Mathematics

Coordinators: Listed below for each level

The discipline

Mathematical techniques and models form a significant component of nearly all branches of modern science. Mathematics is also a vital and growing discipline in its own right, and encompasses the formal study of numerical, algebraic and analytical structures, the development of quantitative methods essential for the practice and development of science, engineering, economics and other fields, and the development and utilisation of mathematical and numerical models in various contexts.

Units are offered in specialist areas of mathematics and statistics, as well as in mathematical methods (designed in part to support units offered for other disciplines). Areas for which specialist units are offered include algebra, analysis and geometry, applied and computational mathematics, statistics and probability, astronomy and astrophysics, atmospheric science and fluid dynamics. Information sheets with suggested programs for these areas are available from the School of Mathematical Sciences prior to re-enrolment.

All units offered for the first three levels of the Bachelor of Science and associated degrees have MTH codes for mathematics units and STA codes for some statistics units. For details of the statistics units that are available at the Clayton campus, see the ‘Statistics’ entry in this handbook. Some second and third-level astronomy and astrophysics (ASP) and atmospheric science (ATM) units can also contribute towards minor and major sequences in mathematics; consult the relevant year coordinator for details. Mathematics units designed specifically to meet the requirements of the faculties of Engineering and Information Technology are listed under the relevant regulations for those courses, often with MAT codes; normally these units cannot be taken as part of a mathematics sequence for the students in the Bachelor of Science and related courses.

For first, second and third-level mathematics units offered at the Clayton campus, the fourth digit (0, 1 or 2) in the unit code indicates the semester in which it is given, where 0 indicates that streams of the unit are normally available in either or both of first and second semester. For some mathematics units not offered at the Clayton campus, the fourth digit in the unit code may be 5, 6, 7 or 9. With the approval of the relevant year coordinator, students can replace some units in a recommended program by equivalent units offered at the Gippsland campus (see ‘Science areas of study and sequences – Gippsland’ in this section of the handbook) or by off-campus learning.

Units offered

Level one

MTH1010 Functions and their applications
MTH1020 Analysis of change
MTH1030 Techniques for modelling
MTH1112 Numbers, logic and graphs
MTH1122 The nature and beauty of mathematics
MTH2010 Multivariable calculus
STA1010 Statistical methods for science

Level two

ASP2062 Introduction to astrophysics
ATM2020 Large-scale weather and climate
ATM2030 Clouds, weather and forecasting
MTH2000 Mathematics research project level 2
MTH2010 Multivariable calculus
MTH2021 Linear algebra with applications
MTH2032 Differential equations and modelling
MTH2051 Introduction to computational mathematics
MTH2122 Algebra and number theory I
MTH2132 The nature and beauty of mathematics
MTH2140 Real analysis
MTH2222 Mathematics of uncertainty
STA2032 Applied data analysis

Level three

ASP3012 Stars and galaxies
ASP3051 Relativity and cosmology
ATM3040 Dynamical and physical processes in meteorology
MTH3000 Mathematics research project level 3
MTH3011 Partial differential equations
MTH3021 Complex analysis and integral transforms
MTH3051 Introduction to computational mathematics
MTH3060 Dynamical systems and boundary value problems
MTH3110 Differential geometry
MTH3122 Algebra and number theory I
MTH3140 Real analysis
MTH3150 Algebra and number theory II
MTH3160 Analysis and topology
MTH3230 Time series and random processes in linear systems
MTH3241 Mathematics for bioinformatics
MTH3251 Financial mathematics
MTH3360 Fluid dynamics

Sequence requirements

Minor sequence in mathematics (24 points):

MTH1020 and MTH1030, or MTH1030 and one of MTH1112, MTH1122, MTH2010, or STA1010, and
MTH2010 (if not already taken at level one), and
The remaining 6 or 12 points from the MTH, STA, ATM or ASP units at level two listed above

Major sequence in mathematics (48 points):

A minor sequence in mathematics, and
24 points from the MTH, STA, ATM and ASP units at level two and three listed above, with at least 18 points at level three

Details of the ASP, ATM and STA units, and some related sequences, are described in the ‘Astronomy and astrophysics’, ‘Atmospheric science’ and ‘Statistics’ entries in this section of the handbook.

Major in computational mathematics:

FIT1002 and MTH1030, and
MTH2010 and MTH2032, and
MTH3060 and one of MTH2051 or MTH3051, and two of MTH2021, MTH3011, or MTH3021, with at least 18 points at level three

Major in pure mathematics:

MTH1020 and MTH1030, or MTH1030 and one of MTH1112, MTH1122 , or MTH2010, and
MTH2010 (if not already taken), and
The remaining five or six units from MTH2021, MTH2032, MTH2122 or MTH3122, MTH2140 or MTH3140, MTH2222, MTH3011, MTH3021, MTH3110, MTH3150, MTH3160 or MTH3230, with at least 18 points at level three

Major in applied mathematics:

Either MTH1020 and MTH1030, or MTH1030 and MTH2010, and
MTH2010 (if not already taken) and MTH2032, and
The remaining five units from MTH2021, MTH2051 or MTH3051, MTH2140 or MTH3140, MTH2222, MTH3011, MTH3021, MTH3060, MTH3230, or MTH3360, with at least 18 points at level three

Recommendations

There are many possible combinations of mathematics units and strong prerequisite requirements on mathematics sequences. Students considering completing a sequence in mathematics or statistics are advised to determine the prerequisites for any higher-level units in their area of interest before finalising their choice of units and may seek the assistance of the relevant year coordinator. Information sheets with suggested programs are available from the school. As a general rule, it is advisable to choose a set of units at any level that leave several options open at higher levels.

Level one

Coordinator: Dr Anthony Lun (School of Mathematical Sciences)

Level one mathematics units are provided for students from a wide variety of backgrounds, from those who have not studied mathematics at VCE level to those who have completed VCE Specialist Mathematics units 3 and 4. It is recommended that all science students should include some level-one mathematics units in their course, particularly those who have not completed VCE Mathematical Methods units 3 and 4.

The units MTH1010, MTH1020 and MTH1030 are provided in support of other science disciplines, as well as preparation for further studies in mathematics. They should be taken sequentially commencing from a point that depends on a student’s previous studies in mathematics, for example by their level of preparation from VCE level. MTH2010 is available to students at both first and second level who have completed MTH1030, including first-year students who have taken MTH1030 in their first semester. Further details of recommended mathematics sequences are provided below.

The units STA1010, MTH1112 and MTH1122 can form part of a mathematics sequence at level one, in combination with one or more of MTH1010, MTH1020 and MTH1030, but any student who is considering completing a minor or major sequence in mathematics may limit their options at higher years if MTH1030 is not taken in their first year. STA1010 is designed specifically as a service unit in data analysis and statistics for students intending to major in other disciplines, particularly in psychology and the life sciences, as well as forming part of the normal statistics sequence. MTH1112 is a specialist mathematics unit but it also has a service role, being recommended for students of computer science. MTH1122 is designed for arts and education students. It would also be useful for science students provided there is room in their program and it does not constrain their progression to higher-level studies.

The School of Mathematical Sciences also offers the unit ASP1022, described in the ‘Astronomy and astrophysics’ entry in this section of the handbook, and contributes to ATM1010, described in the ‘Atmospheric science’ entry.

Recommended level-one mathematics sequences

For students who have completed VCE Mathematical Methods units 3 and 4 with an average grade of C or above in the written examination components, the recommended mathematics level one sequence is MTH1020 and MTH1030.

For students who have completed VCE Specialist Mathematics units 3 and 4 with an average grade of B or above in the written examination components, the recommended level one mathematics sequence is MTH1030 and MTH2010. These students may also choose to take MTH1112, MTH1122 or STA1010 instead of MTH2010 in their first year.

For other students, the recommended level-one mathematics sequence is MTH1010 and MTH1020.

Students not intending to take any level-two mathematics units may choose any one of the above recommended sequences or replace the second unit in any of the sequences by STA1010 or MTH1122.

It is recommended that Bachelor of Science (BSc) students complete SCI1020 prior to STA1010 if they have not completed VCE Specialist Mathematics or achieved at least an average grade of B or above in the written examination components of VCE Mathematical Methods units 3 and 4.

Level two

Coordinator: Dr Leo Brewin (School of Mathematical Sciences)

The School of Mathematical Sciences offers level-two units in mathematical methods as well as in a range of specialist areas. The astrophysics and atmospheric science units given by the school, ASP2062, ATM2020 and ATM2030, can also be taken as part of any mathematics sequence at level two.

The unit MTH2000 (Mathematics research project level 2) is normally only available to students in the Bachelor of Science Advanced with Honours (BScAdv(Hons)) or Bachelor of Science (Science Scholar Program) (BSc(ScSchProg)), or by permission of the head of school.

The School of Applied Sciences and Engineering also offers some level-two mathematics and statistics units at the Gippsland campus and through off-campus learning.

Level three

Coordinator: Associate Professor Michael Page (School of Mathematical Sciences)

The School of Mathematical Sciences offers a broad range of mathematics units at level three. Many of these units are intended for non-specialist third-level studies in mathematics. Specialist unit areas include algebra, analysis and geometry, applied and computational mathematics, mathematical statistics and probability, astrophysics, atmospheric science and fluid dynamics. The astrophysics and atmospheric science units given by the school, ASP3012, ASP3051 and ATM3040 can also be taken as part of any mathematics sequence at level three.

The unit MTH3000 (Mathematics research project level 3) is normally only available to students in the BScAdv(Hons) or BSc(ScSchProg), or by permission of the head of school.

The School of Applied Sciences and Engineering also offers some level-three mathematics and statistics units at the Gippsland campus and through off-campus learning.

Honours

Coordinator: Dr Maria Athanassenas (School of Mathematical Sciences)

The School of Mathematical Sciences offer honours studies in mathematics and mathematical statistics for students commencing in either first or second semester. The program normally consists of some lecture topics in addition to an essay topic and the completion, under supervision, of a major project. A list of the fourth-year topics will be available at the time of enrolment. A limited number of level three units, or units from other schools, may be substituted for fourth-year topics, as approved by the honours coordinator.

The minimum entry requirement to apply for honours studies in mathematical sciences is normally an average of at least distinction grade in 24 points of level-three mathematics or statistics units, or equivalent. This will normally include at least 18 points in the area of study in which the student proposes to enrol. Applications for entry into the program in the following year must be submitted normally before the end of the third year of studies, but it is advisable to approach the honours coordinator as early in that year as possible for advice. The school also offers honours-level studies in astrophysics and atmospheric science and lecture units from these can be taken as part of honours studies in mathematics; further details are provided under the honours entries for those disciplines in this handbook.

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