Monash University Handbook 2010 Undergraduate - Area of Study

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 course 0050 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 level two andlevel three 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 level one, two and three 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.

Objectives

On completion of any of the major sequences in mathematics students will:

• have achieved a broad understanding of how mathematical knowledge is constructed, and developed an appreciation of the importance of mathematical sciences in every part of their lives
• have developed skills in the effective use of mathematical computer software and spreadsheets
• have developed skills in the written and oral presentation of a mathematical argument
• be prepared for a range of further learning and training, including honours, in the sequence studied
• have developed problem solving and critical thinking skills
• be suitable for employment, both national and international, in a range of areas requiring analytical and quantitative skills.

In addition:

(a.) students completing the major sequence in mathematics will:

• have achieved an understanding of the basic single, multivariable and vector calculus, linear algebra, and probability topics
• have acquired an insight into some other broad areas of mathematics and application of mathematics such as pure mathematics, statistics, scientific computing, atmospheric science and astrophysics
• have learned a number of higher level mathematical methods and their applications in science, medicine, economics and engineering

(b.) students completing the major sequence in computational mathematics will:

• have achieved an understanding of the basic single variable, multivariable and vector calculus, linear algebra, and computer programming topics
• have acquired an insight into some other broad areas of computational mathematics and application of computational mathematics such as applied mathematics and scientific computing
• have learned a number of higher level computational methods and their applications in science and engineering

(c.) students completing the major sequence in pure mathematics will:

• have achieved an understanding of the basic single variable, multivariable and vector calculus, linear algebra and discrete mathematics
• have acquired an insight into some broad areas of pure mathematics and their development such as in algebra, geometry and analysis
• have learned a number of higher level pure mathematics and their development in algebra, geometry and analysis

(d.) students completing the major sequence in applied mathematics will:

• have achieved an understanding of the basic single variable, multivariable and vector calculus and linear algebra topics
• have acquired an insight into the areas of mathematical methods and their applications
• be able to apply a variety of higher level mathematical methods to solve problems in science, engineering and economics.

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 Climate dynamics of the atmosphere and oceans
• ATM2030 Clouds, weather and forecasting
• MTH2000 Mathematics research project level 2
• MTH2010 Multivariable calculus
• MTH2021 Linear algebra with applications
• MTH2032 Differential equations with modelling
• MTH2051 Introduction to computational mathematics
• MTH2121 Algebra and number theory
• MTH2132 The nature and beauty of mathematics
• MTH2140 Real analysis
• MTH2222 Mathematics of uncertainty
• STA2032 Advanced data analysis

Level three

• ASP3012 Stars and galaxies
• ASP3051 Relativity and cosmology
• ATM3040 Physical meteorology
• ATM3050 Dynamical meteorology
• MTH3000 Mathematics research project level 3
• MTH3011 Partial differential equations
• MTH3020 Complex analysis and integral transforms
• MTH3051 Introduction to computational mathematics
• MTH3060 Advanced ordinary differential equations
• MTH3110 Differential geometry
• MTH3121 Algebra and number theory
• MTH3140 Real analysis
• MTH3150 Algebra and number theory II
• MTH3160 Analysis and topology
• MTH3230 Time series and random processes in linear systems
• MTH3241 Random processes in the sciences and engineering
• MTH3251 Financial mathematics
• MTH3360 Fluid dynamics

Minor sequence in mathematics (24 points)

• MTH1020 and MTH1030, or MTH1030 and one of MTH1112, MTH1122, MTH2010, or STA1010
• MTH2010 (if not already taken at level one)
• 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
• at least one of MTH3011, MTH3051, MTH3110, MTH3140
• remaining 18 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 sequence in computational mathematics (48 points)

• FIT1002 and MTH1030
• MTH2010 and MTH2032
• MTH3060 and one of MTH2051 or MTH3051, and two of MTH2021, MTH3011, or MTH3020, with at least 18 points at level three

Major sequence in pure mathematics (48 points)

• MTH1020 and MTH1030, or MTH1030 and one of MTH1112, MTH1122 , or MTH2010
• MTH2010 (if not already taken)
• at least one of MTH3110 or MTH3140
• the remaining units (a total of 48 points, including at least 12 points at level three) from MTH2021, MTH2032, MTH2121 or MTH3110, MTH3121, (if not already taken), MTH2140 or MTH3140 (if not already taken), MTH2222, MTH3011, MTH3020, MTH3110, MTH3150, MTH3160 or MTH3230

Major sequence in applied mathematics (48 points)

• Either MTH1020 and MTH1030, or MTH1030 and MTH2010
• MTH2010 (if not already taken) and MTH2032
• at least one of MTH3011 or MTH3051
• the remaining units (a total of 48 points, including at least 12 points at level three) from MTH2021, MTH2051 or MTH3051 (if not already taken), MTH2140 or MTH3140, MTH2222, MTH3011 (if not already taken), MTH3020, MTH3060, MTH3230, or MTH3360

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 of Mathematical Sciences. 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 Chris Hough, Deputy: Mr Simon Teague, (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 in combination with MTH1030 can form part of a mathematics sequence at level one, 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 ATM1020 and ATM1030, 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 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, Deputy: Dr Eric Chu, (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 course 3520 Bachelor of Science Advanced with Honours (BScAdv(Hons)) or 2188 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, Deputy: Dr Aidan Sudbury, (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, ATM3040 and ATM3050 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, Deputy: Dr Andrew Prentice, (School of Mathematical Sciences)

Students with an appropriate level of performance in level-three units within any of the mathematical science sequences may be eligible to undertake a year of research training under the direct supervision of the leader of one of the research groups in the school.

Full details regarding entrance requirements and course structure for honours is described in the course entry in this Handbook for the course 0051 Honours degree of Bachelor of Science.