Undergraduate - Area of Study Mathematics and statistics

NOTE: This area of study has had one or more changes made to it since publication on 1 October 2011. For details of change/s, please consult the change register at http://www.monash.edu.au/pubs/2012handbooks/2012-change-register.html.

Mathematics and statistics encompass 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.

Applied mathematics and computational mathematics deal with the application of techniques and models to the solutions of problems from many branches of modern science, engineering, information technology and commerce.

Pure mathematics deals with the abstract, the rigour and the beauty of perfection. Although pure mathematics constructions are motivated by reasons other than applications, such constructions often become the basis for applied mathematics to solve the most concrete problems.

Statistics is the branch of mathematics that captures the interplay of data and theory. Applied and mathematical statistics combine to extract useful knowledge from data. Mathematical statistics develops the methodology, while applied statistics exploits the theory to learn from real-life information. The use of statistics is constantly expanding, and a sound knowledge of the discipline is important even for those who do not complete a major sequence in the area.

There are cross links between statistics and pure and applied mathematics, and this is reflected in the mix of units students can choose from to complete a major or double major sequence.

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
• have developed, in the context of the discipline, the graduate attributes of effective communication, information and communication literacy, inquiry and critical thinking, and ethical, social and international understanding
• 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 differential equations, computational methods and linear algebra topics
• have acquired an insight into at least one area of application of those methods
• be able to apply a variety of higher level mathematical methods to solve problems in science, engineering and economics

(e.) students completing the major sequence in mathematical statistics will:

• have achieved an understanding of the basic single variable, multivariable and vector calculus, linear algebra, mathematical statistics and probability topics
• have acquired an insight into the area of mathematical statistics and its applications in the handling of statistical data and financial mathematics

(f.) students completing the double major sequence in financial and insurance mathematics will:

• have achieved an understanding of the basic single variable, multivariable and vector calculus, linear algebra, and probability topics
• have acquired an insight into the area of mathematical statistics and its use in handling statistical data and financial mathematics
• be able to understand and implement the inferential technique of maximum likelihood and to have developed an appreciation of the associated asymptotic distribution theory
• have developed an understanding of random processes such as Markov chains, branching processes, random walks, the Brownian motion and diffusions and be able to apply them in modelling real life processes, and financial and risk models
• have developed an understanding of the concepts of arbitrage and fair games and their relevance to finance and insurance
• have developed an understanding of the concepts of conditional expectation and martingales and their relation to the pricing of financial derivatives
• have acquired the skills needed to describe the time series and distributional features of financial data and to specify, estimate and test asset pricing models.

Level one

• MAT1830 Discrete mathematics for computer science
• MTH1000 Special topics in mathematics
• MTH1010 Functions and their applications
• MTH1020 Analysis of change
• MTH1030 Techniques for modelling
• MTH1035 Techniques for modelling (advanced)
• 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
• MTH2015 Multivariable calculus (advanced)
• 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
• MTH2232 Mathematical statistics

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

The units MTH1035 and MTH2015 are advanced versions of MTH1030 and MTH2010, respectively. For the purpose of sequence requirements listed below, MTH1030 and MTH2010 can be replaced by their corresponding advanced version.

Minor sequence in mathematics (24 points)

• MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830, MTH1000 or STA1010
• MTH2010 (if not already taken at level one)
• the remaining 6 or 12 points from MTH2021, MTH2032, MTH2051, MTH2121, MTH2140 and MTH2222

Minor sequence in statistics (24 points)

• MTH1030 and MTH2010
• MTH2222 and MTH2232

Major sequence in mathematics (48 points)

• a minor sequence in mathematics
• at least one of MTH3011, MTH3051, MTH3110, MTH3140
• the remaining 18 points from the MTH units at level two and three listed above
• a total of at least 18 points at level three

Double major sequence in mathematics (72 points)

• a major sequence in mathematics
• the remaining 24 points from the MTH, ATM and ASP units at level two and three listed above
• a total of at least 36 points at level three

Major sequence in applied mathematics (48 points)

• completion of a minor sequence in mathematics that includes MTH2032
• MTH2021 (if not already taken)
• at least three units from MTH3011, MTH3020, MTH3051, MTH3060, MTH3360, ASP3012, ASP3051 or ATM3050 including at least two of MTH3011, MTH3051 and MTH3060
• any remaining points from the MTH, ATM and ASP units at level two and three listed above

Double major sequence in applied mathematics (72 points)

• a minor sequence in mathematics that includes MTH2032
• MTH2021 (if not already taken)
• at least six units (36pts) from MTH3011, MTH3020, MTH3051, MTH3060, MTH3360, ASP3012, ASP3051, ATM3040, ATM3050 or MTH3251 including at least three (18pts) of MTH3011, MTH3020, MTH3051 and MTH3060
• any remaining points from the MTH, ATM and ASP units at level two and three listed above

Major sequence in computational mathematics (48 points)

• FIT1029 and MTH1030
• MTH2010 and MTH2032
• MTH3060 and MTH2051 or MTH3051
• two of MTH2021, MTH3011, or MTH3020
• a total of at least 18 points at level three

Major sequence in pure mathematics (48 points)

• MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830 or MTH1000
• MTH2010 (if not already taken at level one) and MTH2021
• MTH2140 or MTH3140, and MTH2121 or MTH3121
• the remaining 12 or 18 points from MTH2222, MTH3110, MTH3150, MTH3160, MTH3011, MTH3020 and MTH3230
• a total of at least 18 points at level three

Double major sequence in pure mathematics (72 points)

• MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830 or MTH1000
• MTH2010 (if not already taken at level one) and MTH2021
• MTH2140 or MTH3140, and MTH2121 or MTH3121
• the remaining points from MTH2222, MTH3000, MTH3110, MTH3150, MTH3160, MTH3011, MTH3020 and MTH3230
• a total of at least 36 points at level three

Major sequence in mathematical statistics (48 points)

• either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
• MTH2222, MTH2232, and one of MTH2010, MTH2021 or MTH2140 (MTH2010 must be included if not already taken in level one)
• Any three of ETC3400, MTH3230, MTH3241 and MTH3251

Double major sequence in mathematics and mathematical statistics (72 points)

• either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
• MTH2010 (if not already completed in level one), MTH2222, MTH2232
• Any three of ETC3400, MTH3230, MTH3241 and MTH3251
• the remaining units from level two and level three units listed above
• a total of at least 36 points at level three

Double major sequence in financial and insurance mathematics (72 points)

• either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
• MTH2010 (if not already completed in level one), MTH2222, MTH2232
• ETC3400, ETC3460, MTH3230, MTH3241, MTH3251 and at least one of ETC3420 or ETC3530
• the remaining points from level two and level three units ETC2410, MTH2021, MTH2140, ETC3420, ETC3530, MTH3011, MTH3051 and MTH3060

Requirements for honours in mathematics and statistics

• 24 points of relevant level three mathematics and statistics units, of which normally 18 points are relevant to the project

Additional information

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.

* See coordinator details in table above.

Level one

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, MAT1830 and MTH1000 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. MAT1830 is a specialist mathematics unit but it also has a service role, being recommended for students of computer science.

The School of Mathematical Sciences also offers the unit ASP1022, described in the 'astronomy and astrophysics' entry in the Science areas of study section of the Handbook.

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 MAT1830 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.

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

The units MTH1035 and MTH2015 are advanced versions of MTH1030 and MTH2010 and are intended to provide challenge to high achieving students. These units replace MTH1030 and MTH2010 in the minors and majors listed above.

MTH1000 is also designed for high achieving students. The objective of this unit is to allow high achieving students to complement their core first year mathematics units with studies in some areas of exciting new developments in mathematics

Level two

Students intending to undertake a major sequence in applied mathematics are recommended to complete MTH2032 in their second year of enrolment, along with either MTH2010 (if they have not already taken it) or MTH2021.

The unit MTH2222 covers the theoretical material needed to complete a major sequence in mathematical statistics. It is only offered in second semester, so students who wish to complete MTH2222 and who have not completed MTH2010 or MTH2021 by the end of the first semester must take MTH2010 concurrently with MTH2222.

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 1120 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

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.

Students intending to undertake a major sequence in applied mathematics who have not already completed MTH2021 should normally take that unit in their third year of enrolment.

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.

Honours

In addition to the requirements listed above, students must meet the entry requirements for the Science honours program relevant to their course of enrolment. See the entries for:

• 3520 Bachelor of Science Advanced with Honours
• 0051 Honours degree of Bachelor of Science
• 2188 Honours degree of Bachelor of Science (Science Scholar Program)

Full details regarding the course structure for honours in this area of study are outlined in course 0051 Honours degree of Bachelor of Science.

Single degrees

• 0050 Bachelor of Science
• 3520 Bachelor of Science Advanced with Honours
• 1120 Bachelor of Science (Science Scholar Program)

Double degrees

• 0530 Bachelor of Arts and Bachelor of Science
• 3537 Bachelor of Arts (Global) and Bachelor of Science
• 3528 Bachelor of Biomedical Science and Bachelor of Science
• 1469 Bachelor of Commerce and Bachelor of Science
• 3517 Bachelor of Science and Bachelor of Computer Science
• 3711 Bachelor of Science and Bachelor of Education
• 1633 Bachelor of Science and Bachelor of Education
• 3278 Bachelor of Aerospace Engineering and Bachelor of Science
• 4609 Bachelor of Environmental Engineering and Bachelor of Science
• 3282 Bachelor of Mechatronics Engineering and Bachelor of Science
• 0085 Bachelor of Science and Bachelor of Engineering
• 0086 Bachelor of Science and Bachelor of Laws

Honours degrees

• 0051 Honours degree of Bachelor of Science
• 2188 Honours degree of Bachelor of Science (Science Scholar Program)