Senior Mathematics and Statistics Handbook
General Information and Advice
Why Choose Mathematics?
Mathematics in general plays a crucial role in our attempts to understand the world around us. We see this demonstrated in the extensive use of mathematical models in the theoretical and applied sciences: from physics and chemistry through to engineering, operations research, computer science, information theory and economics. Many important models are based on modern mathematical research. Examples from applied mathematics research are the application of stochastic ODE's in finance and physics, our increased understanding of chaotic behaviour and its application to a wide range of physical phenomena and the development of improved largescale numerical techniques used on an everyday basis for applications ranging from weather prediction to models of artificial hearts. Examples from pure mathematics research are the application of number theory to cryptography, applications of singularity theory and group theory to symmetrybreaking and bifurcation in the engineering sciences, the application of category theory to theoretical computer science and the recent developments of general field theories in mathematical physics based on the most profound work in complex analysis and algebraic geometry.
As quantitative reasoning and mathematical modelling techniques extend further into the medical and social sciences, the humanities and all areas of finance, there is an increasing demand for mathematically competent workers in these fields and for teachers of specific mathematical skills in both general and adult education. Employers increasingly value the logical thinking and problem solving skills that are developed by studying mathematics.
Pure Mathematics and Applied Mathematics
There are two separate disciplines within the general subject area – Pure Mathematics and Applied Mathematics. You may choose units from either or both disciplines.
 If you enjoy problem solving, working with computers and using your mathematics to deal with real applications in science, engineering, economics and biology then you should consider enrolling in some Applied Mathematics units. You will attain a high level of mathematical expertise and a good deal of practical computer experience, both of which will stand you in good stead in a wide variety of possible careers, for example in computing, finance, telecommunications and mathematics research.
 If you appreciate the elegance of conceptual reasoning, or enjoy the challenge of abstract problems, you should consider enrolling in some Pure Mathematics units. They are wise choices not only for those whose principal interest lies in mathematics itself, but for all who wish to extend their reasoning ability: many students whose main interests lie in other disciplines find Pure Mathematics an ideal second major. A wide variety of pure units are offered, at both Advanced and Normal levels, covering all major branches of mathematics.
Why Choose Statistics?
Statistical techniques are employed in almost every aspect of daily life. These techniques are basically designed for data analysis and enable, for example, governments to plan our future through use of census data, businesses to forecast consumer demand for products, medical researchers to determine effectiveness of drugs, engineers to establish quality control standards, economists to use various indices of economic growth to attempt predictions of the future state of the economy, agricultural scientists to assess and compare the qualities of various soil types or strains of wheat or types of fertilizers and so on. The three facets of statistics are data analysis, probability modelling and statistical inference. Senior Statistics units provide the opportunity for further study in each of these areas.
As a result of the demand for statistical analysis across a broad spectrum of human endeavour and the ever increasing use of computers in data analysis, there is a growing demand for people trained in statistics both in the private and public sectors. This trend is likely to continue. Modelling and forecasting skills which are taught in the Senior Statistics courses are important in the areas of marketing, banking, finance and scientific research. Also, statistics will be useful for those contemplating a career in teaching. A major in statistics is always received positively by prospective employers as a relevant, useful area of training for potential employees.
How Many Units of Study Should You Choose?
To satisfy the B.Sc degree regulations, each Science student must take at least 24 credit points of Senior (third year) units in a single Science subject Area, such as Mathematics or Statistics. This subject area is then termed a major for that student. Note that the subject area of Mathematics encompasses both Pure and Applied Mathematics, and is separate from the subject area of Statistics.
Very many students take two majors in their third year; for example, majors in Mathematics and Statistics, Mathematics and Computer Science, Statistics and Psychology, Mathematics and Physics, Mathematics and Chemistry, or a double major in Mathematics (48 credit points of Senior Mathematics units).
Each Senior unit of study offered by the School of Mathematics and Statistics is worth 6 credit points. To major in Statistics you must therefore complete four Senior Statistics units. To major in Mathematics you must complete four or more Senior Mathematics units. (A double major consists of eight Senior Mathematics units.) You may choose Pure Mathematics, Applied Mathematics or a mix of the two.
If you are not majoring in Mathematics or Statistics, you can still choose any number of Senior level units of study in from either area to complement your other subjects. In particular, students specialising in Engineering, Physics or Chemistry would find either of the following Statistics units of study useful: Stochastic Processes and Time Series (STAT3011/STAT3911), Applied Linear Models (STAT3012/STAT3912). For appropriate Pure/Applied Mathematics units, see below.
Computational Science
Computational science (COSC) is an interdisciplinary Major comprising units of study offered by several Schools and Departments in the Faculty of Science. In particular, MATH3076 Mathematical Computing and MATH3976 Mathematical Computing(Adv) are Senior Core units in the Major. See the COSC major description for more details.
Financial Mathematics and Statistics
The major in Financial Mathematics and Statistics combines selected units from the subject areas of Statistics and Mathematics. This program is designed for students in double degrees who are interested in pursuing a career in the financial sector, but because of degree restrictions can only take a single Science major. It is also available for any student in the B.Sc. with an interest in finance and forecasting, and caters for those who wish to include Senior units other than Mathematics and Statistics units in their degree or who wish to complete a second major outside the School of Mathematics and Statistics. (Note that students in the B.Sc who wish to specialize in this area can include all the units in the Financial Mathematics and Statistics program while completing a major in Mathematics or Statistics, or a major in Mathematics and a major in Statistics.) Students planning to take the Financial Mathematics and Statistics major and who are considering Honours should consult Dr Neville Weber, Carslaw room 818, or Dr Peter Buchen, Carslaw room 719, before finalizing their electives. To obtain a major in Financial Mathematics and Statistics a candidate will have to successfully complete the Senior units of study listed below. All of the core units must be completed, and at least one of the electives.Core Units
(all to be completed) MATH3075/3975 Financial Mathematics
 STAT3011/3911 Stochastic Processes and Time Series
 STAT3012/3912 Applied Linear Models
Elective Units
(at least one must be completed) MATH3067 Information and Coding Theory
 MATH3076/3976 Mathematical Computing
 MATH3078/3978 Partial Differential Equations and Waves
 STAT3013/3913 Statistical Inference
 STAT3014/3914 Applied Statistics
 INFO3404/3504 Database Systems 2
Senior Year Coordinators
The coordinators are the people you should consult if you need general information about the units of study, or advice on enrolment.
The coordinators for Pure Mathematics Senior units are:
 Dr D. Cartwright, Room 620, Carslaw Building, phone 9351 4534, email: D.Cartwright@maths.usyd.edu.au
 A/Prof Bob Howlett, Room 523, Carslaw Building, tel. 9351 2976, email: R.Howlett@maths.usyd.edu.au
The coordinator for Applied Mathematics Senior units is:
 Dr Chris Cosgrove, Room 716, Carslaw Building, phone 9351 3357, email: chrisc@maths.usyd.edu.au
The coordinator for Mathematical Statistics Senior units is:
 Dr Michael Stewart, Room 820, Carslaw Building, phone 9351 5765, email: M.Stewart@maths.usyd.edu.au
Some Suggested Third Year Mathematics Programs
Choosing four of the units will constitute a major in Mathematics. The usual enrolment is two units per semester. You may, of course, choose fewer than four units or as many as eight units, to suit your own personal circumstances.
The wide choice of units available makes it possible to adapt third year mathematics programs to blend with and enhance the study of many other subjects. Some suggestions are given below. Note that units designated (N) are Normal level units, while those designated (A) are Advanced level.
 To complement Computer Science, students may wish
to take some or all of the following units:
 Semester 1. Logic & Foundations (MATH3065), Rings, Fields & Galois Theory (MATH3962), Mathematical Computing (MATH3076/3976).
 Semester 2. Algebra & Number Theory (MATH3062), Information & Coding Theory (MATH3067), Modules and Group Representations (MATH3966), Geometry & Topology (MATH3061), Financial Mathematics (MATH3075/3975).

To complement Engineering, students enrolled in the
double degree B.Sc/B.E. would find any of the following of benefit to
their professional careers:
 Semester 1. Metric Spaces (MATH3961), Analysis (MATH3068), Differential Equations & Biomathematics (MATH3063/3963), Logic & Foundations (MATH3065), Fluid Dynamics (MATH3974), Mathematical Computing (MATH3076/3976).
 Semester 2. Measure Theory and Fourier Analysis (MATH3969), Partial Differential Equations and Waves (MATH3078/3978), Differential Geometry (MATH3968), Information & Coding Theory (MATH3067), Financial Mathematics (MATH3075/3975), Lagrangian & Hamiltonian Dynamics (MATH3977), Complex Analysis with Applications (MATH3964).
 To complement Physics and Chemistry, students may
wish to consider:
 Semester 1. Metric Spaces (MATH3961), Analysis (MATH3068), Rings, Fields & Galois Theory (MATH3962), Differential Equations & Biomathematics (MATH3063/3963), Logic & Foundations (MATH3065), Fluid Dynamics (MATH3974), Mathematical Computing (MATH3076/3976).
 Semester 2. Measure Theory and Fourier Analysis (MATH3969), Modules and Group Representations (MATH3966), Partial Differential Equations and Waves (MATH3078/3978), Differential Geometry (MATH3968), Information & Coding Theory (MATH3067), Financial Mathematics (MATH3075/3975), Lagrangian & Hamiltonian Dynamics (MATH3977), Complex Analysis with Applications (MATH3964), Geometry & Topology (MATH3061).

Prospective Teachers of Mathematics might consider
choosing from:
 Semester 1. Logic & Foundations (MATH3065), Analysis (MATH3068), Differential Equations & Biomathematics (MATH3063/3963), Rings, Fields & Galois Theory (MATH3962), Metric Spaces (MATH3961), Mathematical Computing (MATH3076/3976).
 Semester 2. Information & Coding Theory (MATH3067), Algebra & Number Theory (MATH3062), Geometry & Topology (MATH3061), Partial Differential Equations and Waves (MATH3078/3978).
Intending Pure Maths 4 and Applied Maths 4 students must take at least 24 credit points of Senior level Mathematics. While students are free to choose from the whole range of units on offer across both Pure and Applied Mathematics, intending Applied Mathematics 4 students are advised to choose at least 3 units from the third year Applied Mathematics program, preferably including one or more at Advanced level. Intending Pure Mathematics 4 students are advised to choose at least 3 units from the third year Pure Mathematics program, and are strongly advised to include Metric Spaces (MATH3961) and Rings, Fields and Galois Theory (MATH3962).
Entry Requirements for 4th Year Applied Mathematics
Students who are considering 4th year in Applied Mathematics are advised to consult members of staff in their areas of interest as well as the Third Year Coordinator for advice on choice of units. The staff members to consult are:
 Nonlinear Mathematics – Prof Nalini Joshi (Carslaw Building Rm 720)
 Applied Mathematics – Dr Dave Galloway (Carslaw Building Rm 712)
Entry Requirements for 4th Year Pure Mathematics
Students who are considering 4th year in Pure Mathematics are advised to consult members of staff in their areas of interest as well as the Third Year Coordinators for advice on choice of units. The staff members to consult are:
 Algebra – Dr David Easdown (Carslaw Building Rm 619)
 Analysis – Dr Donald Cartwright (Carslaw Building Rm 620)
 Computational & Discrete Mathematics – Prof John J Cannon (Carslaw Building Rm 618)
 Geometry & Topology – Dr Jonathan Hillman (Carslaw Building Rm 617)
 Nonlinear Mathematics – Prof E Norman Dancer (Carslaw Building Rm 717)
Entry Requirements for 4th Year Mathematical Statistics
The entry qualification for Mathematical Statistics 4 is a Credit average or better taken over 24 credit points of Senior Mathematical Statistics units, and is subject to the approval of the Head of School. In addition, all Faculty requirements must have been satisfied. Students intending to do Honours in Mathematical Statistics should complete all available Advanced level Senior Statistics units of study. Interested students should see the Mathematical Statistics 4 coordinator, Dr Rafał Kulik, Carslaw room 821, telephone 9351 2307.Attendance Requirement
Students are expected to attend all lectures and tutorials in the units in which they are enrolled. Students who are unable to comply with this requirement should seek immediate advice from one of the coordinators.Change of Enrolment – Important Dates
Withdrawing from a unit in which you have enrolled without incurring HECS charges is permitted during the first few weeks of semester only, up to the HECS census dates. Please note that students are generally not permitted to enrol in additional units after the first two weeks of each semester. It is your responsibility to make any desired changes in your enrolment before the appropriate dates. Changes must be made at your Faculty office.