# 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
large-scale 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 symmetry-breaking 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 Mainstream 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 from either area to complement your other subjects: see below for some recommendations.

## 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 either the Mathematical Statistics 4 Coordinator (Uri Keich, Carslaw room 821, email st4.maths@sydney.edu.au) or the Applied Mathematics 4 Coordinator (Robby Marangell, Carslaw room 720, email am4.maths@sydney.edu.au) 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)

- MATH3076/3976 Mathematical Computing
- MATH3078/3978 Partial Differential Equations and Waves
- MATH3969 Measure Theory & Fourier Analysis
- MATH3974 Fluid Dynamics
- 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 coordinator for Pure Mathematics Senior units is:

- Alexander Fish, Room 712, Carslaw Building, phone 9351 2968, email: pm3.maths@sydney.edu.au

The coordinator for Applied Mathematics Senior units is:

- Georg Gottwald, Room 625, Carslaw Building, phone 9351 5784, email: am3.maths@sydney.edu.au

The coordinator for Mathematical Statistics Senior units is:

- Qiying Wang, Room 825, Carslaw Building, phone 9351 5762, email: st3.maths@sydney.edu.au

## Summary of Enrolment Advice

- Taking four of the Pure or Applied Mathematics Senior units (either mainstream or advanced level) constitutes a major in Mathematics. The usual enrolment is two units per semester. Taking eight of these units constitutes a double major in Mathematics.
- Taking four Statistics Senior units (either mainstream or advanced level) constitutes a major in Mathematical Statistics.
- To obtain a major in Financial Mathematics and Statistics, you must take STAT3011/3911, STAT3012/3912, MATH3075/3975, and a fourth unit chosen from the following: MATH3076/3976, MATH3078/3978, MATH3969, MATH3974, STAT3013/3913, STAT3014/3914, INFO3404/3504.
- If you are intending to do honours in Applied Mathematics, you must take at least 4 units (24 credit points) of Senior level Mathematics. At least 3 of these should come from the list of Applied Mathematics units, and at least two of these should be at advanced level. MATH3963 and MATH3978 are strongly recommended for all students, along with some of the following according to your interests: MATH3974, MATH3975, MATH3976, MATH3977.
- If you are intending to do honours in Pure Mathematics, you must take at least 4 units (24 credit points) of Senior level Mathematics. At least 3 of these should come from the list of Pure Mathematics units, and at least two of these should be at Advanced level. You are strongly advised to take the core units MATH3961 and MATH3962, along with some of the following according to your interests: MATH3963, MATH3968, MATH3969.
- If you are intending to do honours in Statistics, you must complete 4 units (24 credit points) of Senior level Mathematical Statistics. You should therefore take all 4 advanced-level Senior Statistics units: STAT3911, STAT3912, STAT3913, and STAT3914. Among the Mathematics units, MATH3961 and MATH3969 would also be useful.
- Engineering students would benefit from taking any of the following units: MATH3063/3963, MATH3974, MATH3076/3976, MATH3078/3978.
- If your major interest is in Computer Science, you would be well advised to consider MATH3065 and/or MATH3076/3976.
- Students whose interest lies in Physics or other sciences would benefit especially from MATH3974, MATH3977, and MATH3078/3978, and should also consider the following units: MATH3063/3963, MATH3968, MATH3076/3976, STAT3011/3911, STAT3012/3912.
- Prospective teachers of mathematics should take as many senior Mathematics units as they can. The following would be particularly useful: MATH3061/3961, MATH3065, MATH3068, MATH3063/3963, MATH3076/3976, 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 entry qualification for Applied
Mathematics 4 is normally a Credit average or better taken over
**24 credit points of Senior Mathematics units**, and is
subject to the approval of the Head of School. You must also have
satisfied Faculty requirements. Students who do not meet these
criteria but are particularily interested and motivated to do Honours
should consult the Applied Maths 4 coordinator,
Robby Marangell
(Carslaw room 720,
email am4.maths@sydney.edu.au
or phone 9351 5795).

Further details are given in the Applied Mathematics 4 handbook.

## 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 entry qualification for Pure Mathematics 4 is either a Credit average or better taken over
**24 credit points of Senior Mathematics units**,
(including a credit on at least one
Senior Pure Mathematics **Advanced unit**), or a Distinction
average or better taken over
**24 credit points of Senior Mathematics units**. Entry is also
subject to the approval of the Head of School. In addition, all
Faculty requirements must have been satisfied. Students who do not meet these
criteria but are particularily interested and motivated to do Honours
should see the Pure Mathematics 4 coordinator,
Laurentiu Paunescu
(Carslaw room 721,
email pm4.maths@sydney.edu.au
or phone 9351 2969).

As mentioned above, it is highly recommended to take the Advanced level third year units MATH3961 Metric Spaces and MATH3962 Rings, Fields and Galois Theory in preparation for Pure Mathematics 4. Note that third year Advanced units that have not been taken for credit in third year are generally available in 4th year. Further details are given in the Pure Mathematics 4 handbook.

## 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,
Uri Keich
(Carslaw room 821,
email st4.maths@sydney.edu.au
or phone 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.