciences;
the interpretation of economic phenomena in mathematical terms.

Content:

Vectors and matrices: introduction to vectors: scalar, vector, triple products, equations of lines, planes; elementary properties of matrices and determinants; row operations on matrices; solution of linear equations, matrix inverse. Calculus and its applications: functions and their inverses, differentiation, linear approximation, marginalism, elasticity; maxima and minima, concavity; integration, area, consumer and producer surplus, approximate integration; introduction to differential equations; Taylor polynomials; functions of several variables, level curves, chain rules, Lagrange multipliers, Jacobi and Hessian matrices.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-161 | Prev:618-142

2. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Prev:618-122

618-151 Mathematics for Economics

Credit points: 12.5

Coordinator: Prof C J Thompson

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic properties and representation of vectors;
fundamental concepts in linear algebra, particularly those associated with solution of linear equations;
fundamental aspects of calculus of one and two variables.

Have developed:

skills in manipulating vectors;
skills in systematically solving systems of linear equations;
skills in differentiating and integrating the basic functions of calculus.

Appreciate:

the relationship between various branches of mathematics;
the application of mathematics to solving problems in economics and the social sciences;
the interpretation of economic phenomena in mathematical terms.

Content:

Vectors and matrices Introduction to vectors: scalar, vector, triple products, equations of lines, planes; elementary properties of matrices and determinants; row operations on matrices; solution of linear equations, matrix inverse. Calculus and its applications Functions and their inverses, differentiation, linear approximation, marginalism, elasticity; maxima and minima, concavity; integration, area, consumer and producer surplus, approximate integration; introduction to differential equations; Taylor polynomials; functions of several variables, level curves, chain rules, Lagrange multipliers, Jacobi and Hessian matrices.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTENT, OBJECTIVES differs from the maintainer's version above. A log of variations is available.

2. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Prev:618-122

Source for 618-161 v4, p208 (Differences)

618-161 "Introductory Mathematics A" appears differently in several places - choose the one you want:


618-161 Mathematics, Faculty of Science.
618-161 Math. & Stats., Faculty of Educ(Parkville).
618-161 Agriculture, Faculty of Agric, For & Hort.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-162 | Prev:618-151

618-161 Introductory Mathematics A

Note: Students will not be permitted to enrol in this subject unless directed to do so by a member of the Mathematics Department. Credit cannot be obtained for 618-161 if any of 618-190 (1995 Handbook), 618-100 (1995 Handbook), 618-101 (1995 Handbook), 618-102 (1995 Handbook), 618-111, 618-112, 618-121, 618-122, 618-141, 618-142, 618-151, 618-162, 618-200 or 618-211 has already been passed.

Credit points: 12.5

Coordinator: Dr F R Barrington

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

concepts of basic functions and the calculus of functions of one variable.

Have developed:

manipulative skills in the use of polynomial, exponential, logarithmic and trigonometric functions;
the skills to find derivatives and antiderivatives of the above mentioned functions, and functions compounded from them;
an ability to apply these skills to coordinate geometry and to word problems.

Appreciate:

the sequential conceptual structure of the mathematics of functions;
the value of sketch graphs as an aid to the understanding of algebraic functional and calculus concepts.

Content:

Functions and relations: graphs of functions and relations, basic skills of graph sketching, conic sections Calculus: functions of one variable, compositions, inverse; special functions, circular, exponential, logarithmic, hyperbolic; limits, continuity; product, quotient, chain rules, maxima, minima, approximations, rates of change, curve sketching; antidifferentiation, applications
Additional topics A selection of one topic from polar graphs, vectors, matrices, complex numbers.

Assessment:

Up to 26 pages of written project and assignment work, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-162 | Prev:618-151

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-162 | Prev:618-142

618-161 Introductory Mathematics A

Credit points: 12.5

Coordinator: Dr F R Barrington.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

concepts of basic functions and the calculus of functions of one variable.

Have developed:

manipulative skills in the use of polynomial, exponential, logarithmic and trigonometric functions;
the skills to find derivatives and antiderivatives of the above mentioned functions, and functions compounded from them;
an ability to apply these skills to coordinate geometry and to word problems.

Appreciate:

the sequential conceptual structure of the mathematics of functions;
the value of sketch graphs as an aid to the understanding of algebraic functional and calculus concepts.

Content:

Functions and relations Graphs of functions and relations, basic skills of graph sketching, conic sections Calculus Functions of one variable, compositions, inverse; special functions, circular, exponential, logarithmic, hyperbolic; limits, continuity; product, quotient, chain rules, maxima, minima, approximations, rates of change, curve sketching; antidifferentiation, applications Additional topics A selection of one topic from polar graphs, vectors, matrices, complex numbers.

Assessment:

Up to 26 pages of written project and assignment work, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-162 | Prev:618-142

3. Agriculture, Faculty of Agric, For & Hort (v4, p15) : Next:212-105 | Prev:618-141

618-161 Introductory Mathematics

Year 1 Agriculture.

Credit points: 12.5

Timetable: First semester

See additional details under the Mathematics subject above.

* Note that TITLE differs from the maintainer's version above. A log of variations is available.

3. Agriculture, Faculty of Agric, For & Hort (v4, p15) : Next:212-105 | Prev:618-141

Source for 618-162 v4, p208 (Differences)

618-162 "Introductory Mathematics B" appears differently in several places - choose the one you want:


618-162 Mathematics, Faculty of Science.
618-162 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p208) : Next:618-191 | Prev:618-161

618-162 Introductory Mathematics B

Note:

Students may not gain credit for both Mathematics 618-162 and any of 618-100 (1995 Handbook), 618-141 or 618-151. Furthermore, credit cannot be obtained for 618-162 if any of 618-101 (1995 Handbook), 618-111, 618-121 or 618-141 has already been passed.
This subject is normally taken after 618-161, but may also be taken by students who would otherwise have selected 618-141 in first semester.

Credit points: 12.5

Coordinator: Dr I R Aitchison

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: Semester 2

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of vectors, matrices, and systems of linear equations;
the concepts of solid geometry;
the properties of basic functions of calculus.

Have developed:

the skills required to solve systems of linear equations;
the skills required to differentiate and integrate the basic functions of calculus;
the skills to work with functions of two variables;
the skills to solve simple first order differential equations;

Appreciate:

the fundamental concepts in linear algebra and calculus necessary for further serious studies in mathematics.

Content:

Vectors and matrices: matrices, row operations, solution of linear equations, inverses; vectors, scalar product, equations of lines and planes. Calculus: functions of one real variable, differentiation and integration, maxima and minima, Taylor series; approximate integration; functions of several variables, contours, partial differentiation. Differential equations: gradient fields, simple first-order; applications; numerical solutions.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

1. Mathematics, Faculty of Science (v4, p208) : Next:618-191 | Prev:618-161

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-200 | Prev:618-161

618-162 Introductory Mathematics B

Note:

Students may not gain credit for both Mathematics 618-162 and any of 618-100 (1995 Handbook), 618-141 or 618-151. Furthermore, credit cannot be obtained for 618-162 if any of 618-101 (1995 Handbook), 618-111, 618-121 or 618-141 has already been passed.
This subject is normally taken after 618-161, but may also be taken by students who would otherwise have selected 618-141 in first semester.

Credit points: 12.5

Coordinator: Dr I R Aitchison.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of vectors, matrices, and systems of linear equations;
the concepts of solid geometry;
the properties of basic functions of calculus.

Have developed:

the skills required to solve systems of linear equations;
the skills required to differentiate and integrate the basic functions of calculus;
the skills to work with functions of two variables;
the skills to solve simple first order differential equations;

Appreciate:

the fundamental concepts in linear algebra and calculus necessary for further serious studies in mathematics.

Content:

Vectors and matrices Matrices, row operations, solution of linear equations, inverses; vectors, scalar product, equations of lines and planes. Calculus Functions of one real variable, differentiation and integration, maxima and minima, Taylor series; approximate integration; functions of several variables, contours, partial differentiation. Differential equations Gradient fields, simple first order; applications; numerical solutions.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-200 | Prev:618-161

Source for 618-191 v4, p208

618-191 Mathematics Project (Advanced)

Credit points: 12.5

Coordinator: Dr W D Neumann

Prerequisite: Invitation by the Head of Department

Contact: Weekly seminars and 39 hours project work

Timetable: First semester

Objectives:

On the completion of this subject students should:
Comprehend:

in some detail and depth the mathematical theory and techniques associated with some topic or topics of interest to staff members.

Have developed:

an ability to pursue mathematical themes at some depth;
an ability to work with a certain amount of independence.

Appreciate:

the methods and techniques required to complete an in-depth study of mathematical topics;
an insight into higher level mathematics;
the interaction of various branches of mathematics.

Content:

Regular attendance at seminars and group discussions together with the completion of selected projects. The work will be closely supervised by members of staff.

Assessment:

Written reports and/or assignments and oral presentations.

Source for 618-200 v4, p209 (Differences)

618-200 "Mathematics 2" appears differently in several places - choose the one you want:


618-200 Mathematics, Faculty of Science.
618-200 Math. & Stats., Faculty of Educ(Parkville).
618-200 Geomatics, Faculty of Engineering.

1. Mathematics, Faculty of Science (v4, p209) : Next:618-201 | Prev:618-191
3. Geomatics, Faculty of Engineering (v4, p123) : Next:619-100 | Prev:618-142

618-200 Mathematics 2

Note: Students may not gain credit for more than one of 618-200, 618-211, 618-102 (1995 Handbook), 618-112, 618-122.

Credit points: 13.5

Coordinator: Dr J Clark

Prerequisite: One of Mathematics 618-101 (1995 Handbook) or 121 or 142.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving.

Timetable: Offered in both semesters

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra to find invariants and bring out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real-symmetric and orthogonal matrices. Multivariable calculus: functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours

1. Mathematics, Faculty of Science (v4, p209) : Next:618-201 | Prev:618-191
3. Geomatics, Faculty of Engineering (v4, p123) : Next:619-100 | Prev:618-142

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-212 | Prev:618-162

618-200 Mathematics 2

Note: Students may not gain credit for more than one of 618-200, 618-211, 618-102 (1995 Handbook), 618-112, 618-122.

Credit points: 13.5

Coordinator: Dr J Clark.

Prerequisite: Mathematics 618-101 (1995 Handbook) or 618-121 or 618-142.

Contact: 39 lectures (three each week), 13 1-hour tutorials and 39 hours problem solving.

Timetable: First or second semester.

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra to find invariants and bring out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series Convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra Vector spaces in general, axioms, linear independence, basis sets, dimensionality, Rⁿ and Cⁿ; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real- symmetric and orthogonal matrices. Multivariable calculus Functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; surface areas and volumes of solids of revolution; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours

* Note that CONTACT, CONTENT, PREREQUISITES, SEMESTER differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-212 | Prev:618-162

Source for 618-201 v4, p209

618-201 Real Analysis (Advanced)

Credit points: 12.0

Coordinator: Dr J J Koliha

Prerequisite: Mathematics 618-112 or 618-211, or by invitation (See Note 2 below)

Contact: 39 lectures (three a week).

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the structure and methods of proof;
the concept of convergence of sequences and series; elementary topology of the real line;
the fundamentals of continuity, differentiability and integration; interchange of limiting operations and elementary properties of metric spaces.

Have developed:

skills in constructing rigorous and accurate arguments;
skills in determining the convergence or otherwise of sequences and series;
an understanding of integration and how it is an extension of antidifferentiation;
a knowledge of when limiting operations can be interchanged.

Appreciate:

the importance and satisfaction of rigorous arguments via proofs;
the fundamental concepts of topology of the real line and how they extend to more abstract settings;
the inter-relationships of various branches of real analysis; applications of real analysis;
the deeper and more abstract aspects of real analysis and how they can sometimes defy intuition.

Content:

Sequences: standard sequences, least upper and greatest lower bounds, Bolzano-Weierstrass theorem, upper and lower limits, Cauchy convergence. Elementary topology: open and closed sets, nested intervals, Heine - Borel theorem. Series: standard series, ratio and n-th root tests, absolute and conditional convergence, re-arrangements, power series. Continuity: sequential continuity, differentiability, uniform continuity, approximation of continuous function by step functions, introduction to Riemann integration. Metric spaces: examples of metric spaces, convergence. Uniform convergence: term-by-term operations on sequences and series, application to power series.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
Notes:

Credit cannot be obtained for both 618-201 and 618-300 (1995 Handbook).
Students with a high level of achievement in 618-102 (1995 Handbook) or 618-122 may approach the Head of the Department of Mathematics to seek permission to enrol in this subject.

Source for 618-202 v4, p209

618-202 Complex Analysis (Advanced)

Note: Credit cannot be gained for both 618-202 and 618-252.

Credit points: 12.0

Coordinator: Dr J J Koliha

Prerequisite: Mathematics 618-201 or by invitation of the head of the Department of Mathematics.

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
basic topological concepts in the complex plane
Cauchy's theorem and its applications.

Have developed:

skills in differentiating functions of a complex variable;
skills in calculating contour integrals;
the ability to work with analytic functions in the cut plane;
the ability to apply Cauchy's integral formula and the residue theorem.

Appreciate:

differences between functions of a real and a complex variable;
the role of complex analytic methods in solving important problems in science and engineering.

Content:

Convergence: convergence of sequences and series, real and complex; ratio and n-th root tests; power series, circle of convergence. Functions of a complex variable: elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration: Riemann integral for real and complex functions; line and contour integrals, Cauchy's integral theorem; Taylor and Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-211 v4, p210

618-211 Mathematics 2 (Advanced)

Note: Students may gain credit for only one of 618-102 (1995 Handbook), 618-112, 618-122, 618-200 and 618-211.

Credit points: 13.5

Coordinator: Professor J H Rubinstein

Prerequisite: Mathematics 618-111 or by invitation by the Head of Department.

Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Timetable: First semester

Objectives:

On completion of this subject, students should :
Comprehend:

the basic properties of sequences and series, including Taylor series for functions;
the concepts of abstract vector spaces and inner product spaces;
the uses and properties of linear transformations;
the role of eigenvalues and eigenvectors in the study of such mappings;
the fundamental ideas in the calculus of functions of several variables.

Have developed:

an ability to use tests to decide if sequences and series converge or diverge;
the skills to find coordinates and matrices to represent vectors and linear transformations;
the ability to change coordinate systems to simplify problems involving vector spaces and linear transformations;
the skills to solve problems involving contours of surfaces;
skills to find extrema of functions and to find volumes using differentiation and integration.

Appreciate:

the role of series in estimation of functions;
the role of linear algebra in finding invariants and bringing out the underlying geometry in problems;
the similarities and differences between functions of one variable and multivariate functions.

Content:

Sequences and series: convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: vector spaces in general, axioms, linear independence, basis sets, dimension, Rn and Cn; inner products in real and complex spaces; linear transformations, matrix of a linear transformation, change of basis; eigenvectors and eigenvalues, diagonalisation of real symmetric matrices, applications -- including applications to geometry; symmetry groups of matrices of R2 and R3. Multivariable calculus: functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; coordinate transformations, Jacobi matrix and determinant; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.

Source for 618-212 v4, p210 (Differences)

618-212 "Applied Linear Algebra" appears differently in several places - choose the one you want:


618-212 Mathematics, Faculty of Science.
618-212 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p210) : Next:618-222 | Prev:618-211

618-212 Applied Linear Algebra

Credit points: 12.0

Coordinator: Dr J J Koliha

Prerequisite: One of Mathematics 618-112, 618-122, 618-200, 618-211

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

basic and more advanced concepts of linear algebra such as vector spaces, inner product spaces, linear transformations, diagonalization of matrices, Jordan canonical form and spectral decomposition.

Have developed:

skills in calculating eigenvalues and eigenvectors including iterative methods;
skills in the diagonalization of matrices;
skills in solving systems of ordinary differential equations using matrix methods;
skills in using a linear algebra software package for operations on matrices. and for implementing matrix numerical techniques.

Appreciate:

the power and importance of abstract linear algebra techniques in solving concrete problems in numerical analysis, science, the social sciences and engineering.

Content:

Vector Spaces: vector spaces; norms; inner products; linear transformations; application to Fourier series. Matrices: review of general properties of matrices - multiplication, inverse, transpose, partitioning; computing determinants, inverses, rank; LU - factorisation. Eigenvalues: Eigenvalues of square matrices; multiplicity of eigenvalues; eigenvalues and eigenvectors of special matrices, including triangular, hermitian, real symmetric and positive definite matrices; diagonalisation of matrices by unitary matrices and by nonsingular matrices; Jordan canonical form; minimal polynomial; Cayley - Hamilton theorem; spectral decomposition; diagonalisation of quadratic forms; positive definite forms. Differential Equations: systems of ordinary differential equations; Laplace transforms; control systems; stability; Gershgorin's circle theorem; estimation of dominant eigenvalue. Coding theory: linear codes; generator and parity check matrices; Hamming distance, encoding and decoding; error-detecting and error-correcting codes; syndromes and standard arrays; hamming codes and perfect codes.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p210) : Next:618-222 | Prev:618-211

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-231 | Prev:618-200

618-212 Applied Linear Algebra

Credit points: 12.0

Coordinator: Dr J J Koliha.

Prerequisite: One of Mathematics 618-102 (1995 Handbook) 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

basic and more advanced concepts of linear algebra such as vector spaces, inner product spaces, linear transformations, diagonalization of matrices, Jordan canonical form and spectral decomposition.

Have developed:

skills in calculating eigenvalues and eigenvectors including iterative methods;
skills in the diagonalization of matrices;
skills in solving systems of ordinary differential equations using matrix methods;
skills in using a linear algebra software package for operations on matrices. and for implementing matrix numerical techniques.

Appreciate:

the power and importance of abstract linear algebra techniques in solving concrete problems in numerical analysis, science, the social sciences and engineering.

Content:

Vector Spaces Vector spaces; norms; inner products; linear transformations; application to Fourier series. Matrices Review of general properties of matrices - multiplication, inverse, transpose, partitioning; computing determinants, inverses, rank; LU - factorisation. Eigenvalues Eigenvalues of square matrices; multiplicity of eigenvalues; eigenvalues and eigenvectors of special matrices, including triangular, hermitian, real symmetric and positive definite matrices; diagonalisation of matrices by unitary matrices and by nonsingular matrices; Jordan canonical form; minimal polynomial; Cayley - Hamilton theorem; spectral decomposition; diagonalisation of quadratic forms; positive definite forms. Differential Equations Systems of ordinary differential equations; Laplace transforms; control systems; stability; Gershgorin's circle theorem; estimation of dominant eigenvalue. Coding theory Linear codes; generator and parity check matrices; Hamming distance, encoding and decoding; error-detecting and error-correcting codes; syndromes and standard arrays; hamming codes and perfect codes.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-231 | Prev:618-200

Source for 618-222 v4, p210

618-222 Algebra (Advanced)

Note: Students with a high level of achievement in 618-102 (1995 Handbook) or 618-122 may approach the Head of the Department of Mathematics to seek permission to enrol in this subject.

Credit points: 12.0

Coordinator: Dr J R J Groves

Prerequisite: Mathematics 618-112 or 618-211 or by invitation (See Note below).

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic algebraic structure of abstract rings, fields and groups;
the concepts of isomorphism, homomorphism and quotient algebraic structures; Euclidean algorithm, irreducibility and unique factorization in polynomial rings;
basic isomorphism theorems.

Have developed:

the ability to understand and write proofs of basic theorems;
the ability to use the Euclidean algorithm in integers and polynomial rings;
a knowledge of basic examples of the abstract algebraic structures;
the ability to construct quotient objects.

Appreciate:

the clarity and economy of abstract algebra, and the pleasure of proofs involving concepts rather than calculations.

Content:

Rings: congruences, modular arithmetic and the division algorithm in the integers; abstract rings and isomorphisms; examples including matrix rings; polynomial rings, the division algorithm, irreducible polynomials and unique factorisation; ideals and quotient rings in polynomial rings. Groups: introduction to the symmetry groups of two and three dimensional Euclidean geometry; abstract groups, examples including matrix groups; homomorphism, normal subgroups, quotients and the first homomorphism theorem; group actions and permutation groups; conjugacy classes and their interpretation in symmetry groups, permutation groups and matrix groups.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-231 v4, p210 (Differences)

618-231 "Vector Analysis" appears differently in several places - choose the one you want:


618-231 Mathematics, Faculty of Science.
618-231 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p210) : Next:618-232 | Prev:618-222

618-231 Vector Analysis

Credit points: 12.0

Coordinator: Professor A J Guttmann

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; or all of 618-141, 618-142, 618-130, with concurrent enrolment in 618-200.

Contact: 39 lectures (three a week)

Timetable: Offered in both semesters

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of partial derivatives and vector differential operators.

Have developed:

the skills to obtain extrema of functions of several variables;
the skills required to calculate line, surface and volume integrals;
the skills to work in curvilinear coordinates.

Appreciate:

the fundamental concepts of vector calculus;
the relations between line, surface and volume integrals.

Content:

Functions of several variables: functions of several variables; inverse and implicit function theorems; Lagrange multipliers. Vector calculus: vector fields, gradient, divergence and curl; line, surface and volume integrals; divergence theorem, Stokes' theorem and Green's theorem; curvilinear coordinates; calculus of variations.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p210) : Next:618-232 | Prev:618-222

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-232 | Prev:618-212

618-231 Vector Analysis

Credit points: 12.0

Coordinator: Professor A J Guttmann.

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; or all of 618-141, 618-142, 618-130, with concurrent enrolment in 618-200.

Contact: 39 lectures (three each week)

Timetable: First or second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the manipulation of partial derivatives and vector differential operators.

Have developed:

the skills to obtain extrema of functions of several variables;
the skills required to calculate line, surface and volume integrals;
the skills to work in curvilinear coordinates.

Appreciate:

the fundamental concepts of vector calculus;
the relations between line, surface and volume integrals.

Content:

Functions of several variables Functions of several variables; inverse and implicit function theorems; Lagrange multipliers. Vector calculus Vector fields, gradient, divergence and curl; line, surface and volume integrals; divergence theorem, Stokes' theorem and Green's theorem; curvilinear coordinates; calculus of variations.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-232 | Prev:618-212

Source for 618-232 v4, p210 (Differences)

618-232 "Mathematical Methods" appears differently in several places - choose the one you want:


618-232 Mathematics, Faculty of Science.
618-232 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p210) : Next:618-242 | Prev:618-231

618-232 Mathematical Methods

Credit points: 12.0

Coordinator: Dr D Y C Chan

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; and one of 618-130 or 618-132.

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of classifying and describing ordinary and partial differential equations;
the concept of obtaining complete and general solutions;
the role of Fourier series, Laplace transforms and special functions in providing solutions to such equations.

Have developed:

a competent working knowledge on general methods to solve linear ordinary differential equations and partial differential equations;
know how to use standard methods such as Laplace transforms, series solutions, separation of variables for obtaining solutions.

Appreciate:

the complexity and the necessary ingredients required in obtaining solutions to ordinary and partial differential equations;
more advanced techniques available in further courses on mathematical methods.

Content:

Partial differential equations: Laplace's equation, wave equation and heat equation; separation of variables; Fourier series. Ordinary differential equations: introduction to Laplace transforms and applications; differential equations with variable coefficients, independent solutions, Wronskians; series solutions of ordinary differential equations; Bessel functions, Legendre polynomials and other special functions.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p210) : Next:618-242 | Prev:618-231

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-242 | Prev:618-231

618-232 Mathematical Methods

Credit points: 12.0

Coordinator: Dr D Y C Chan.

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; and one of 618-130 or 618-132.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of classifying and describing ordinary and partial differential equations;
the concept of obtaining complete and general solutions;
the role of Fourier series, Laplace transforms and special functions in providing solutions to such equations.

Have developed:

a competent working knowledge on general methods to solve linear ordinary differential equations and partial differential equations;
know how to use standard methods such as Laplace transforms, series solutions, separation of variables for obtaining solutions.

Appreciate:

the complexity and the necessary ingredients required in obtaining solutions to ordinary and partial differential equations;
more advanced techniques available in further courses on mathematical methods.

Content:

Partial differential equations Laplace's equation, wave equation and heat equation; separation of variables; Fourier series. Ordinary differential equations Introduction to Laplace transforms and applications; differential equations with variable coefficients, independent solutions, Wronskians; series solutions of ordinary differential equations; Bessel functions, Legendre polynomials and other special functions.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-242 | Prev:618-231

Source for 618-242 v4, p211 (Differences)

618-242 "Computational Mathematics" appears differently in several places - choose the one you want:


618-242 Mathematics, Faculty of Science.
618-242 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-251 | Prev:618-232

618-242 Computational Mathematics

Credit points: 12.0

Coordinator: Dr N Wormald

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; and either Computer Science 433-141 and 433-142, or one of 617-141, 617-142, 617-160 (1995 Handbook).

Contact: 18 lectures and 56 hours project work.

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the underlying basis for numerical techniques to solve a variety of problems;
the solution of linear equations by Gaussian elimination and LU factorization; polynomial interpolation and approximation of functions by polynomials;
methods of solution of differential equations;
numerical evaluation of integrals.

Have developed:

skills in implementing the techniques referred to above, and in interpreting results obtained by computer programs.

Appreciate:

the difficulties and possible pitfalls of numerical computation and of broad spectrum numerical analysis algorithms.

Content:

Linear equations: matrix norm, scaling, pivoting, stability, iterative methods, tri-diagonal systems. Function approximation: minimax, least squares, orthogonal polynomials, cubic splines; finite differences; interpolation, differentiation, integration. Ordinary differential equations: initial value problems; boundary value problems; numerical integration, asymptotic error formula; Runge-Kutta procedures.

Assessment:

A 1.5-hour end-of-semester written examination and project work as required.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-251 | Prev:618-232

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-251 | Prev:618-232

618-242 Computational Mathematics

Credit points: 12.0

Coordinator: Dr N Wormald.

Prerequisite: One of Mathematics 618-102 (1995 Handbook), 112, 122, 200, 211; and either Computer Science 433-141 and 433-142, or one of 617-141, 617-142, 617-160 (1995 Handbook).

Contact: 18 lectures and 56 hours project work

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the underlying basis for numerical techniques to solve a variety of problems;
the solution of linear equations by Gaussian elimination and LU factorization; polynomial interpolation and approximation of functions by polynomials;
methods of solution of differential equations;
numerical evaluation of integrals.

Have developed:

skills in implementing the techniques referred to above, and in interpreting results obtained by computer programs.

Appreciate:

the difficulties and possible pitfalls of numerical computation and of broad spectrum numerical analysis algorithms.

Content:

Linear equations Matrix norm, scaling, pivoting, stability, iterative methods, tri-diagonal systems. Function approximation Minimax, least squares, orthogonal polynomials, cubic splines; finite differences; interpolation, differentiation, integration. Ordinary differential equations Initial value problems; boundary value problems; numerical integration, asymptotic error formula; Runge-Kutta procedures.

Assessment:

A 1.5-hour end-of-semester written examination and project work as required.

* Note that CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-251 | Prev:618-232

Source for 618-251 v4, p211 (Differences)

618-251 "Discrete Mathematics" appears differently in several places - choose the one you want:


618-251 Mathematics, Faculty of Science.
618-251 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-252 | Prev:618-242

618-251 Discrete Mathematics

Note: Students may not gain credit for more than one of 618-251, 618-131 (1996 Handbook) 618-141 (1995 Handbook), and the Mathematical Sciences subject 617-170 Discrete Mathematics and Statistics taught in previous years.

Credit points: 12

Coordinator: Professor C F Miller.

Prerequisite: One of 618-102 (1995 Handbook), 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the notion of validity of a mathematical formula
the concept of a mathematical proof
the principle of mathematical induction
the use of logical notation
countability and uncountability

Have developed:

skills and experience in using the language of sets, functions and relations
skills in counting and combinatorics
elementary skills in analysing graphs
the ability to prove simple theorems properly
skills in proving results by mathematical induction.

Appreciate:

the need for mathematical rigour
the variety of applications of discrete mathematical techniques

Content:

The natural numbers: well-ordering, forms of mathematical induction, division algorithm, greatest common divisor, prime factorization, recursion. Combinatorics: graphs and trees, paths, cycles, counting principles. Logic: logical notation, propositional connectives, quantifiers, truth tables, logical validity, counter-examples, methods of proof. Set theory: sets and set operations, functions, relations, orderings, equivalence relations and partitions, cardinality, countable and uncountable sets. Additional topics selected from: difference equations, generating functions, graph theory.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-252 | Prev:618-242

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-252 | Prev:618-242

618-251 Discrete Mathematics

Credit points: 12.0

Coordinator: Professor C F Miller.

Prerequisite: One of 618-102 (1995 Handbook), 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the notion of validity of a mathematical formula;
the concept of a mathematical proof;
the principle of mathematical induction;
the use of logical notation;
countability and uncountability.

Have developed:

skills and experience in using the language of sets, functions and relations;
skills in counting and combinatorics;
elementary skills in analysing graphs;
the ability to prove simple theorems properly;
skills in proving results by mathematical induction.

Appreciate:

the need for mathematical rigour;
the variety of applications of discrete mathematical techniques.

Content:

The natural numbers Well-ordering, forms of mathematical induction, division algorithm, greatest common divisor, prime factorization, recursion. Combinatorics Graphs and trees, paths, cycles, counting principles. Logic Logical notation, propositional connectives, quantifiers, truth tables, logical validity, counter-examples, methods of proof. Set theory Sets and set operations, functions, relations, orderings, equivalence relations and partitions, cardinality, countable and uncountable sets. Additional topics selected from: Difference equations, generating functions, graph theory.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, OBJECTIVES, POINTS differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-252 | Prev:618-242

Source for 618-252 v4, p211 (Differences)

618-252 "Analysis" appears differently in several places - choose the one you want:


618-252 Mathematics, Faculty of Science.
618-252 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-261 | Prev:618-251

618-252 Analysis

Credit points: 12.0

Coordinator: Dr M Ross

Prerequisite: Mathematics 618-102 (1995 Handbook) or any of 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the concept of convergence of sequences and series; elementary topology of the real line;
the fundamentals of continuity, differentiability of functions of several real variables;
the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
basic topological concepts in the complex plane;
Cauchy's theorem and its applications;

Have developed:

skills in determining the convergence or otherwise of sequences and series;
skills in differentiating functions of a complex variable;
skills in calculating contour integrals;
the ability to work with analytic functions in the cut plane;
the ability to apply Cauchy's integral formula and the residue theorem;

Appreciate:

differences between functions of a real and a complex variable;
the role of complex analytic methods in solving important problems in science and engineering.

Content:

Sequences and Series: standard sequences and series, Cauchy convergence, ratio and n-th root tests, absolute and conditional convergence, re-arrangements, power series. Continuity: continuity and differentiability of functions of several real variables. Functions of a complex variable: elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration:line and contour integrals, Cauchy's integral theorem; Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals using contour integration.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
Note. Credit cannot be gained for both 618-202 and 618-252.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-261 | Prev:618-251

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-261 | Prev:618-251

618-252 Analysis

Note: Credit cannot be gained for both 618-202 and 618-252.

Credit points: 12.0

Coordinator: Dr M Ross.

Prerequisite: Mathematics 618-102 (1995 Handbook) or any of 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the concept of convergence of sequences and series; elementary topology of the real line;
the fundamentals of continuity, differentiability of functions of several real variables;
the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
basic topological concepts in the complex plane;
Cauchy's theorem and its applications;
Have developed:
skills in determining the convergence or otherwise of sequences and series;
skills in differentiating functions of a complex variable;
skills in calculating contour integrals;
the ability to work with analytic functions in the cut plane;
the ability to apply Cauchy's integral formula and the residue theorem;

Appreciate:

differences between functions of a real and a complex variable;
the role of complex analytic methods in solving important problems in science and engineering.

Content:

Sequences and Series Standard sequences and series, Cauchy convergence, ratio and n-th root tests, absolute and conditional convergence, re-arrangements, power series. Continuity Continuity and differentiability of functions of several real variables. Functions of a complex variable Elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration Line and contour integrals, Cauchy's integral theorem; Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals using contour integration.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that ASSESSMENT, CONTACT, CONTENT, NOTE, OBJECTIVES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-261 | Prev:618-251

Source for 618-261 v4, p211 (Differences)

618-261 "Linear Programming and Optimization" appears differently in several places - choose the one you want:


618-261 Mathematics, Faculty of Science.
618-261 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-262 | Prev:618-252

618-261 Linear Programming and Optimization

Credit points: 12.0

Coordinator: Dr M Sniedovich

Prerequisite: Mathematics 618-101 and 618-102 (1995 Handbook), or 618-121 and 618-122, or 618-200, or 618-211, or 618-100, 618-101, 618-130, with concurrent enrolment in 618-200, or 618-141, 618-142, 618-130, with concurrent enrolment in 618-200; 618-231 is also desirable.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the essential features of optimization problems encountered in operations research investigations; what kind of practical problems have these features;
a number of basic mathematical techniques used to solve linear and nonlinear optimization problems;
the theoretical foundations of these techniques; the essential role that computers play in the analysis and solutions of operations research problems.

Have developed:

basic skills required to construct formal mathematical models for practical optimization problems;
skills needed to solve linear programming problems with the aid of the simplex method and to assess the results;
skills to make use of the relationship between primal and dual problems and their respective optimal solutions;
skills in using dynamic programming techniques in the solution of a number of problem-areas;
skills in deriving and analysing necessary and sufficient optimality conditions pertaining to classical nonlinear optimization problems.

Appreciate:

the extent and limitations of a number of operations research techniques such as linear programming, dynamic programming and classical first and second order analysis as far as solving practical real-world optimization problems is concerned;
the important role that linear algebra and calculus play in the development of these techniques;
why computers are so important in solving real-world optimization problems of the operational research type.

Content:

Linear programming:linear programming, simplex and revised simplex methods, sensitivity analysis; formulation of optimisation problems; transportation problems; use of computer packages on the Macintosh. Optimisation:optimisation of functions of several variables, constraints, Lagrange multipliers; other operations research techniques, including critical path, and some dynamic programming models; applications in economics and management; use of computer packages on the Macintosh.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-262 | Prev:618-252

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-262 | Prev:618-252

618-261 Linear Programming and Optimization

Note: It is not possible to gain credit for both 618-261 and the Mathematical Sciences subject 617-261 taught in previous years.

Credit points: 12.0

Coordinator: Dr M Sniedovich.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the essential features of optimization problems encountered in operations research investigations; what kind of practical problems have these features;
a number of basic mathematical techniques used to solve linear and nonlinear optimization problems;
the theoretical foundations of these techniques; the essential role that computers play in the analysis and solutions of operations research problems.

Have developed:

basic skills required to construct formal mathematical models for practical optimization problems;
skills needed to solve linear programming problems with the aid of the simplex method and to assess the results;
skills to make use of the relationship between primal and dual problems and their respective optimal solutions;
skills in using dynamic programming techniques in the solution of a number of problem-areas;
skills in deriving and analysing necessary and sufficient optimality conditions pertaining to classical nonlinear optimization problems.

Appreciate:

the extent and limitations of a number of operations research techniques such as linear programming, dynamic programming and classical first and second order analysis as far as solving practical real-world optimization problems is concerned;
the important role that linear algebra and calculus play in the development of these techniques;
why computers are so important in solving real-world optimization problems of the operational research type.

Content:

Linear programming Linear programming, simplex and revised simplex methods, sensitivity analysis; formulation of optimisation problems; transportation problems; use of computer packages on the Macintosh. Optimisation Optimisation of functions of several variables, constraints, Lagrange multipliers; other operations research techniques, including critical path, and some dynamic programming models; applications in economics and management; use of computer packages on the Macintosh.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, NOTE differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-262 | Prev:618-252

Source for 618-262 v4, p211 (Differences)

618-262 "Decision-making" appears differently in several places - choose the one you want:


618-262 Mathematics, Faculty of Science.
618-262 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-291 | Prev:618-261

618-262 Decision-Making

Credit points: 12.0

Coordinator: Dr M Sniedovich.

Prerequisite: Mathematical Sciences 617-261 (1995 Handbook) or Mathematics 618-261.

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the essential features of decision-making situations encountered in operations research investigations;
the difference between these situations and ordinary optimization problems;
what kind of practical problems have these features;
a number of basic mathematical approaches to such situations;
techniques used to solve decision-making situations represented by these approaches; the theoretical foundations of these techniques;
practical issues involved in the implementation of these techniques.

Have developed:

basic skills required to construct formal mathematical models for practical decision-making situations;
skills needed to solve a number of two-person games, including zero-sum and non-zero-sum games, cooperative and non-cooperative games, with the aid of linear and nonlinear programming techniques;
skills to make use of the relationship between primal and dual problems and their respective optimal solutions in the context of zero-sum two-person games;
skills in using linear programming and dynamic programming techniques in the solution of a number of multi-objective optimization problems;
skills to evaluate rules for decision-making problems under strict uncertainty.

Appreciate:

the complexity of decision-making situations encountered in operations research investigations;
the subjective nature of what constitutes a solution to a problem of this type;
the extent and limitations of a number of operations research techniques used to solve such problems;
the important role that linear algebra and calculus play in the development of these techniques;
the important role that computers play in solving problems of this type.

Content:

Decision analysis: a selection of topics in decision analysis, including single-stage and multi-stage decision models, in particular those using linear programmes; zero-sum games; preference relations and optimisation; multi-criteria decision making; decision trees. Use of computer packages on the Macintosh.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-291 | Prev:618-261

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-311 | Prev:618-261

618-262 Decision-Making

Note: It is not possible to gain credit for both 618-262 and the Mathematical Sciences subject 617-262 taught in previous years.

Credit points: 12.0

Coordinator: Dr M Sniedovich.

Prerequisite: Mathematical Sciences 617-261 (1995 Handbook) or Mathematics 618-261.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the essential features of decision-making situations encountered in operations research investigations;
the difference between these situations and ordinary optimization problems;
what kind of practical problems have these features;
a number of basic mathematical approaches to such situations;
techniques used to solve decision-making situations represented by these approaches; the theoretical foundations of these techniques;
practical issues involved in the implementation of these techniques.

Have developed:

basic skills required to construct formal mathematical models for practical decision-making situations;
skills needed to solve a number of two-person games, including zero-sum and non-zero-sum games, cooperative and non-cooperative games, with the aid of linear and nonlinear programming techniques;
skills to make use of the relationship between primal and dual problems and their respective optimal solutions in the context of zero-sum two-person games;
skills in using linear programming and dynamic programming techniques in the solution of a number of multi-objective optimization problems;
skills to evaluate rules for decision-making problems under strict uncertainty.

Appreciate:

the complexity of decision-making situations encountered in operations research investigations;
the subjective nature of what constitutes a solution to a problem of this type;
the extent and limitations of a number of operations research techniques used to solve such problems;
the important role that linear algebra and calculus play in the development of these techniques;
the important role that computers play in solving problems of this type.

Content:

Decision analysis A selection of topics in decision analysis, including single-stage and multi-stage decision models, in particular those using linear programmes; zero-sum games; preference relations and optimisation; multi-criteria decision making; decision trees. Use of computer packages on the Macintosh.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, NOTE differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-311 | Prev:618-261

Source for 618-291 v4, p212

618-291 Mathematics Project A (Advanced)

Credit points: 12.0

Coordinator: Dr W D Neumann

Corequisite: 200-level subjects in Mathematics totalling at least 48 points. Enrolment in this subject requires the invitation of the Head of the Department of Mathematics.

Contact: 26 lectures (two a week) and 35 hours project work

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

in some detail and depth the mathematical theory and techniques associated with some topic or topics of interest to a staff member.

Have developed:

an ability to pursue a substantial mathematical theme at some depth;
an ability to work with a certain amount of independence;
an insight into advanced mathematics.

Appreciate:

the methods and techniques required to complete an in-depth study of some mathematical topic;
integration of mathematical concepts and methods to solve problems.

Content:

An in-depth study of one or more topics in analysis, algebra, geometry and topology, methods, modelling and optimization or any other topic of interest to a staff member. Material will be presented through lectures, talks, seminars, and project work will be supervised by a staff member.
Note. The detailed contents of the two project subjects 618-291 and 618-292 will be different, and suitably qualified students may choose to do either or both of these subjects.

Source for 618-292 v4, p212

618-292 Mathematics Project B (Advanced)

Credit points: 12.0

Coordinator: Dr W D Neumann

Corequisite: 200-level subjects in Mathematics totalling at least 48 points. Enrolment in this subject requires the invitation of the Head of the Department of Mathematics.

Contact: 26 lectures (two a week) and 35 hours project work

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

in some detail and depth the mathematical theory and techniques associated with some topic or topics of interest to a staff member.

Have developed:

an ability to pursue a substantial mathematical theme at some depth;
an ability to work with a certain amount of independence;
an insight into advanced mathematics.

Appreciate:

the methods and techniques required to complete an in-depth study of some mathematical topic;
integration of mathematical concepts and methods to solve problems.

Content:

An in-depth study of one or more topics in analysis, algebra, geometry and topology, methods, modelling and optimization or any other topic of interest to a staff member. Material will be presented through lectures, talks, seminars, and project work will be supervised by a staff member.
NOTE. The detailed contents of the two project subjects 618-291 and 618-292 will be different, and suitably qualified students may choose to do either or both of these subjects.

Source for 618-301 v4, p212

618-301 Metric Spaces

Credit points: 15.0

Coordinator: Dr D A Robbie

Prerequisite: Mathematics 618-201.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should :
Comprehend:

the idea of a generalized distance (metric) between elements of an abstract set, including sets of functions;
the notion of a general topological space and the generation of such a space from a metric space, and that such spaces may be generated in other ways.

Have developed:

a number of classical results for a finite product space including products of the real numbers by using general methods for arbitrary topological spaces as far as possible, including standard results concerning compactness and connectedness;
the theory of completion of non-complete metric spaces;
applications of theory to the approximate solution of differential equations by Picard's method.

Appreciate:

the power of more general methods free of convergence arguments where applicable, and that the more specialised the structure the richer the theorems are likely to be;
that there will be theorems true in products of the reals but not true in every metric space, and theorems true in any metric space but not in every topological (even Hausdorff) space;
the power of convergence methods in the latter case.

Content:

Metric spaces:properties of the real line; metrics and norms, open and closed sets. Convergence: convergence, completeness, continuity, compactness, connectedness; contraction mappings; applications.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-302 v4, p212

618-302 Linear Analysis

Credit points: 15.0

Coordinator: Dr K Ecker

Prerequisite: Mathematics 618-301

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

fundamental concepts about measures and Lebesgue integration with respect to a variety of measures;
how basic concepts of linear algebra can be generalized to infinite dimensional situations using techniques from analysis;
how these concepts arise in many branches of mathematics, as for example, in partial differential equations, operations research and probability, but also in areas of theoretical physics such as quantum mechanics.

Have developed:

the ability to give rigorous mathematical arguments at an advanced level; to apply abstract concepts to solving problems in other areas of mathematics such as differential equations.

Appreciate:

the necessity for a rigorous theoretical foundation of concepts used frequently in mathematics and physics.

Content:

Linear spaces and operators Normed and inner product spaces, Hilbert spaces, abstract Fourier series; linear functionals and operators; dual spaces. Measure and integration Introduction to measure and integration; dominated convergence and applications.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-311 v4, p213 (Differences)

618-311 "Mathematical Modelling" appears differently in several places - choose the one you want:


618-311 Mathematics, Faculty of Science.
618-311 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p213) : Next:618-312 | Prev:618-302

618-311 Mathematical Modelling

Credit points: 15.0

Coordinator: Dr S L Carnie

Prerequisite: Mathematics 618-130 or 618-132 and one of 618-201, 618-202, 618-231, 618-232, 618-252. Some exposure to 100-level Statistics is desirable.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of mathematical modelling;
the principles and essential information regarding the modelling process, empirical modelling and parameter estimation, dimensional analysis and the qualitative behaviour of differential and difference equation models.

Have developed:

the ability to use dimensional analysis to reduce the complexity of mathematical formulations in the physical sciences;
skills in parameter estimation and empirical model building; skills in applying the modelling process to unfamiliar problems;
skills in interpreting the qualitative behaviour of differential equation models; confidence in their modelling skills through completion of a modelling project.

Appreciate:

the modelling cycle of problem formulation, solution, testing and refinement;
the differences between causal and empirical models.

Content:

The modelling process: some physical phenomena as case studies; empirical modelling versus model fitting/parameter estimation. Dimensional analysis: a tool for the physical sciences; stability and structural stability in systems of differential equations; limit cycles and nonlinear difference equations.

Assessment:

Up to 40 pages of project reports and written assignments, and up to two hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p213) : Next:618-312 | Prev:618-302

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-312 | Prev:618-262

618-311 Mathematical Modelling

Credit points: 15.0

Coordinator: Dr S L Carnie.

Prerequisite: Mathematics 618-130 or 618-132 and one of 618-201, 618-202, 618-231, 618-232, 618-252. Some exposure to 100-level Statistics is desirable.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the terminology of mathematical modelling;
the principles and essential information regarding the modelling process, empirical modelling and parameter estimation, dimensional analysis and the qualitative behaviour of differential and difference equation models.

Have developed:

the ability to use dimensional analysis to reduce the complexity of mathematical formulations in the physical sciences;
skills in parameter estimation and empirical model building; skills in applying the modelling process to unfamiliar problems;
skills in interpreting the qualitative behaviour of differential equation models; confidence in their modelling skills through completion of a modelling project.

Appreciate:

the modelling cycle of problem formulation, solution, testing and refinement;
the differences between causal and empirical models.

Content:

The modelling process Some physical phenomena as case studies; empirical modelling versus model fitting/parameter estimation. Dimensional analysis A tool for the physical sciences; stability and structural stability in systems of differential equations; limit cycles and nonlinear difference equations.

Assessment:

Up to 40 pages of project reports and written assignments, and up to two hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-312 | Prev:618-262

Source for 618-312 v4, p213 (Differences)

618-312 "Number Theory" appears differently in several places - choose the one you want:


618-312 Mathematics, Faculty of Science.
618-312 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p213) : Next:618-321 | Prev:618-311

618-312 Number Theory

Credit points: 15.0

Coordinator: Dr W D Neumann

Prerequisite: One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook).

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

elementary concepts of divisibility;
basic theory and use of congruences;
properties of powers of elements in congruences, particularly Euler's theorem;
the definition and use of primitive roots;
the law of quadratic reciprocity;
basic properties of continued fractions and some applications;
applications of all of the above to primality testing, factorization algorithms and cryptanalysis.

Have developed:

an ability to perform the algorithms inherent in the course material;
the ability to understand and to present proofs related to the course material.

Appreciate:

the extent and uses of elementary number theory; its applicability in other parts of mathematics; its potential for application outside of mathematics.

Content:

Factorisation, primes, greatest common divisors. Congruences. Primitive roots; quadratic reciprocity; continued fractions, Pell's equation. Compositeness testing and factorisation. Applications to cryptanalysis.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p213) : Next:618-321 | Prev:618-311

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-331 | Prev:618-311

618-312 Number Theory

Credit points: 15.0

Coordinator: Dr W D Neumann.

Prerequisite: One of Mathematics 618-111, 618-121, 618-142, 618-200, 618-211; or Mathematics 101 (1995 Handbook. )

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

elementary concepts of divisibility;
basic theory and use of congruences;
properties of powers of elements in congruences, particularly Euler's theorem;
the definition and use of primitive roots;
the law of quadratic reciprocity;
basic properties of continued fractions and some applications;
applications of all of the above to primality testing, factorization algorithms and cryptanalysis.

Have developed:

an ability to perform the algorithms inherent in the course material;
the ability to understand and to present proofs related to the course material.

Appreciate:

the extent and uses of elementary number theory; its applicability in other parts of mathematics; its potential for application outside of mathematics.

Content:

Factorisation, primes, greatest common divisors. Congruences. Primitive roots; quadratic reciprocity; continued fractions, Pell's equation. Compositeness testing and factorisation. Applications to cryptanalysis.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-331 | Prev:618-311

Source for 618-321 v4, p213

618-321 Algebra

Note: To enter 618-321 a grade of H3 or better will normally be required in 618-222.

Credit points: 15.0

Coordinator: Dr S Gadde

Prerequisite: Mathematics 618-222(See Note below)

Contact: 39 lectures (three a week).

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the concepts of unique factorization domains;
fields of fractions; modules;
algorithmic nature of the structure theorem for modules over Principal Ideal Domains when specialized to Euclidean Domains;
Galois correspondence; unsolvability in general of equations by radicals.

Have developed:

the ability to find the structure of finitely generated abelian groups from their presentations;
the ability to test polynomials of low degree for irreducibility; an understanding of the impossibility of trisecting an angle by ruler and compass;
the ability to calculate Galois groups of equations in special cases.

Appreciate:

the structure of special rings like Principal Ideal Rings;
the possibility of relating problems in different areas by correspondences like Galois correspondence;
that certain problems are not solvable and that it is possible to prove that they are not solvable in some interesting cases.

Content:

Modules over principal ideal domains: review of basic ring theory; ideals, quotients, the homomorphism theorems, prime and maximal ideals; integral domains and the field of quotients; Euclidean domains and principal ideal domains; definition and examples of modules; submodules, homomorphisms of modules, quotient modules; free modules and bases; structure of a finitely generated module over a principal ideal domain; applications to abelian groups. Field Theory: field extensions and their construction; the degree of a field extension; ruler and compass constructions; splitting fields; the Galois group of a field extension; the fundamental theorem of Galois theory.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-322 v4, p213

618-322 Topology

Credit points: 15.0

Coordinator: Dr C Hodgson

Prerequisite: Mathematics 618-231, 618-301 and 321

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic concepts and examples of topological spaces;
the definition of manifolds and the classification of surfaces;
the idea of homotopy of mappings;
how to calculate and use the fundamental group;
the concept of covering spaces and their relationship with fundamental groups;
the basic ideas of homology theory.

Have developed:

skills in working with the fundamental group and homology groups;
the ability to convert problems involving topological spaces and continuous maps into problems in algebra;
the ability to distinguish between different topological spaces;
the ability to construct homeomorphisms and homotopy equivalences between spaces.

Appreciate:

the basic questions in topology;
the power of topological methods in dealing with problems involving shape and position of objects and continuous mappings;
how topology can be applied to many areas, including geometry, analysis, group theory and physics.

Content:

Introduction to topology: homotopy and the fundamental group of a space; covering spaces; simplicial homology. Introduction to manifolds: manifolds, tangent vectors, differential forms. Selection of additional topics: connections, Riemannian metrics, curvature, Gauss-Bonnet theorem; integration on manifolds, de Rham's theorem.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Source for 618-331 v4, p213 (Differences)

618-331 "Mathematical Methods A" appears differently in several places - choose the one you want:


618-331 Mathematics, Faculty of Science.
618-331 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p213) : Next:618-332 | Prev:618-322

618-331 Mathematical Methods A

Note: To enter 618-331 using 618-252 or 618-202 (1995 Handbook) a grade of H3 or better will normally be required.

Credit points: 15.0

Coordinator: Dr R Brak

Prerequisite: Mathematics 618-202 or 618-252 (See Note below), 231 and 232.

Contact: 39 lectures ( three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

how to evaluate real integrals using complex analysis;
how to evaluate and invert Fourier, Laplace and Mellin transforms, and how these can be applied to solve differential and integral equations, to sum series and to compute asymptotic series;
what an asymptotic expansion is and how it provides approximations;
how to use Watson's lemma and the methods of Laplace, stationary phase and steepest descents to evaluate asymptotic expressions;
how to find asymptotic solutions to ordinary differential equations.

Have developed:

the necessary mathematical skills and knowledge to apply a range of mathematical techniques to correctly solve applied mathematics problems.

Appreciate:

the power of these techniques to solve mathematical problems.

Content:

Complex analysis: contour integration, branch cuts, evaluation of integrals. Integral transforms: wave equation, Fourier series; Fourier transform, Fourier integral theorem, convolution, applications; Laplace transform, inversion, examples; application to ordinary differential equations; convolution, examples; application to partial differential equations; Mellin transform examples. Asymptotics: asymptotic expansions, application of Mellin transform; Laplace's method for integrals, method of steepest descent, applications; method of stationary phase, examples; WKB method for ordinary differential equations.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p213) : Next:618-332 | Prev:618-322

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-332 | Prev:618-312

618-331 Mathematical Methods A

Note: To enter 618-331 using 618-252 or 618-202 (1995 Handbook) a grade of H3 or better will normally be required.

Credit points: 15.0

Coordinator: Dr R Brak.

Prerequisite: Mathematics 618-202 or 618-252 (See Note above), 231 and 232.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

how to evaluate real integrals using complex analysis;
how to evaluate and invert Fourier, Laplace and Mellin transforms, and how these can be applied to solve differential and integral equations, to sum series and to compute asymptotic series;
what an asymptotic expansion is and how it provides approximations;
how to use Watson's lemma and the methods of Laplace, stationary phase and steepest descents to evaluate asymptotic expressions;
how to find asymptotic solutions to ordinary differential equations.

Have developed:

the necessary mathematical skills and knowledge to apply a range of mathematical techniques to correctly solve applied mathematics problems.

Appreciate:

the power of these techniques to solve mathematical problems.

Content:

Complex analysis Contour integration, branch cuts, evaluation of integrals. Integral transforms Wave equation, Fourier series; Fourier transform, Fourier integral theorem, convolution, applications; Laplace transform, inversion, examples; application to ordinary differential equations; convolution, examples; application to partial differential equations; Mellin transform examples. Asymptotics Asymptotic expansions, application of Mellin transform; Laplace's method for integrals, method of steepest descent, applications; method of stationary phase, examples; WKB method for ordinary differential equations.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-332 | Prev:618-312

Source for 618-332 v4, p213 (Differences)

618-332 "Mathematical Methods B" appears differently in several places - choose the one you want:


618-332 Mathematics, Faculty of Science.
618-332 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p213) : Next:618-340 | Prev:618-331

618-332 Mathematical Methods B

Credit points: 15.0

Coordinator: Dr K A Landman

Prerequisite: Mathematics 618- 231 and 232

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the various types of partial differential equations and their methods for solution, and how they arise from physical problems.

Have developed:

skills to solve first order linear and nonlinear partial differential equations using the methods of characteristics and shocks;
skills to solve second order linear partial differential equations using various methods, including Green's functions and integral representation of solutions and similarity transformations;
skills to solve dispersive wave equations and some nonlinear second order differential equations.

Appreciate:

the description of many physical processes (for example traffic flow, sedimentation, heat transfer, fluid flow) as partial differential equations;
the idea of characteristics and propogation of information; the need for shocks;
the role of dispersive effects.

Content:

First-order partial differential equations: solution of linear, quasi-linear and general first order partial differential equations in two independent variables by characteristics; non-classical solutions, shocks; applications from traffic flow, sedimentation, gas dynamics and water waves. Second-order partial differential equations: classification of second order linear partial differential equations; existence and uniqueness of solutions with a variety of boundary conditions; Green's function techniques for wave, diffusion and Laplace equations in 2 and 3 dimensions.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p213) : Next:618-340 | Prev:618-331

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-340 | Prev:618-331

618-332 Mathematical Methods B

Credit points: 15.0

Coordinator: Dr K A Landman.

Prerequisite: Mathematics 618- 231 and 232

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the various types of partial differential equations and their methods for solution, and how they arise from physical problems.

Have developed:

skills to solve first order linear and nonlinear partial differential equations using the methods of characteristics and shocks;
skills to solve second order linear partial differential equations using various methods, including Green's functions and integral representation of solutions and similarity transformations;
skills to solve dispersive wave equations and some nonlinear second order differential equations.

Appreciate:

the description of many physical processes (for example traffic flow, sedimentation, heat transfer, fluid flow) as partial differential equations;
the idea of characteristics and propogation of information; the need for shocks;
the role of dispersive effects.

Content:

First-order partial differential equations Solution of linear, quasi-linear and general first order partial differential equations in two independent variables by characteristics; non-classical solutions, shocks; applications from traffic flow, sedimentation, gas dynamics and water waves. Second-order partial differential equations Classification of second order linear partial differential equations; existence and uniqueness of solutions with a variety of boundary conditions; Green's function techniques for wave, diffusion and Laplace equations in 2 and 3 dimensions.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-340 | Prev:618-331

Source for 618-340 v4, p214 (Differences)

618-340 "Statistical Mechanics" appears differently in several places - choose the one you want:


618-340 Mathematics, Faculty of Science.
618-340 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-341 | Prev:618-332

618-340 Statistical Mechanics

Credit points: 15

Coordinator: Dr P A Pearce

Prerequisite: 618-130 (or 132) and either 231 or 232. Some knowledge of thermodynamics will be assumed.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the formalism of thermodynamics and statistical mechanics and how to apply it to a range of models.

Have developed:

the necessary skill and knowledge to compute the properties of simple models using the formalism of statistical mechanics.

Appreciate:

the power of statistical mechanics to describe the properties of collections of interacting objects.

Content:

Basic thermodynamics and statistical mechanics: ensembles and the partition function, thermodynamic limit. Phase transitions: first order and continuous transitions, singularities, critical exponents, universality, scaling and homogeneous functions, mean field theory, correlation functions. Enumeration: transfer matrices, generating functions, random walks. Applications: ideal gas, Van der Waals-Maxwell fluid, Ising magnets, percolation.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-341 | Prev:618-332

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-341 | Prev:618-332

618-340 Statistical Mechanics

Credit points: 15.0

Coordinator: Dr P A Pearce.

Prerequisite: 618-130 (or 132) and either 231 or 232. Some knowledge of thermodynamics will be assumed.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the formalism of thermodynamics and statistical mechanics and how to apply it to a range of models.

Have developed:

the necessary skill and knowledge to compute the properties of simple models using the formalism of statistical mechanics.

Appreciate:

the power of statistical mechanics to describe the properties of collections of interacting objects.

Content:

Basic thermodynamics and statistical mechanics Ensembles and the partition function, thermodynamic limit. Phase transitions First order and continuous transitions, singularities, critical exponents, universality, scaling and homogeneous functions, mean field theory, correlation functions. Enumeration Transfer matrices, generating functions, random walks. Applications Ideal gas, Van der Waals-Maxwell fluid, Ising magnets, percolation.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, POINTS differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-341 | Prev:618-332

Source for 618-341 v4, p214 (Differences)

618-341 "Dynamical Systems and Chaos" appears differently in several places - choose the one you want:


618-341 Mathematics, Faculty of Science.
618-341 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-342 | Prev:618-340

618-341 Dynamical Systems and Chaos

Credit points: 15.0

Coordinator: Professor C J Thompson

Prerequisite: Mathematics 618-130 or 618-132 together with one of 618-201, 618-231, 618-232, 618-252.

Contact: 39 lectures (three a week).

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalization theory of transitions to chaos.

Have developed:

the ability to analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos.

Appreciate:

the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems such as ecologies and financial markets.

Content:

Dynamical systems:phase space, Poincare sections, phase portraits, Hamiltonian systems, invariant measures. Chaos:integrable and chaotic systems, maps on an interval, period doubling and universality, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos, applications to ecology, chemical reactions, economics, management and meteorology.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-342 | Prev:618-340

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-342 | Prev:618-340

618-341 Dynamical Systems and Chaos

Credit points: 15.0

Coordinator: Professor C J Thompson.

Prerequisite: Mathematics 618-130 or 618-132 together with one of 618-201, 618-231, 618-232, 618-252.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalization theory of transitions to chaos.

Have developed:

the ability to analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos.

Appreciate:

the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems such as ecologies and financial markets.

Content:

Dynamical systems Phase space, Poincare sections, phase portraits, Hamiltonian systems, invariant measures. Chaos Integrable and chaotic systems, maps on an interval, period doubling and universality, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos, applications to ecology, chemical reactions, economics, management and meteorology.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-342 | Prev:618-340

Source for 618-342 v4, p214 (Differences)

618-342 "Industrial and Applied Mathematics" appears differently in several places - choose the one you want:


618-342 Mathematics, Faculty of Science.
618-342 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-352 | Prev:618-341

618-342 Industrial and Applied Mathematics

Credit points: 15.0

Coordinator: Dr B D Hughes

Prerequisite: Mathematics 618-231, 618-232. Students are encouraged to take, in addition, one or both of 331, 332.

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic principles governing the flow of continuous media and transport processes within continuous media;
the apparatus needed to formulate these principles mathematically (including vector and tensor methods);
the concept of a constitutive equation.

Have developed:

the ability to select a constitutive equation and correctly pose relevant boundary-value problems;
skill in solving transport and flow problems in simple geometries;
insight into the validity of approximate analyses;
the ability to interpret solutions in physical terms.

Appreciate:

the potential for mathematical modelling of flow and transport processes which arise in manufacturing, mineral exploitation and other areas of science and technology;
the intimate connection between continuum mechanical problems and fundamental mathematical problems previously studied in methods-oriented subjects such as 618-231 and 618-232.

Content:

Basic principles of continuum mechanics: thermodynamics of continua, stress tensors, laws for transport of mass, momentum and energy. Fluid dynamics: The Newtonian viscous fluid: exact solutions, dynamical similarity, flow at low Reynolds number, lubrication theory, flow at high Reynolds number; effectively inviscid fluids: potential flow, isentropic gas flow, acoustics, shock waves; flow in porous media; diffusion and convection in a flowing fluid. Elasticity:the linear theory of elasticity; Navier's equation; elastic waves, applications.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-352 | Prev:618-341

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-352 | Prev:618-341

618-342 Industrial and Applied Mathematics

Credit points: 15.0

Coordinator: Dr B D Hughes.

Prerequisite: Mathematics 618-231, 618-232. Students are encouraged to take, in addition, one or both of 331, 332.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic principles governing the flow of continuous media and transport processes within continuous media;
the apparatus needed to formulate these principles mathematically (including vector and tensor methods);
the concept of a constitutive equation.

Have developed:

the ability to select a constitutive equation and correctly pose relevant boundary-value problems;
skill in solving transport and flow problems in simple geometries;
insight into the validity of approximate analyses;
the ability to interpret solutions in physical terms.

Appreciate:

the potential for mathematical modelling of flow and transport processes which arise in manufacturing, mineral exploitation and other areas of science and technology;
the intimate connection between continuum mechanical problems and fundamental mathematical problems previously studied in methods-oriented subjects such as 618-231 and 618-232.

Content:

Basic principles of continuum mechanics Thermodynamics of continua, stress tensors, laws for transport of mass, momentum and energy. Fluid dynamics The Newtonian viscous fluid: exact solutions, dynamical similarity, flow at low Reynolds number, lubrication theory, flow at high Reynolds number; effectively inviscid fluids: potential flow, isentropic gas flow, acoustics, shock waves; flow in porous media; diffusion and convection in a flowing fluid. Elasticity - The linear theory of elasticity; Navier's equation; elastic waves, applications.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-352 | Prev:618-341

Source for 618-352 v4, p214 (Differences)

618-352 "Graph Theory" appears differently in several places - choose the one you want:


618-352 Mathematics, Faculty of Science.
618-352 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-360 | Prev:618-342

618-352 Graph Theory

Credit points: 15.0

Coordinator: Dr A Byrne.

Prerequisite: Either 618-101 and 618-102 (1995 Handbook), or 618-111 and 618-112, or 618-121 and 618-122, or 618-200, or 618-100 and 618-101 (1995 Handbook), or 618-141 and 618-142. Alternatively, Mathematics 618-290 (Institute of Education).

Contact: 39 lectures (three a week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic concepts of graph theory including paths and cycles, trees and counting, automorphism groups, planar graphs, colouring properties, chromatic polynomials, matching theory, cycle space.

Have developed:

skills in implementing algorithms on graphs for finding objects such as minimum spanning trees, maximum matchings and flows;
skills at implementing approximation algorithms.

Appreciate:

the variety of applications of graph theory both within and outside mathematics.

Content:

Introduction to Graph Theory: basic concepts, paths and cycles, trees and counting, automorphism groups; planar graphs, colouring properties, chromatic polynomials, matching theory, cycle space. Algorithms:minimum spanning trees, maximum matchings, flows, approximation algorithm.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-360 | Prev:618-342

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-360 | Prev:618-342

618-352 Graph Theory

Credit points: 15.0

Coordinator: Dr A Byrne.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic concepts of graph theory including paths and cycles, trees and counting, automorphism groups, planar graphs, colouring properties, chromatic polynomials, matching theory, cycle space.

Have developed:

skills in implementing algorithms on graphs for finding objects such as minimum spanning trees, maximum matchings and flows;
skills at implementing approximation algorithms.

Appreciate:

the variety of applications of graph theory both within and outside mathematics.

Content:

Introduction to Graph Theory Basic concepts, paths and cycles, trees and counting, automorphism groups; planar graphs, colouring properties, chromatic polynomials, matching theory, cycle space. Algorithms Minimum spanning trees, maximum matchings, flows, approximation algorithm.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-360 | Prev:618-342

Source for 618-360 v4, p214 (Differences)

618-360 "Applied Operations Research" appears differently in several places - choose the one you want:


618-360 Mathematics, Faculty of Science.
618-360 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-361 | Prev:618-352

618-360 Applied Operations Research

Credit points: 15.0

Coordinator: Dr N Boland

Prerequisite: Mathematics 618-361. Also recommended are one of Mathematical Sciences 617-141, 617-142, 617-160 (1995 Handbook) or Computer Science 433-141; Mathematics 618-262; Statistics 619-360.

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the issues involved in applying operations research principles, methods, and algorithms in the solution of real-world problems;
the technical issues involved in using and developing operations research software for practical problems;
the practical aspects of group projects in operations research.

Have developed:

skills to apply various operations research methods and algorithms in the solution of practical problems;
skills to participate successfully in group projects in operations research, including preparing reports and giving presentations;
skills to use commercial operations research software in the solution of practical problems.

Appreciate:

the scope and limitation of operations research methods and algorithms as far as solving practical problems is concerned;
the scope and limitations of commercial operations research software as far as solving practical operations research problems is concerned;
the practical issues and difficulties involved in group projects in operations research.

Content:

Operations Research Methods and Techniques: practical aspects of various operations research methods such as linear programming, integer programming, dynamic programming, and nonlinear programming, decision trees, and issues involved in their applications. Project: individual and group projects in operations research and appropriate computer usage. Principles of computerised mathematical modelling paradigms: selected topics from Matrix generators; mathematical modelling languages; array oriented languages; constraint logic programming, and report generators. Software: familiarisation with operations research software in the solution of practical problems. Software packages will cover a selection from the following areas: linear, integer, and nonlinear programming; project management; network problems; scheduling problems; simulation; dynamic programming; branch and bound, and constraint logic programming.

Assessment:

Up to 52 pages of project reports and written assignments, and up to two hours mid-semester test.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-361 | Prev:618-352

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-361 | Prev:618-352

618-360 Applied Operations Research

Credit points: 15.0

Coordinator: Dr N Boland.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the issues involved in applying operations research principles, methods, and algorithms in the solution of real-world problems;
the technical issues involved in using and developing operations research software for practical problems;
the practical aspects of group projects in operations research.

Have developed:

skills to apply various operations research methods and algorithms in the solution of practical problems;
skills to participate successfully in group projects in operations research, including preparing reports and giving presentations;
skills to use commercial operations research software in the solution of practical problems.

Appreciate:

the scope and limitation of operations research methods and algorithms as far as solving practical problems is concerned;
the scope and limitations of commercial operations research software as far as solving practical operations research problems is concerned;
the practical issues and difficulties involved in group projects in operations research.

Content:

Operations Research Methods and Techniques Practical aspects of various operations research methods such as linear programming, integer programming, dynamic programming, and nonlinear programming, decision trees, and issues involved in their applications. Project Individual and group projects in operations research and appropriate computer usage. Principles of computerised mathematical modelling paradigms Selected topics from Matrix generators; mathematical modelling languages; array oriented languages; constraint logic programming, and report generators. Software Familiarisation with operations research software in the solution of practical problems. Software packages will cover a selection from the following areas: linear, integer, and nonlinear programming; project management; network problems; scheduling problems; simulation; dynamic programming; branch and bound, and constraint logic programming.

Assessment:

Up to 52 pages of project reports and written assignments, and up to two hours mid-semester test.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-361 | Prev:618-352

Source for 618-361 v4, p214 (Differences)

618-361 "Operations Research A" appears differently in several places - choose the one you want:


618-361 Mathematics, Faculty of Science.
618-361 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p214) : Next:618-362 | Prev:618-360

618-361 Operations Research A

Credit points: 15.0

Coordinator: Dr D Ralph

Prerequisite: Mathematics 618-261

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

basic techniques of operations research, including advanced linear programming, decision-tree models, network models and inventory models;
formulation of operations research models for a variety of planning and management problems, including models for production planning, scheduling, inventory management and capital budgeting.

Have developed:

skills in setting up and analysing operations research models for a number of planning problems;
competence in the use of several appropriate computer packages on Macintosh and other computers.

Appreciate:

the factors and restrictions involved in building and using models for planning and management problems.

Content:

Models:operations research models; formulation of planning and management problems, including linear programming models, scheduling models, inventory management, and capital budgeting. Techniques: advanced linear programming, decision tree models, inventory models, networks, nonlinear optimisation algorithms. Applications: case studies and projects; use of computer programmes on Macintosh and other computers.

Assessment:

Up to 26 pages of written assignments, a group project and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p214) : Next:618-362 | Prev:618-360

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-362 | Prev:618-360

618-361 Operations Research A

Note: It is not possible to gain credit for both 618-361 and the Mathematical Sciences subject 617-361 taught in previous years.

Credit points: 15.0

Coordinator: Dr D Ralph.

Prerequisite: Mathematics 618-261

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

basic techniques of operations research, including advanced linear programming, decision-tree models, network models and inventory models;
formulation of operations research models for a variety of planning and management problems, including models for production planning, scheduling, inventory management and capital budgeting.

Have developed:

skills in setting up and analysing operations research models for a number of planning problems;
competence in the use of several appropriate computer packages on Macintosh and other computers.

Appreciate:

the factors and restrictions involved in building and using models for planning and management problems.

Content:

Models Operations research models; formulation of planning and management problems, including linear programming models, scheduling models, inventory management, and capital budgeting. Techniques Advanced linear programming, decision tree models, inventory models, networks, nonlinear optimisation algorithms. Applications Case studies and projects; use of computer programmes on Macintosh and other computers.

Assessment:

Up to 26 pages of written assignments, a group project and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT, NOTE differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p149) : Next:618-362 | Prev:618-360

Source for 618-362 v4, p215 (Differences)

618-362 "Operations Research B" appears differently in several places - choose the one you want:


618-362 Mathematics, Faculty of Science.
618-362 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p215) : Next:618-380 | Prev:618-361

618-362 Operations Research B

Credit points: 15.0

Coordinator: Dr D Ralph.

Prerequisite: Mathematics 618-361. Also recommended are one of Mathematical Sciences 617-141, 617-142 or 617-160 (1995 Handbook); or Computer Science 433-141; Mathematics 618-262; and Statistics 619-230 and 360

Contact: 39 lectures (three a week)

Timetable: Second semester

Objectives:

On completion of this subject, students should:
Comprehend:

the basic principles and theory underlying various operations research optimization methods, algorithms, and models;
the extensions and advanced features of a variety of operations research methods and algorithms;
the inherent difficulties associated with the solution of some major classes of operations research problems;
the modelling issues associated with the use of operations research methods and techniques;
the computational aspects of various operations research algorithms.

Have developed:

the ability to solve a variety of optimization problems using operations research methods and algorithms;
skills to tackle various modelling issues associated with the use of operations research models and algorithms;
skills to use operations research software.

Appreciate:

the complexities of operational research problems and the methods available for solving them, including the scope and limitations of various optimization methods and algorithms;
the central role that mathematical modelling plays in the formulation and modelling of operations research problems.

Content:

Selected topics from linear programming, quadratic programming, dynamic programming, fractional programming, composite concave programming, nonlinear optimization, parametric optimization, global optimization, combinatorial optimization, branch and bound, and simulation.

Assessment:

Up to 52 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-380 | Prev:618-361

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p150) : Next:618-380 | Prev:618-361

618-362 Operations Research B

Note: It is not possible to gain credit for both 618-362 and the Mathematical Sciences subject 617-362 taught in previous years.

Credit points: 15.0

Coordinator: Dr D Ralph.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the basic principles and theory underlying various operations research optimization methods, algorithms, and models;
the extensions and advanced features of a variety of operations research methods and algorithms;
the inherent difficulties associated with the solution of some major classes of operations research problems;
the modelling issues associated with the use of operations research methods and techniques;
the computational aspects of various operations research algorithms.

Have developed:

the ability to solve a variety of optimization problems using operations research methods and algorithms;
skills to tackle various modelling issues associated with the use of operations research models and algorithms;
skills to use operations research software.

Appreciate:

the complexities of operational research problems and the methods available for solving them, including the scope and limitations of various optimization methods and algorithms;
the central role that mathematical modelling plays in the formulation and modelling of operations research problems.

Content:

Selected topics from linear programming, quadratic programming, dynamic programming, fractional programming, composite concave programming, nonlinear optimization, parametric optimization, global optimization, combinatorial optimization, branch and bound, and simulation.

Assessment:

Up to 52 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, NOTE differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p150) : Next:618-380 | Prev:618-361

Source for 618-380 v4, p215 (Differences)

618-380 "Geometry" appears differently in several places - choose the one you want:


618-380 Mathematics, Faculty of Science.
618-380 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p215) : Next:618-391 | Prev:618-362

618-380 Geometry

Credit points: 15.0

Coordinator: Dr A Byrne.

Contact: 39 lectures (three a week)

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

the concept of an axiomatic system and the use of models in axiomatic systems;
the basic ideas of non-Euclidean, projective and affine geometry;
the role of geometric transformations in geometry;
ideas unifying various geometries, particularly the notion of symmetry.

Have developed:

an understanding of various geometries from an axiomatic and transformational viewpoint, as well as a deeper understanding of Euclidean geometry;
skills and techniques of geometrical reasoning, including the methods of proof in axiomatic systems.

Appreciate:

the interaction of algebraic and group theory ideas in the study of geometry, as well as the classical arguments;
the mathematical and intellectual importance of Euclidean geometry;
that geometry is becoming more important in an age of computer graphics.

Content:

Axiomatic systems Euclidean, spherical, hyperbolic (non-Euclidean) geometry. Transformation and matrix groups. Isometry groups and tessellations. Projective and affine geometry.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-391 | Prev:618-362

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p150) : Next:485-398 | Prev:618-362

618-380 Geometry

Credit points: 15.0

Coordinator: Dr A Byrne.

Contact: 39 lectures (three each week)

Timetable: First semester.

Objectives:

On completion of this subject, students should:
Comprehend:

the concept of an axiomatic system and the use of models in axiomatic systems;
the basic ideas of non-Euclidean, projective and affine geometry;
the role of geometric transformations in geometry;
ideas unifying various geometries, particularly the notion of symmetry.

Have developed:

an understanding of various geometries from an axiomatic and transformational viewpoint, as well as a deeper understanding of Euclidean geometry;
skills and techniques of geometrical reasoning, including the methods of proof in axiomatic systems.

Appreciate:

the interaction of algebraic and group theory ideas in the study of geometry, as well as the classical arguments;
the mathematical and intellectual importance of Euclidean geometry;
that geometry is becoming more important in an age of computer graphics.

Content:

Axiomatic systems Euclidean, spherical, hyperbolic (non-Euclidean) geometry. Transformation and matrix groups. Isometry groups and tessellations. Projective and affine geometry.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p150) : Next:485-398 | Prev:618-362

Source for 618-391 v4, p215

618-391 Mathematics Project A

Credit points: 12.0

Coordinator: Dr W D Neumann

Corequisite: 300-level subjects in Mathematics totalling at least 50 points. Enrolment in this subject requires the permission of the Head of the Department of Mathematics.

Contact: 78 hours project work

Timetable: First semester

Objectives:

On completion of this subject, students should:
Comprehend:

in some detail and depth the mathematical theory and techniques associated with some topic or topics of interest to a staff member.

Have developed:

an ability to pursue a substantial mathematical theme at some depth;
an ability to work with a certain amount of independence;
an insight into advanced mathematics, with a possible introduction to research material.

Appreciate:

the methods and techniques required to complete an in-depth study of some mathematical topic, possibly at research level;
integration of mathematical concepts and methods to solve problems.

Content:

An in-depth study of one or more topics in analysis, algebra, geometry and topology, methods and modelling, mathematical physics, and optimization. The work may be undertaken either as a project under the supervision of a staff member, or as an appropriate 400 - level subject.
A selection of topics includes Euclidean symmetry groups, combinatorial optimization, interactive computing with nested arrays.

Appropriate 400-level subjects that can be taken are 618-471 Advanced Mathematical Methods, 618-482 Statistical Mechanics and 618-485 Enumeration.

Assessment:

Written report and/or assignments totalling up to 26 pages, and up to three hours of written examination.

Source for 618-392 v4, p215

618-392 Mathematics Project B

Credit points: 12.0

Coordinator: Dr W D Neumann.

Corequisite: 300-level subjects in Mathematics totalling at least 50 points. Enrolment in this subject requires the permission of the Head of the Department of Mathematics.

Contact: 78 hours project work.

Timetable: Second semester.

Objectives:

On completion of this subject, students should:
Comprehend:

in some detail and depth the mathematical theory and techniques associated with some topic or topics of interest to a staff member.

Have developed:

an ability to pursue a substantial mathematical theme at some depth;
an ability to work with a certain amount of independence;
an insight into advanced mathematics, with a possible introduction to research material.

Appreciate:

the methods and techniques required to complete an in-depth study of some mathematical topic, possibly at research level;
integration of mathematical concepts and methods to solve problems.

Content:

An in-depth study of one or more topics in analysis, algebra, geometry and topology, methods and modelling, mathematical physics, and optimisation. The work may be undertaken either as a project under the supervision of a staff member, or as an appropriate 400 - level subject.
A selection of topics includes cryptanalysis and number theory, using a simulation package in the context of Operations Research, multistage decision processes, random walks, percolation and fractals.

Appropriate 400-level subjects that can be taken are 618-444 Deterministic Chaos and 618-473 Modelling Case Studies.

Assessment:

Written report and/or assignments totalling up to 26 pages, and up to three hours of written examination.

Source for 618-496 v4, p215 (Differences)

HANDBOOK ERROR - Subject is listed more than once in Mathematics:Sci.
# split descriptions.

618-496 "Mathematics Research Project (25 Points)" appears differently in several places - choose the one you want:


618-496 Mathematics, Faculty of Science.
618-496 Mathematics, Faculty of Science.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-497 | Prev:618-392

618-496 Mathematics Research Project (25 Points)

Note: Must be taken concurrently with 618-497 Mathematics Advanced Coursework (75 Points).

Content:

A list of the research interests of the Department is outlined in the departmental research report available from the Mathematics Office. Intending fourth year students should approach individual staff members to discuss possible research projects. Any difficulties in reaching decisions about research topics should be discussed with the fourth year coordinator.
Preliminary reading should commence by the end of February with the bulk of the project being completed in Semester 2. Performance in the research project will be assessed by a Project Report to be examined by the supervisor and one other departmental member nominated by the fourth year coordinator.

Assessment:

The project report submitted is examined by the supervisor and another departmental member nominated by the coordinator, taking into account clarity and exposition; mathematical insight; coverage of field and references.

See additional details under the Mathematics subject 618-497 Mathematics Advanced Coursework (75 Points).

1. Mathematics, Faculty of Science (v4, p215) : Next:618-497 | Prev:618-392

2. Mathematics, Faculty of Science (v4, p216) : Next:618-497 | Prev:618-392

618-496 Combined Mathematics/Statistics Research Project

Note: Must be taken concurrently with 618-497 Combined Mathematics/Statistics Course Work.

Credit Points: 100 in total; points make-up as agreed by coordinators

Coordinator: Dr K Ecker (Mathematics) and Dr K Sharpe (Statistics)

Prerequisite: As approved by coordinators

Contact: All year

Objectives:

To provide a coordinated advanced level training in Mathematics and Statistics and/or Probability, together with an introduction to research studies in one of these disciplines.

Content:

A special research project plus six 400-level courses in Mathematics, Statistics and/or Probability, as approved by coordinators.

* Note that CONTACT, CONTENT, COORDINATOR, NOTE, OBJECTIVES, PREREQUISITES, TITLE differs from the maintainer's version above. A log of variations is available.

2. Mathematics, Faculty of Science (v4, p216) : Next:618-497 | Prev:618-392

Source for 618-497 v4, p215 (Differences)

HANDBOOK ERROR - Subject is listed more than once in Mathematics:Sci.
# split descriptions.

618-497 "Mathematics Advanced Coursework (75 Points)" appears differently in several places - choose the one you want:


618-497 Mathematics, Faculty of Science.
618-497 Mathematics, Faculty of Science.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-477 | Prev:618-496

618-497 Mathematics Advanced Coursework (75 Points)

Note: Must be taken concurrently with 618-496 Mathematics Research Project (25 Points).

Credit points: 100 in total

Coordinator: Dr K Ecker

Students doing joint Honours degrees with other departments should arrange their Mathematics workload with the fourth year coordinator.

Prerequisite: As approved by the co-ordinator.

Objectives:

The Honours program in Mathematics is designed to train mathematics graduates in advanced mathematics topics and to provide an opportunity for students to participate in mathematical research.

Content:

All Mathematics Honours students must complete six subjects of coursework which are listed in the Mathematics fourth year (Honours) Guide. The Honours Guide which is updated every year, is available from the Mathematics Office.
Each subject will be of one Semester length and will consist of twenty-six lectures (usually two per week), some or all of which may be replaced by seminars, guided reading or project work. Four subjects will normally be taken in Semester 1 and two subjects in Semester 2. There will be six streams: Analysis, Algebra, Geometry and Topology, Methods and Modelling, Mathematical Physics, Operations Research. Each stream will offer three subjects, two of which will usually be available in Semester 1 and one in Semester 2. Each student will normally take at least two subjects from each of two different streams, one of which will normally be in the same stream as that of the research project.

Seminars: Honours students will be required to give two seminars, before their results are finalised. One seminar will be on a general topic in Semester 1 and the second on their research project in Semester 2. Students should plan these seminars with their supervisors.

Any student may, with permission, study and be assessed in more than six subjects. In determining the final grade, only the best six subjects will be considered.

Assessment:

For all subjects, up to forty pages of written assignments and up to three hours of written and/or oral examinations are required.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-477 | Prev:618-496

2. Mathematics, Faculty of Science (v4, p216) : Next:618-477 | Prev:618-496

618-497 Combined Mathematics/Statistics Course Work

Note: Must be taken concurrently with 618-496 Combined Mathematics/Statistics Research Project.

See additional details under the Mathematics subject 618-496 Mathematics Research Project (25 Points).

* Note that NOTE, TITLE, XREFSUBJECT(does not point to this subject) differs from the maintainer's version above. A log of variations is available.

2. Mathematics, Faculty of Science (v4, p216) : Next:618-477 | Prev:618-496

Source for 618-477 v4, p216

618-477 Combined Mathematics/Physics Course Work

Note: Must be taken concurrently with 618-476 Combined Mathematics/Physics Research Project.

See additional details under the Mathematics subject 618-476 Combined Mathematics/Physics Research Project.

Source for 618-476 v4, p216

618-476 Combined Mathematics/Physics Research Project

Note: 618-477 Combined Mathematics/Physics Course Work.

Credit Points: 100 in total; points make-up as agreed by coordinators.

Coordinator: Dr K Ecker (Mathematics) and Dr S Tovey (Physics)

Prerequisite: As approved by coordinators

Contact: All year

Objectives:

To provide a coordinated advanced level training in both Mathematics and Physics together with a research training component.

Content:

A program of study and research selected from both the Mathematics and Physics Honours programs, which must be approved by both the Department of Mathematics and School of Physics.

Source for 618-497 v4, p215 (Differences)

HANDBOOK ERROR - Subject is listed more than once in Mathematics:Sci.
# split descriptions.

618-497 "Mathematics Advanced Coursework (75 Points)" appears differently in several places - choose the one you want:


618-497 Mathematics, Faculty of Science.
618-497 Mathematics, Faculty of Science.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-477 | Prev:618-496

618-497 Mathematics Advanced Coursework (75 Points)

Note: Must be taken concurrently with 618-496 Mathematics Research Project (25 Points).

Credit points: 100 in total

Coordinator: Dr K Ecker

Students doing joint Honours degrees with other departments should arrange their Mathematics workload with the fourth year coordinator.

Prerequisite: As approved by the co-ordinator.

Objectives:

The Honours program in Mathematics is designed to train mathematics graduates in advanced mathematics topics and to provide an opportunity for students to participate in mathematical research.

Content:

All Mathematics Honours students must complete six subjects of coursework which are listed in the Mathematics fourth year (Honours) Guide. The Honours Guide which is updated every year, is available from the Mathematics Office.
Each subject will be of one Semester length and will consist of twenty-six lectures (usually two per week), some or all of which may be replaced by seminars, guided reading or project work. Four subjects will normally be taken in Semester 1 and two subjects in Semester 2. There will be six streams: Analysis, Algebra, Geometry and Topology, Methods and Modelling, Mathematical Physics, Operations Research. Each stream will offer three subjects, two of which will usually be available in Semester 1 and one in Semester 2. Each student will normally take at least two subjects from each of two different streams, one of which will normally be in the same stream as that of the research project.

Seminars: Honours students will be required to give two seminars, before their results are finalised. One seminar will be on a general topic in Semester 1 and the second on their research project in Semester 2. Students should plan these seminars with their supervisors.

Any student may, with permission, study and be assessed in more than six subjects. In determining the final grade, only the best six subjects will be considered.

Assessment:

For all subjects, up to forty pages of written assignments and up to three hours of written and/or oral examinations are required.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-477 | Prev:618-496

2. Mathematics, Faculty of Science (v4, p216) : Next:618-477 | Prev:618-496

618-497 Combined Mathematics/Statistics Course Work

Note: Must be taken concurrently with 618-496 Combined Mathematics/Statistics Research Project.

See additional details under the Mathematics subject 618-496 Mathematics Research Project (25 Points).

* Note that NOTE, TITLE, XREFSUBJECT(does not point to this subject) differs from the maintainer's version above. A log of variations is available.

2. Mathematics, Faculty of Science (v4, p216) : Next:618-477 | Prev:618-496

Source for 618-496 v4, p215 (Differences)

HANDBOOK ERROR - Subject is listed more than once in Mathematics:Sci.
# split descriptions.

618-496 "Mathematics Research Project (25 Points)" appears differently in several places - choose the one you want:


618-496 Mathematics, Faculty of Science.
618-496 Mathematics, Faculty of Science.

1. Mathematics, Faculty of Science (v4, p215) : Next:618-497 | Prev:618-392

618-496 Mathematics Research Project (25 Points)

Note: Must be taken concurrently with 618-497 Mathematics Advanced Coursework (75 Points).

Content:

A list of the research interests of the Department is outlined in the departmental research report available from the Mathematics Office. Intending fourth year students should approach individual staff members to discuss possible research projects. Any difficulties in reaching decisions about research topics should be discussed with the fourth year coordinator.
Preliminary reading should commence by the end of February with the bulk of the project being completed in Semester 2. Performance in the research project will be assessed by a Project Report to be examined by the supervisor and one other departmental member nominated by the fourth year coordinator.

Assessment:

The project report submitted is examined by the supervisor and another departmental member nominated by the coordinator, taking into account clarity and exposition; mathematical insight; coverage of field and references.

See additional details under the Mathematics subject 618-497 Mathematics Advanced Coursework (75 Points).

1. Mathematics, Faculty of Science (v4, p215) : Next:618-497 | Prev:618-392

2. Mathematics, Faculty of Science (v4, p216) : Next:618-497 | Prev:618-392

618-496 Combined Mathematics/Statistics Research Project

Note: Must be taken concurrently with 618-497 Combined Mathematics/Statistics Course Work.

Credit Points: 100 in total; points make-up as agreed by coordinators

Coordinator: Dr K Ecker (Mathematics) and Dr K Sharpe (Statistics)

Prerequisite: As approved by coordinators

Contact: All year

Objectives:

To provide a coordinated advanced level training in Mathematics and Statistics and/or Probability, together with an introduction to research studies in one of these disciplines.

Content:

A special research project plus six 400-level courses in Mathematics, Statistics and/or Probability, as approved by coordinators.

* Note that CONTACT, CONTENT, COORDINATOR, NOTE, OBJECTIVES, PREREQUISITES, TITLE differs from the maintainer's version above. A log of variations is available.

2. Mathematics, Faculty of Science (v4, p216) : Next:618-497 | Prev:618-392

Source for 618-487 v4, p216 (Differences)

618-487 "Combined Mathematics/Computer Science Course Work" appears differently in several places - choose the one you want:


618-487 Mathematics, Faculty of Science.
618-487 Computer Science, Faculty of Science.

1. Mathematics, Faculty of Science (v4, p216) : Next:618-486 | Prev:618-496

618-487 Combined Mathematics/Computer Science Course Work

Note: Must be taken concurrently with 618-486 Combined Mathematics/Computer Science Research Project.

See additional details under the Mathematics subject 618-486 Combined Mathematics/Computer Science Research Project.

1. Mathematics, Faculty of Science (v4, p216) : Next:618-486 | Prev:618-496

2. Computer Science, Faculty of Science (v4, p185) : Next:618-486 | Prev:433-402

618-487 Combined Mathematics Computer Science Course Work

See additional details under the Mathematics subject above.

* Note that TITLE differs from the maintainer's version above. A log of variations is available.

2. Computer Science, Faculty of Science (v4, p185) : Next:618-486 | Prev:433-402

Source for 618-486 v4, p216

618-486 Combined Mathematics/Computer Science Research Project

Note: Must be taken concurrently with 618-487 Combined Mathematics/Computer Science Course Work.

Credit Points: 100 points in total; points make-up as agreed by coordinators

Coordinator: Dr K Ecker (Mathematics) and Dr H Sondergaard (Computer Science)

Prerequisite: As approved by coordinators

Contact: All year

Objectives:

To provide coordinated advanced level training in both Mathematics and Computer Science together with a research training component.

Content:

A program of study and research selected from both the Mathematics and Computer Science Honours programs, which must be approved by both the Department of Mathematics and the Department of Computer Science.

ERROR SUMMARY:

USAGE XREF POINTS TO 158-268 AND NOT TO SOURCE IN 158-267 [Chinese:Ed-P]
SOURCE XREF TO ITSELF ERROR IN 640-228 [CompSci:Eng]
SOURCE XREF TO ITSELF ERROR IN 483-430 [Education:Ed-P]
SOURCE XREF TO ITSELF ERROR IN 183-120 [Engineering:Eng]
SOURCE XREF TO ITSELF ERROR IN 610-172 [Engineering:Eng]
USAGE XREF POINTS TO 618-496 AND NOT TO SOURCE IN 618-497 [Mathematics:Sci]
USAGE XREF POINTS TO 618-496 AND NOT TO SOURCE IN 618-497 [Mathematics:Sci]

Mon Oct  9 16:30:34 1995
./S50-v2writeHTML.pl