Search : Index : Faculty of Science
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 on 1 January 1997, by the amalgamation of the Department of Mathematics and the Department of Statistics. The former School of Mathematical Sciences, which coordinated activities of the Department of Mathematics, the Department of Statistics, and the Department of Computer Science, has been abolished.
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Sciences), 618 (Mathematics), and 619 (Statistics), which were used in the 1997 Handbook and earlier handbooks, have been replaced by the subject prefix 620 (Mathematics and Statistics).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 before 1998, in statements of prerequisites and notes on credit exclusions references are given to 1996 and 1997 Handbook subjects as well as to current subjects. Where a 1996 Handbook subject and a 1997 Handbook subject coincide, only the 1997 subject is mentioned explicitly. Students who studied 617, 618, or 619 prefix subjects in 1995 or earlier years should consult a Department of Mathematics and Statistics course adviser for guidance concerning prerequisites and credit exclusions.
In most cases, the last digit of a Mathematics and Statistics (620) subject code corresponds to the semester in which the subject is offered. The exceptions are 620-130, 620-142, 620-160, 620-200, 620-231, 620-270 which are available in both semesters, the first semester subject 620-140 Probability and Applications, and the second semester subject 620-150 Number, Shape and Choice.
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.
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). See Natural sequences and credit exclusions for core 620 (Mathematics and Statistics) subjects containing basic calculus and linear algebra for guidance to approximately equivalent subjects which may be considered if a desired subject is not available in a given semester.
Students with VCE Specialist Mathematics 3/4 are not permitted to enrol in 620-161. They are recommended to enrol in 620-121 or 620-141 in their first semester; 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 should be selected.
Students who have gained accelerated entry (e.g. via MUPHAS, the Melbourne University Program for High-Achieving Students), or who have been invited to enter any of the advanced level subjects 620-111, 620-112, 620-132, 620-191 or 620-211, should discuss their subject selection with the Department's Director of First-year Studies.
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.
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 620-111, 620-121, 620-141, 620-161. The selection of the appropriate one is largely dictated by secondary school preparation (see Normal background for 100-level subjects). Each of these subjects has a calculus and linear algebra sequel in semester 2 (620-112 follows on from 620-111, and so on). Students wishing to include only one second semester subject may select either
Students contemplating transferring out of the B.Sc. 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.
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 pair of calculus and linear algebra subjects (620-111 and 620-112; or 620-121 and 620-122; or 620-141 and 620-142), depending on their background and advice from the Department's Director of First-year Studies. 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 one of 620-130 or 620-132 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), 620-140 (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 the Computer Science subjects 433-141 Computing Fundamentals A and 433-142 Computing Fundamentals B (which are prerequisites for all 200-level Computer Science subjects).
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 one of 620-130, 620-140 or 620-160 with the Department's Director of First-year Studies.
Some sample selections based on three or four 100-level Mathematics and Statistics subjects are summarized in Sample selections at 100-level.
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Students who have studied university-level mathematics at school via the Melbourne University Program for High-Achieving Students (in 1997, 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 into 620-201 Probability. The recommended minimum Mathematics and Statistics enrolment for MUPHAS students is 620-200 or 620-211 in semester 1, and 620-130 or 620-132 in semester 2. All MUPHAS students are requested to discuss their subject selection with the Department's Director of First-year Studies
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Students with accelerated entry or exceptional results in VCE mathematics may be invited to enter the advanced level subjects 620-111, 620-112, 620-132, 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 Director of First-year Studies before finalising their course. Students from 620-121 with a grade of H2A or better are also permitted to enrol in 620-112 and 620-132.
The Department of Mathematics and Statistics has established a First-year Learning Centre through which 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.
Natural sequences and credit exclusions for core 620 (Mathematics and Statistics) subjects containing basic calculus and linear algebra are shown inNatural sequences and credit exclusions for core 620 (Mathematics and Statistics) subjects containing basic calculus and linear algebra.
Each row of Natural sequences and credit exclusions for core 620 (Mathematics and Statistics) subjects containing basic calculus and linear algebra corresponds to a sequence of subjects, and at the end of each sequence the student will have covered the same core topics in calculus and linear algebra. Row (a) has the least demanding entry standard. Rows (b) and (c) correspond to standard selections suitable for students intending to continue with studies in mathematics beyond first year. Entry to (d) requires the invitation of the Head of the Department of Mathematics and Statistics; to seek this permission interested students should approach the Department's Director of First-year Studies in the first instance. Students who have studied an appropriate tertiary mathematics subject at school through the MUPHAS program (or another program) are normally directed to (e) or (f). Other high-achieving students may also be considered for entry into (e) or (f).
It is not possible to gain credit for two different subjects in the same column of the table, nor is it possible to gain credit in a subject listed in the table if any subject appearing in a column to the right of it has already been passed. It is also not possible to obtain credit for any of the 620-prefix subjects in the table if the corresponding 618-prefix subject in the 1997 Handbook has already been passed.
The following additional credit restrictions should be noted. Students cannot gain credit for:
Students wishing to delay studying mathematics, or needing to repeat a failed mathematics subject to progress in their course, may desire to enrol for a subject in a semester in which it is not offered. Such students should consult the Director of First-year Studies for advice on the possibility of taking instead a different subject from the same column of Natural sequences and credit exclusions for core 620 (Mathematics and Statistics) subjects containing basic calculus and linear algebra as the desired subject.
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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 one of 620-131, 620-140 or 620-160 (or one of the 1997 Handbook subjects 617-141, 619-100). The other probability and statistics subjects 620-201, 620-202 have as additional prerequisites one of 620-111, 620-121, 620-141 (or one of the 1997 Handbook subjects 618-111, 618-121, 618-141), 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 620-130 or 620-132 is not taken in first year, then unless 620-130 is taken in the first semester of second year, enrolment in 620-232 is not possible. If 620-141, 620-142, 620-130 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. High-achieving students from 620-142 (or the 1997 Handbook subject 618-142) should enquire about the possibility of enrolment in 620-211 as an alternative to 620-200.
Students envisaging 200-level studies in mathematics who are recommended to commence in 620-161 should continue on to 620-162 in second semester, and take the subjects 620-142 (first semester stream) and 620-130 (second semester stream) in their second year, with 200-level mathematics subjects, commencing with 620-200, becoming available to them in their third year. However, if a high level of achievement is attained in 620-162 (1997 Handbook 618-162), concurrent enrolment in 620-130 and 620-142 in semester 1 of second year, and enrolment in 620-200 in semester 2 of second year, is available.
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 the 1997 Handbook subject 617-141), which also serves as a prerequisite for all 200-level subjects emphasising statistics (620-201, 620-202, 620-270), or both of the Computer Science subjects 433-141, 433-142, which are prerequisites for 200-level Computer Science.
MUPHAS students should discuss the possibility of direct entry to second year via 620-200 or 620-211 and/or 620-201 with the Director of First-year Studies. Very high-achieving students may also consider taking 620-191 Mathematics and Statistics Project (Advanced).
The subject 620-150 Number, Shape and Choice, which gives an introduction to applications and concepts of mathematics without assuming any prior knowledge of calculus, is not a prerequisite for any 200-level Mathematics and Statistics subject.
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.
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. Note, however, that this table also includes 620-130, which is often taken in the first semester of their second year by students who are unable to accommodate it in first year.
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.
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The subjects shown in Mathematics and Statistics 200-Level Subjects and detailed below may be classified as follows.
Analysis and Algebra: 620-200, 620-211, 620-221, 618-222, 618-252. The subjects 620-200 and 620-211 are not available to students who have passed 620-112 or 620-122 (or the 1997 Handbook subjects 618-112 or 618-122). 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 620-142 (or the 1997 Handbook subject 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. Although 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), students who have completed 620-142 need to pass 620-200 or 620-211 before they can enrol in 620-232; note that one of 620-130 or 620-132 (or the corresponding 618-prefix 1997 Handbook subjects) is also needed before enrolment in 620-232. With the permission of their home Faculty of Engineering department, some Bachelor of Engineering students may use 620-231, 620-232 to replace 200-level Mathematics for Engineers subjects taught by the Faculty of Engineering. Students who have completed both 620-171 and 620-172 (1997 Handbook 618-171, 618-172) will also be permitted to enrol in 620-231, 620-232. Students who have completed both 620-181 and 620-182 (1997 Handbook 618-181, 618-182) and have obtained a grade of H3 or better in 620-182 (1997 Handbook 618-182), will be permitted to enrol in 620-231, but have to complete 620-200 before enrolling in 620-232. Similarly, students may take 620-160 and 620-200 to replace 620-001; and they may take 620-141 and 620-201 to replace 620-005.
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 for students intending 300-level studies in 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:
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)
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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:
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 "a" 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:
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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 Bachelor of Science (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.
Students in the combined-degree programs in which the Science Faculty participates 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, 620-140, 620-160; either 620-121 and 620-122, or 620-141 and 620-142; 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).
Students in combined degrees with the Faculty of Engineering should consult Typical Course Plan - Combined Degree Programs in Science and Engineering.
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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.
620-111 Mathematics 1A (Advanced)
620-112 Mathematics 1B (Advanced)
620-121 Mathematics 1A
620-122 Mathematics 1B
620-130 Applied Mathematics
620-131 Scientific Programming and Simulation
620-132 Applied Mathematics (Advanced)
620-140 Probability and Applications
620-141 Intermediate Mathematics A
620-142 Intermediate Mathematics B
620-150 Number, Shape and Choice
620-160 Experimental Design and Data Analysis
620-161 Introductory Mathematics A
620-162 Introductory Mathematics B
620-191 Mathematics and Statistics Project (Advanced)
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 Mathematics and Statistics Project A (Advanced)
620-292 Mathematics and Statistics Project B (Advanced)
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 and Asymptotics
620-341 Dynamical Systems and Chaos
620-342 Industrial and Applied Mathematics
620-351 Number Theory
620-352 Graph Theory
620-361 Operations Research Techniques and Algorithms
620-362 Applied Operations Research
620-371 Linear Models
620-372 Inference and Applied Statistics
620-381 Computational Mathematics
620-382 Time Series and Forecasting
620-391 Mathematics and Statistics Topics A
620-392 Mathematics and Statistics Topics B
The subjects 620-001, 620-005, 620-171, 620-172, 620-181, 620-182 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 any of 620-001, 620-005, 620-171, 620-172, 620-181, 620-182
620-001 Statistics for Engineers
620-005 Probability for Electrical Engineers
620-171 Mathematics 1P
620-172 Mathematics 1Q
620-181 Mathematics 1R
620-182 Mathematics 1S
| 1. | Subject is considered useful but not essential. Unmarked subjects are regarded as core subjects. |
| 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. |
Search : Index : Faculty of Science
Status: Official 1998 Last Modified: Tuesday October 21 17:12 SGML to HTML Conversion: Information Technology Services Authorised by: Academic Registrar Email Enquiries: Course_Information@registrar.unimelb.edu.au