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 Mathematics and Statistics


Table of Contents

1. Choosing 100-level Mathematics and Statistics subjects
    1.1. Choosing a single subject
    1.2. Choosing two subjects
    1.3. Choosing three or more subjects
    1.4. First-year Learning Centre
    1.5. VCE extensions studies (MUPHAS) students
    1.6. Extended subjects
    1.7. Credit exclusions
    1.8. Mathematics and Statistics subjects for Bachelor of Biomedical Sciences
2. Entry into 200-level Mathematics and Statistics
3. 100-level subjects
4. 200-level subjects
5. 300-level subjects
6. Sample Mathematics and Statistics selections for the BSc degree
7. Interdisciplinary programs within the BSc
8. Mathematics and Statistics in combined degrees
9. Bachelor of Science (Honours)

Subject Lists
    Mathematics and Statistics 100-level subjects
    Mathematics and Statistics 200-level subjects
    Mathematics and Statistics 300-level subjects
    Mathematics and Statistics subjects available to Engineering students only


Archaeological evidence shows that the mathematical sciences have been practised continuously for more than 4000 years, from the ancient civilizations of Mesopotamia to the research laboratories of Silicon Valley. They have always been highly valued for the development of logical and analytical modes of thought, and their high points, which contain ideas as profound and beautiful as may be encountered anywhere, are among the greatest achievements of the human intellect. More pragmatically, the mathematical sciences are the foundation of much of modern technology, and studies in the mathematical sciences prepare the student for life in a rapidly changing and increasingly technological world.

At the University of Melbourne, most of the teaching in mathematical science areas is done by the Department of Mathematics and Statistics, which is a department of the Faculty of Science. The Department offers a variety of subjects at first, second and third year levels which are designed to prepare students for professional careers in mathematics and statistics, the pure and applied sciences, commerce, education, engineering, industry and technology, and the social sciences. More generally, the subjects offered provide training in logical reasoning and cultivate analytical skills invaluable for professional life in any discipline, and prepare students for a future in which ever-increasing volumes of information make informed and intelligent analysis essential.

The Department of Mathematics and Statistics was created in 1997 by the amalgamation of the Department of Mathematics and the Department of Statistics. The subject prefixes 617 (Mathematical Sciences), 618 (Mathematics), and 619 (Statistics), which were used in the 1997 Handbook and earlier handbooks, have been replaced by the subject prefix 620 (Mathematics and Statistics). To assist students who enrolled in 1998, or earlier, in statements of prerequisites and notes on credit exclusions references are given to 1998 and 1997 Handbook subjects as well as to current subjects. Students who studied 617, 618, or 619 prefix subjects in 1996 or earlier years should consult a Department of Mathematics and Statistics course adviser for guidance concerning prerequisites and credit exclusions.

 1. Choosing 100-level Mathematics and Statistics subjects

The Department of Mathematics and Statistics offers a number of subjects which are listed in Normal background for 100-level subjects, together with their normal entry requirements. An assumed VCE background for most but not all of these subjects is VCE Mathematical Methods (3/4 level). Further details about the subjects and recommended course combinations are given below.

 Table 1: Normal background for 100-level subjects

Subject  

Normal entry requirements  

620-121 Mathematics A (Advanced)  

A high level of achievement in VCE Specialist Mathematics 3/4 or equivalent, or special permission of the Director of First-year Studies.  

620-122 Mathematics B (Advanced)  

620-121 or equivalent.  

620-123 Applied Mathematics (Advanced)  

620-121 or equivalent; or any one of 620-141 with a grade of H2A or better, or 620-180 with a grade of H2A or better, or 620-211, or invitation by the Head of Department. Note:with subjects from 1998 (or earlier) as pre-requisites, students must have taken [98]620-121, or both of [98]620-141 and [98]620-142, and achieved at the required standand.  

620-131 Scientific Programming & Simulation  

Corequisites: one of 620-121, 620-141 or equivalent.  

620-141 Mathematics A  

VCE Mathematical Methods 3/4; VCE Specialist Mathematics 3/4 is recommended but not compulsory.  

620-142 Mathematics B  

620-141 or special permission of the Director of First Year Studies - for example, having achieved a high grade in 620-161.  

620-143 Applied Mathematics  

620-141 or equivalent; or any one of 620-121, 620-180, 620-200 or 620-211; or concurrent enrolment in one of 620-180, 620-200, 620-211. Note: with subjects from 1998 (or earlier) as pre-requisites, students must have taken [98]620-121, or both of [98]620-141 and [98]620-142. Students with only [98]620-141 will need to take 620-180 in 1999.  

620-151 Introduction to Biomedical Mathematics  

VCE Mathematical Methods 3/4 or equivalent.  

620-152 Introduction to Biomedical Statistics  

VCE Mathematical Methods 3/4 or equivalent.  

620-160 Experimental Design & Data Analysis  

VCE Mathematical Methods 3/4 or equivalent.  

620-161 Introductory Mathematics A  

VCE Mathematical Methods 3/4 or equivalent.  

620-162 Introductory Mathematics B  

620-161  

620-180 Intermediate Mathematics  

620-141; or both of [98]620-161, [98]620-162; or special permission of the Director of First Year Studies. Note that this subject is available in 1999 only.  

Detailed discussions of how students should select one, two, or three or more subjects offered at 100-level by the Department of Mathematics and Statistics are given below, and summarized in Sample selections at 100-level. Note that each 100-level subject is worth 12.5 points (or 1/8 of the normal full-time student workload).

Students with VCE Specialist Mathematics 3/4 should enrol in 620-121 or 620-141 in their first semester: they are not normally permitted to enrol in 620-161. 620-121 requires a high level of achievement in Specialist Mathematics 3/4. The Department's Director of First-year Studies will advise as to which of the two subjects (620-121 or 620-141) should be selected.

Students who take 620-161 who wish to go on to further studies in Mathematics can continue on to 620-162 in second semester, and take the subjects 620-142 (first semester stream) and 620-143 (second semester stream) in their second year, with 200-level mathematics subjects becoming available to them in their third year. However, if a high level of achievement is attained in 620-161 in semester 1, then enrolment in one or both of 620-142 and 620-143 in semester 2 is possible. This enables entry into 200-level Mathematics subjects in second year.

Students without VCE Specialist Mathematics 3/4 (or equivalent) are normally advised to select 620-161 (and 620-162). However, students who wish to progress to 200-level mathematics, and with a high level of achievement in VCE Mathematical Methods 3/4 should discuss the possibility of taking 620-141 in semester 1 (and 620-142, 620-143 in semester 2) with the Department's Director of First-year Studies.

 1.1. Choosing a single subject

Students who plan to take only one semester-length subject in Mathematics and Statistics in their first year are usually advised to select 620-160 Experimental Design and Data Analysis, especially if their interests lie in the biological, environmental or social sciences.

 1.2. Choosing two subjects

Students planning studies in Mathematics and Statistics beyond 100-level should select a 100-level subject containing core mathematics material in calculus and linear algebra in first semester. Listed in decreasing order of difficulty, the calculus and linear algebra subjects are 620-121, 620-141, 620-161. The selection of the appropriate one is largely dictated by secondary school preparation (see table) Normal background for 100-level subjects.

Each of the subjects 620-121, 620-141 has a linear algebra sequel in semester 2 (620-122, 620-142) and an applied calculus sequel in semester 2 (620-123, 620-143). Having taken 620-141 (620-121), students wishing to include only one second semester subject may select either of 620-142 or 620-143 (620-122 or 620-123), or they may choose instead the subject 620-160, which leads to further studies in statistics and is especially valuable in biological and environmental sciences.

The subject 620-161 has a calculus and linear algebra sequel in semester 2 (620-162). Having taken 620-161, students wishing to include only one second semester subject may choose 620-162 or 620-160.

Students contemplating transferring out of the BSc program at the end of their first year should seek advice from other faculties on whether all subjects receive equal weight in the ranking of applicants for transfer.

Some sample selections based on two 100-level Mathematics and Statistics subjects are summarized in Sample selections at 100-level.

 1.3. Choosing three or more subjects

Students entering with VCE Specialist Mathematics 3/4 or equivalent preparation who are able to accommodate more than two subjects in Mathematics and Statistics in their first year should select a calculus and linear algebra subject (620-121 or 620-141), and one or both of the linear algebra or applied calculus subjects (620-122, 620-123 or 620-142, 620-143) depending on their background and advice from the Department's Director of First-year Studies. One of the linear algebra or applied calculus subjects may be replaced by a probability or statistics subject (620-131 or 620-160). The additional Mathematics and Statistics subject or subjects taken depends on the individual student's companion subjects and interests.

Students enrolled in the BE/BSc or BSc/BE combined degree programs, or intending major studies in pure or applied mathematics or physics, should take 620-123 or 620-143 for an introduction to differential equations and applied mathematics. These subjects are also valuable for other disciplines including earth sciences and chemistry.

To open options for the study of probability and statistics in later years, students should select in their first year one of 620-131 (available in first semester only) or 620-160 (available in both semesters). Since 620-131 contains a scientific programming component, it is particularly suitable for students who require hands-on programming experience but are not taking either the pair of Computer Science subjects 433-141 and 433-142 (which are prerequisites for all 200-level Computer Science subjects) or the single Computer Science subject 433-171.

Students without VCE Specialist Mathematics 3/4 (or equivalent preparation) are normally advised to select 620-160, 620-161, 620-162. However, students with a high level of achievement in VCE Mathematical Methods 3/4 should discuss the possibility of taking 620-141, 620-142 and 620-143 with the Department's Director of First-year Studies. Students may choose to take 620-131 or 620-160 instead of either 620-142 or 620-143.

Some sample selections based on three or four 100-level Mathematics and Statistics subjects are summarized in Sample selections at 100-level.

 Table 2: Sample selections at 100-level

Course  

Recommended subjects  

The four-subject and three-subject selections (a) and (b) give a wide range of 200-level options in Mathematics and Statistics.  

Mathematics and Statistics,

Computer Science, Operations Research, Physics, Chemistry, Earth Sciences  

Four-subject selections

(a) 620-141, 620-142, 620-143, with one of 620-131 or 620-160

(b) 620-121, 620-122, 620-123, with one of 620-131 or 620-160

Three-subject selections

(a) 620-141, with two of 620-142, 620-143, 620-131 or 620-160

(b) 620-121, with two of 620-122, 620-123, 620-131 or 620-160

(c) 620-160, 620-161, 620-162

Two-subject selections

(a) 620-141, with one of 620-142, 620-143, 620-131 or 620-160

(b) 620-121, with one of 620-122, 620-123, 620-131 or 620-160

(c) 620-161, 620-162

Note: In each case, add 433-141, 433-142 for Computer Science; 610-141, 610-142 for Chemistry; 640-121, 640-122 or 640-141, 640-142 for Physics. Care has to be taken in the two-subject selection in choosing subjects to satisfy prerequisites for desired 200-level subjects. For Physics, a three or four subject selection including 620-123 or 620-143 is recommended. For combined degree programs in Science and Engineering, 620-123 or 620-143 should be taken. High-achieving students should refer below for the extended alternatives to 620-121, 620-122 and 620-123. Students who have studied university mathematics at school should refer to Extension studies (MUPHAS) students below for the possibility of direct entry to 200-level subjects.  

Biological

Sciences, Psychology, Economics and Commerce  

Two-subject selections

620-160 with one of 620-121, 620-141, 620-161

Single-subject selections

Either 620-160 or 620-161

 

 1.4. First-year Learning Centre

The Department of Mathematics and Statistics has a First-Year Learning Centre (FYLC) through which the teaching and administration of first-year subjects is coordinated. This centre is located on the ground floor of the Richard Berry Building. Near this centre students will find notice-boards relevant to first year, boxes for the submission of assignments, and Note Room G53 from which printed material is usually distributed. Within the centre are the office of the Department of Mathematics and Statistics Director of First-year Studies (Dr Barrington), offices of tutors in Mathematics and Statistics, tutorial rooms, a student waiting area, and a consultation room.

 1.5. VCE extensions studies (MUPHAS) students

Students who have studied university-level mathematics at school via the Melbourne University Program for High-Achieving Students ([98]620-120 or [97]618-120 MUPHAS Mathematics), or another program acceptable to the Department's Director of First-year Studies, may be permitted direct entry into the 200-level advanced level subject 620-211 Mathematics 2 (Advanced), or the standard 200-level subject 620-200 Mathematics 2, and possibly into 620-201 Probability. The recommended minimum Mathematics and Statistics enrolment for MUPHAS students is 620-200 or 620-211 in semester 1, and 620-113 or 620-123 in semester 2. Very high-achieving students may also consider taking 620-191 Mathematics and Statistics Project (Advanced). All MUPHAS students are requested to discuss their subject selection with the Department's Director of First-year Studies.

 1.6. Extended subjects

Students who have gained accelerated entry (for example, via MUPHAS or Exemption Examination), should discuss their subject selection with the Department's Director of First-year Studies. Students with accelerated entry or exceptional results in VCE mathematics may be invited to enter the extended subjects 620-111, 620-112, 620-113, or the advanced subject 620-191, all of which are designed for prospective honours students and those who intend to proceed to postgraduate studies. They may also be invited to accept direct entry into the 200-level subject 620-201 Probability. Students in this category should consult the Director of First-year Studies before finalising their course. Students from 620-121 with a grade of H2A or better are invited to enrol in 620-112 and/or 620-113.

 Table 3: Extended subjects at 100-level

Subject  

Normal entry requirement  

620-111 Mathematics A (Extended)  

Invitation by the Head of Department, normally requiring a very high level of achievement in VCE Specialist Mathematics 3/4 or in an equivalent secondary school program  

620-112 Mathematics B (Extended)  

620-111 or 620-121 with a grade of H2A or better, or invitation by the Head of Department.  

620-113 Applied Mathematics (Extended)  

A grade of H2A or better in any one of 620-111, 620-120 (MUPHAS), 620-121, 620-141, [98]620-142 or 620-211, or invitation by the Head of Department.  

620-191 Mathematics & Statistics Project (Adv.)  

Invitation by the Head of Department.  

 1.7. Credit exclusions

Credit exclusions for core 620 (Mathematics and Statistics) subjects containing calculus and linear algebra are as follows.

Students cannot gain credit for:

There are also credit exclusions between these subjects and similarly numbered subjects from previous years handbooks. Note that credit for 620-162 cannot be obtained once any of 620-142, 620-143, 620-122 or 620-123 has been passed. These exclusions are specified on a subject-by-subject basis in the details of subjects given below. For further information students should consult the Director of First-year Studies.

The following additional credit restrictions should also be noted. Students cannot gain credit for:

There are no credit exclusions between any of the subjects in this list and those in the list of core subjects above.

 1.8. Mathematics and Statistics subjects for Bachelor of Biomedical Sciences

The subjects 620-151 and 620-152 are new subjects introduced in 1999 to cater for the Biomedical Science course. Students may progress to 200-level subjects in probability and statistics (620-201, 620-202 or 620-270). To progress to 200-level mathematics subjects, students with good results in 620-151 could take 620-142 and/or 620-143 and may then proceed to 200-level mathematics subjects. For further information students should consult the Director of First-year Studies.

 2. Entry into 200-level Mathematics and Statistics

At 200-level, the Department of Mathematics and Statistics offers subjects in several areas of pure and applied mathematics and several areas of probability and statistics. Students may focus on a single area (pure mathematics, applied mathematics, operations research, probability, applied statistics), or pursue interests in several areas.

For 200-level studies in applied statistics, the subject 620-270 is open to any student who has completed 620-131 or 620-160 (or one of [98]620-140, [97]617-141, [97]619-100). The other probability and statistics subjects 620-201, 620-202 have as additional prerequisites one of 620-141 or 620-121, although accelerated entry students and students from the MUPHAS program may seek direct entry into 620-201.

For 200-level studies in pure or applied mathematics with a reasonable choice of options to be possible, one of the following combinations is recommended for first year:

If one of 620-123 or 620-143 is not taken in first year, then unless 620-143 is taken in the first semester of second year, enrolment in 620-232 is not possible. If 620-141, 620-142, 620-143 are taken in first year, to avoid unnecessary delay in progress through 200-level mathematics, 620-200 should be taken in first semester of second year. Note that from 2000, 620-200 will be replaced by 620-241, which will be offered only in first semester. High-achieving students from [98]620-142 (or [97]618-142) should enquire about the possibility of enrolment in 620-211 as an alternative to 620-200.

Students who are interested in applied mathematics are encouraged (though not required) to take 620-381 Computational Mathematics in a later year. This subject requires some prior experience in scientific programming, which may be gained by taking either 620-131 (or [97]617-141), which also serves as a prerequisite for all 200-level subjects emphasising probability and statistics (620-201, 620-202, 620-270), or the Computer Science subject 433-171, or both of the Computer Science subjects 433-141, 433-142, which are prerequisites for 200-level Computer Science.

 3. 100-level subjects

Coordinator: Dr F R Barrington (Director of First-year Studies)

To determine which 100-level Mathematics and Statistics subjects a student should take, refer to the section entitled Choosing 100-level Mathematics and Statistics subjects. While referring to this section students should also take careful note of the credit exclusions listed.

 4. 200-level subjects

Coordinator: Dr O Foda (200-Level Coordinator)

The 200-level subjects offered by the Department of Mathematics and Statistics are listed below in Mathematics and Statistics 200-level subjects.

For students who will be taking 200-level subjects in 2000, it should be noted that 620-200 will be replaced by a new subject 620-241 which will be offered in semester 1 only; and the role of 620-211 will change.

Students may take any combination of subjects if the prerequisites and conditions prescribed are satisfied. Some recommended selections of 200-level subjects have been given in the sample course plans given previously.

 Table 4: Mathematics and Statistics 200-level subjects

Sem 1  

620-200 Mathematics 21  

620-201 Probability  

620-211 Mathematics 2 (Advanced)1  

620-221 Real and Complex Analysis  

620-231 Vector Analysis  

620-261 Introduction to Operations Research  

620-270 Applied Statistics  

620-291 Maths & Stats Project A (Advanced)  

Sem 2  

620-200 Mathematics 21  

620-202 Statistics  

620-222 Linear and Abstract Algebra  

620-231 Vector Analysis  

620-232 Mathematical Methods  

620-252 Analysis  

620-262 Decision Making  

620-270 Applied Statistics  

620-292 Maths & Stats Project B (Advanced)  

The subjects listed in Mathematics and Statistics 200-level subjects and detailed below may be classified as follows.

Analysis and Algebra: 620-200, 620-211, 620-221, 620-222, 620-252. The subjects 620-200 and 620-211 are not available to students who have passed 620-112 or 620-122 (or [97]618-112 or [97]618-122). In 1999, either 620-200 or 620-211 can be used for direct entry to second year for students from the MUPHAS program; 620-211 is an advanced subject for exceptionally well-qualified incoming students, and is also suitable for high-achieving students from [98]620-142 (or [97]618-142). Students must pass one of 620-112, 620-122, 620-200 or 620-211 (or the corresponding 618-prefix 1997 Handbook subjects) before they may enrol in any of 620-221, 620-222, 620-252, and may gain credit for only one of 620-221, 620-252.

Methods and Applications: 620-231 and 620-232. (a) Students who completed 100-level mathematics subjects in 1998 or earlier shoud note the following pre-requisites for 620-231 and 620-232. Entry to 620-231 is available to students who have passed any of 620-112, 620-122, 620-142, 620-200, 620-211 (or the corresponding 618-prefix 1997 Handbook subjects). Entry to 620-232 requires:

Engineering students who have passed both [98]620-171 and [98]620-172 ([97]618-171 and [97]618-172) will also be permitted to enrol in 620-231, 620-232.

(b) For students who complete 100-level mathematics subjects in 1999: to enter 620-231 in 2000 you will need to take one of 620-111, 620-121, 620-141, and one of 620-112, 620-113, 620-122, 620-123, 620-142, 620-143. However, to enter 620-232, you will need to have done one of 620-111, 620-121, 620-141,and one of 620-112, 620-122, 620-142, and one of 620-113,620-123, 620-143. Although both 620-142 nd 620-143 are expected to be available in first semester of 2000, it is preferable to take all three of 620-111, 620-112, 620113; or all three of 620-121, 620-122, 620-123; or all three of 620-141, 620-142, 620-143 in first year if possible.

Note also that to enter 620-232 from 620-142, 620-143 in 2000, it will also be necessary to take a new first semester subject 620-241 which will replace the subject 620-200 (which is offered for the last time in 1999).

Operations Research: 620-261 and 620-262. Note that 620-261 is a prerequisite for the 300-level subjects 620-361 and 620-362.

Probability and Statistics: 620-201, 620-202, 620-270. The pair of subjects 620-201 and 620-202 constitute the basic second year course for students intending 300-level studies in probability and statistics, and is appropriate for students with a good mathematical background; 620-201 is a course on probability and probability modelling and may be usefully taken as a single subject. The subject 620-270 is an applied statistics subject which can be taken by students majoring in other disciplines, as well as by students planning further studies in statistics, and is required for students in Environmental Sciences; the emphasis is on applications and methods.

Projects: 620-291 and 620-292. These subjects are designated as Advanced and are especially suited to prospective Honours students. These subjects have as prerequisites Advanced 100-level subjects and/or the permission of the Head of Department.

Notes:

  1. Enrolment in any subject without the stated prerequisites must be approved by the Head of Department.

  2. Students are advised that they may not gain credit for current 200-level Mathematics and Statistics (620-) subjects and some 200-level Mathematical Sciences (617-), Mathematics (618-) and Statistics (619-) subjects offered in 1997 or earlier years. Credit exclusions for 1997 Handbook subjects are given with the individual subject details. For subjects taken in 1996 or before, the 200-Level Coordinator should be consulted.

 5. 300-level subjects

Coordinator: Professor W D Neumann (300-Level Coordinator)

The 300-level subjects offered by the Department of Mathematics and Statistics are listed in Mathematics and Statistics 300-level subjects. Students intending to proceed to the Honours degree in Mathematics and Statistics should make sure that all 400-level prerequisites are satisfied; see Bachelor of Science (Honours) and Bachelor of Information Systems (Honours)

 Table 5: Mathematics and Statistics 300-level subjects

Sem 1  

620-301 Stochastic Modelling  

620-311 Metric Spaces  

620-321 Algebra  

620-331 Applied Partial Differential Equations  

620-341 Dynamical Systems & Chaos  

620-351 Number Theory  

620-361 Operations Research Techniques & Algorithms  

620-371 Linear Models  

620-381 Computational Mathematics  

620-391 Mathematics & Statistics Topics A  

Sem 2  

620-302 Modern Probability  

620-312 Linear Analysis  

620-322 Topology  

620-332 Integral Transforms & Asymptotics  

620-342 Industrial & Applied Mathematics  

620-352 Graph Theory  

620-362 Applied Operations Research  

620-372 Inference & Applied Statistics  

620-382 Time Series and Forecasting  

620-392 Mathematics & Statistics Topics B  

Students may take any combination provided that prerequisites and conditions are satisfied. Suggested combinations are listed above under the heading Sample Mathematics and Statistics selections for the BSc degree. The subjects shown in Mathematics and Statistics 300-level subjects and detailed below may be classified as follows.

Analysis, Algebra and Topology: 620-311, 620-312, 620-321, 620-322. These subjects give the necessary background for students who wish to study fourth-year subjects in the pure mathematics, as part of an Honours degree.

Applied Statistics: 620-371, 620-372, 620-382. These subjects teach useful strategies in the analysis and interpretation of data, modelling, and the design of experiments. They give the necessary background for students who wish to study fourth-year subjects in applied statistics, as part of an Honours degree.

Methods and Applications: 620-331, 620-332, 620-341, 620-342. These subjects are particularly suited to students of engineering, physics, and other areas of physical science and technology. They give the necessary background for students who wish to study fourth-year subjects in the applications of mathematics in science and technology, as part of an Honours degree.

Operations Research: 620-361, 620-362. These subjects offer an introduction to the application of mathematics to problems arising in industry and commerce. They give the necessary background for students who wish to study fourth-year subjects in operations research, as part of an Honours degree.

Probability and Stochastic Processes: 620-301, 620-302. These subjects deal with the modern theory of probability and its applications. They give the necessary background for students who wish to study fourth-year subjects in probability and stochastic processes, as part of an Honours degree.

Additional Subjects: 620-351 Number Theory, 620-352 Graph Theory, 620-381 Computational Mathematics, 620-391 Mathematics and Statistics Topics A, and 620-392 Mathematics and Statistics Topics B. These subjects are supplementary to the subjects above and are designed to broaden the scope of studies in mathematics and statistics. Prospective secondary-school mathematics teachers are encouraged to take at least one of 620-351, 620-352, while 620-381 is especially valuable to students also taking 620-331, 620-332 and 620-342.

Notes:

  1. Students proposing to take an Honours degree should take careful note of the requirements for entry into the various Honours schools as set out in this Handbook. In particular, students wishing to take Mathematics and Statistics Honours should make sure that all prerequisites for prospective 400-level subjects are satisfied. Honours entry is possible from an appropriate selection of four 300-level Mathematics and Statistics subjects. If only four subjects are taken, 620-351 or 620-352 would not normally be included in the selection. For a wider choice of Honours options, additional Mathematics and Statistics subjects may be included.

  2. Enrolment in any subject without stated prerequisites must be approved by the Head of Department, but students should first seek advice from the Department of Mathematics and Statistics Course Advisers or the 300-Level Coordinator.

  3. Students are advised that they may not gain credit for current 300-level subjects and some 300-level Mathematical Sciences (617), Mathematics (618), Statistics (619) and Education (486) subjects offered in previous years. Credit exclusions for 1997 Handbook subjects are given with the individual subject details. For subjects taken in 1996 or before, the 300-level Year Coordinator should be consulted.

  4. Students interested in careers in the applications of mathematics in science, technology or commerce are strongly encouraged to include at least one of the subjects 620-201, 620-261 (if not taken in second year) or 620-381 before completing their science degree.

 6. Sample Mathematics and Statistics selections for the BSc degree

Typical course plans for students wishing to take Mathematics and Statistics beyond 100-level are given here in tables. To read the course plan first select the area of interest (e.g., Operations Research, Statistics or Economics). For each area, several course plans are given in the tables, with the one with the highest entry requirement listed first. In each course plan, a column corresponds to a semester. Subjects that are marked with an asterisk are considered useful but not essential, while all other subjects shown are strongly recommended and may be regarded as core subjects. In most cases, companion subjects from other departments are not listed. The standard load at 100-level is four 12.5 point subjects per semester. All Mathematics and Statistics subjects available for the BSc degree are semester-length, 12.5 point subjects.

Notes:

  1. Additional Mathematics and Statistics subjects beyond those listed are available at all years.

  2. All of the sample courses are suitable for prospective school mathematics teachers.

  3. Students with excellent results, or with interests not served by the standard subject selections, may consider taking one or both of the Mathematics and Statistics Topics subjects 620-391, 620-392. Enrolment in these subjects, the content of which varies from year to year, requires the permission of the Head of the Department of Mathematics and Statistics.

  4. Students who have successfully completed the advanced subjects 620-111 and 620-112, or are permitted to enrol in the advanced subject 620-211, and other high-achieving students, may be invited to enrol in one or both of 620-291 Mathematics and Statistics Project A (Advanced) and 620-292 Mathematics and Statistics Project B (Advanced).

  5. In most cases, the last digit of a Mathematics and Statistics subject code corresponds to the semester in which the subject is offered. The exceptions are 620-113, 620-123 which are available in second semester and 620-142, 620-143, 620-160, 620-200, 620-231, 620-270 which are available in both semesters.

  6. Science students are warned that quotas may be imposed on Economics subjects, and that there are restrictions placed on the number of non-Science points counted towards the B.Sc. degree.

  7. The Faculty of Science will be introducing majors for science courses in 1999. Refer to the Faculty for details of standard courses for major sequences.

  8. In 2000, the subject 620-200 will be replaced by a new subject 620-241 (offered in first semester only).

  9. Students who achieve a high grade in 620-161 and wish to continue studies in Mathematics and Statistics beyond 100-level should approach the Director of First-year Studies to discuss the possibility of being allowed to progress to 620-142 and/or 620-143 as an alternative to 620-162.

 Table 6: Typical Course Plan - Mathematics and Statistics with Economics

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

316-102  

316-101  

316-202  

316-201  

620-3012  

620-3122  

620-121  

620-122  

620-201  

620-202  

620-3112  

620-3522  

620-131  

620-1232  

620-2212  

620-2222  

620-361  

620-362  

   

620-261  

620-252  

620-3712  

620-3722  

   

620-270  

620-262  

620-3812  

620-3822  

(b)  

316-102  

316-101  

316-202  

316-201  

620-3012  

620-3522  

620-131  

620-1432  

620-270  

620-200  

620-361  

620-362  

620-141  

620-142  

620-261  

620-2622  

620-3712  

620-3722  

   

620-2012  

620-2022  

620-3812  

620-3822  

(c)  

316-102  

316-101  

316-202  

316-201  

620-201  

620-262 2  

620-160  

620-162  

620-270  

620-200  

620-261  

620-352 2  

620-161  

 

620-143  

 

620-371  

620-382  

 Table 7: Typical Course Plan - Operations Research

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

620-121  

620-122  

620-2013  

620-2023  

620-3013  

620-3123  

620-160  

620-123  

620-221  

620-2223  

620-311  

620-352  

   

620-261  

620-2523  

620-361  

620-362  

   

620-2703  

620-2623  

620-3713  

620-3723  

       

620-3813  

620-3823  

(b)  

620-160  

620-1433  

620-2013  

620-2023  

620-3013  

620-3523  

620-141  

620-142  

620-200  

620-2223  

620-361  

620-362  

   

620-261  

620-2523  

620-3713  

620-3723  

   

620-2703  

620-2623  

620-3813  

620-3823  

(c)  

620-160  

 

620-142  

620-1433  

620-261  

620-2623  

620-161  

620-162  

620-270  

620-200  

620-3713  

620-3823  

 Table 8: Typical Course Plan - Applied Statistics

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

620-121  

620-122  

620-201  

620-202  

620-301  

620-3024  

620-160  

620-1234  

620-2214  

620-2224  

620-3114  

620-3124  

   

620-2614  

620-2524  

620-3614  

620-3624  

   

620-2704  

620-2624  

620-371  

620-372  

         

620-382  

(b)  

620-160  

620-1434  

620-201  

620-2004  

620-3614  

620-3624  

620-141  

620-142  

620-2614  

620-202  

620-371  

620-372  

   

620-2704  

620-2624  

620-3814  

620-382  

(c)  

620-161  

620-160  

620-142  

620-200  

620-2614  

620-372  

 

620-162  

620-201  

620-202  

620-371  

620-3824  

(d)  

620-161  

620-160  

620-1414  

620-1424  

620-200  

620-3824  

   

620-270  

 

620-371  

 

 Table 9: Typical Course Plan - Stochastic Processes

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

620-121  

620-122  

620-201  

620-202  

620-301  

620-302  

620-160  

620-1435  

620-221  

620-222  

620-3115  

620-3125  

   

620-2615  

620-2525  

620-3615  

620-3625  

   

620-2705  

620-2625  

620-3715  

620-3725  

         

620-3825  

(b)  

620-160  

620-1435  

620-201  

620-200  

620-301  

620-302  

620-141  

620-142  

620-2615  

620-202  

620-3615  

620-3625  

   

620-2705  

620-2625  

620-3715  

620-3725  

       

620-3815  

620-3825  

(c)  

620-161  

620-160  

620-142  

620-200  

620-301  

620-3025  

 

620-162  

620-201  

620-202  

620-3715  

620-3725  

   

620-2705  

   

620-3825  

 Table 10: Typical Course Plan - Physical Sciences or Applied Mathematics

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

620-121  

620-122  

620-2016  

620-2226  

620-331  

620-332  

620-1316  

620-123  

620-221  

620-232  

620-3416  

620-3426  

   

620-231  

620-2826  

620-3816  

620-3526  

(b)  

620-121  

620-122  

620-2016  

620-232  

620-331  

620-332  

620-1316  

620-123  

620-231  

620-252  

620-3416  

620-3426  

   

620-2616  

 

620-3816  

620-3526  

(c)  

620-141  

620-142  

620-200  

 

620-331  

620-3326  

620-1316  

620-143  

620-231  

620-232  

620-3416  

620-3426  

     

620-2526  

620-3816  

620-3526  

620-161  

620-162  

620-142  

620-200  

620-231  

620-232  

   

620-1316  

620-143  

620-3816  

620-2526  

 Table 11: Typical Course Plan - Pure Mathematics

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

620-121  

620-122  

620-2017  

620-222  

620-3017  

620-3027  

620-1607  

620-123  

620-221  

620-232  

620-311  

620-312  

   

620-231  

 

620-321  

620-322  

   

620-2617  

 

620-3317  

620-3327  

       

620-3517  

620-3527  

(b)  

620-141  

620-142  

620-200  

620-222  

620-311  

620-312  

620-1607  

620-143  

620-2017  

620-2327  

620-321  

620-322  

   

620-231  

620-252  

620-3317  

620-332  

   

620-2617  

 

620-3517  

620-3527  

(c)  

620-161  

620-162  

620-142  

620-1437  

620-2317  

620-2227  

620-1607  

   

620-200  

620-2617  

620-2327  

       

620-351  

620-2527  

         

620-352  

 Table 12: Typical Course Plan - Biological Sciences, Environmental Science and Psychology

First year  

Second year  

Third year  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

Sem 1  

Sem 2  

(a)  

621-141  

620-1428  

620-2018  

620-2008  

620-3018  

620-3628  

620-160  

620-1438  

620-2618  

620-2028  

620-3618  

620-3728  

   

620-270  

620-2628  

620-3718  

620-3828  

(b)  

620-141  

620-1428  

620-2018  

620-2008  

620-3018  

620-3628  

   

620-2618  

620-2028  

620-3618  

620-3728  

 

620-160  

620-270  

620-2628  

620-3718  

620-3828  

(c)  

620-160  

 

620-1428  

620-1438  

620-2618  

620-3828  

620-161  

620-162  

620-270  

620-2008  

620-3718  

 

(d)  

620-161  

620-160  

620-1428  

620-1438  

620-2618  

620-3828  

 

620-1628  

620-270  

620-2008  

620-3718  

 

 7. Interdisciplinary programs within the BSc

The Faculty of Science supports an identified interdisciplinary stream within the BSc degree, covering Environmental Science.

Details of the Environmental Sciences stream will be found in Environmental Science. For this stream, 620-160 and 620-270 are compulsory subjects. Additional Mathematics and Statistics subjects are also available, and at 100-level a choice from 620-161, 620-162, 620-141, 620-142 is recommended. Some later-year possibilities are shown in Typical Course Plan - Biological Sciences, Environmental Science and Psychology.

For interdisciplinary studies in the area of Chemical Physics, based on an appropriate selection of subjects in Chemistry, Mathematics and Statistics and Physics consult a Department of Mathematics and Statistics course adviser.

 8. Mathematics and Statistics in combined degrees

Students in the combined-degree programs in which the Science Faculty participates or in the four year Bachelor of Arts and Science program, usually choose Mathematics and Statistics subjects in the BSc component of the course which enrich their studies in the companion component, as well as constituting an academically logical and rewarding science selection.

Students in the BCom/BSc program are strongly advised to include: one of 620-131 or 620-160; either 620-121 or 620-141 and one of 620-122, 620-123 or 620-142, 620-143; and either additional subjects in probability and statistics (620-201 and 620-202; and a selection from 620-270, 620-301, 620-371, 620-372, 620-382) or subjects in operations research (620-261, 620-262, 620-361, 620-362). Actuarial Studies students are normally required to take 620-121, 620-123, 620-131, 620-201 and 620-202; students commencing at mid year should discuss alternative options with the Director of First-year Studies.

Students in combined degrees with the Faculty of Engineering should consult Typical Course Plan - Combined Degree Programs in Science and Engineering.

 Table 13: Typical Course Plan - Combined Degree Programs in Science and Engineering

All Engineering departments  

Select one of options (a), (b) or (c) under Typical Course Plan - Physical Sciences or Applied Mathematics.  

Electrical Engineering or Mechanical Engineering  

If following option (c) under Typical Course Plan - Physical Sciences or Applied Mathematics, include also as core 620-252.  

In an Engineering course, some Statistics subjects must be included. The Engineering subject 620-001 can be replaced by 620-160 and 620-270; the Engineering subject 620-005 can be replaced by 620-131 and 620-201.

In each case, the 300-level Mathematics and Statistics subjects can be taken in the third, fourth or fifth year of the five year program, depending on the choice of companion science subjects and the needs of the engineering components of the course.  

 9. Bachelor of Science (Honours)

For information about the Faculty and departmental entry requirements for Honours, please refer to Bachelor of Science (Honours) and Bachelor of Information Systems (Honours) for details. These requirements should be considered when planning your course.

Mathematics and Statistics 100-level subjects

620-111 Mathematics A (Extended)
620-112 Mathematics B (Extended)
620-113 Applied Mathematics (Extended)
620-121 Mathematics A (Advanced)
620-122 Mathematics B (Advanced)
620-123 Applied Mathematics (Advanced)
620-131 Scientific Programming & Simulation
620-141 Mathematics A
620-142 Mathematics B
620-143 Applied Mathematics
620-151 Introduction to Biomedical Mathematics
620-152 Introduction to Biomedical Statistics
620-160 Experimental Design & Data Analysis
620-161 Introductory Mathematics A
620-162 Introductory Mathematics B
620-180 Intermediate Mathematics
620-191 Mathematics & Statistics Project (Adv.)

Mathematics and Statistics 200-level subjects

620-200 Mathematics 2
620-201 Probability
620-202 Statistics
620-211 Mathematics 2 (Advanced)
620-221 Real and Complex Analysis
620-222 Linear and Abstract Algebra
620-231 Vector Analysis
620-232 Mathematical Methods
620-252 Analysis
620-261 Introduction to Operations Research
620-262 Decision Making
620-270 Applied Statistics
620-291 Maths & Stats Project A (Advanced)
620-292 Maths & Stats Project B (Advanced)

Mathematics and Statistics 300-level subjects

620-301 Stochastic Modelling
620-302 Modern Probability
620-311 Metric Spaces
620-312 Linear Analysis
620-321 Algebra
620-322 Topology
620-331 Applied Partial Differential Equations
620-332 Integral Transforms & Asymptotics
620-341 Dynamical Systems & Chaos
620-342 Industrial & Applied Mathematics
620-351 Number Theory
620-352 Graph Theory
620-361 Operations Research Techniques & Algorithms
620-362 Applied Operations Research
620-371 Linear Models
620-372 Inference & Applied Statistics
620-381 Computational Mathematics
620-382 Time Series and Forecasting
620-391 Mathematics & Statistics Topics A
620-392 Mathematics & Statistics Topics B

Mathematics and Statistics subjects available to Engineering students only

The subjects 620-001, 620-005 are only available to Engineering Students. Combined Science/Engineering students should speak to an Engineering Course Adviser before enrolling in these subjects as it may be recommended that they complete 'Science' Mathematics and Statistics subjects instead. Credit toward the Bachelor of Science will not be awarded for the completion of either of these subjects.

620-001 Statistics for Engineers
620-005 Probability for Electrical Engineers


1. Note that from 2000, 620-200 will be replaced by 620-241 and the role of 620-211 will change.
2. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
3. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
4. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
5. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
6. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
7. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.
8. Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects.

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