# 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?

*
Please note that this section has been rewritten in accordance with the new
B.Sc. regulations, introduced in 2017. It does not apply for those students
enrolled under the old regulations. The previous version of this section
can be found in last
year's handbook.
*

To satisfy the B.Sc degree regulations, each Science student must complete a major (48 credit points) or program from Table A of the regulations, and also a minor (36 credit points) or a second major. The School of Mathematics and Statistics offers majors and minors in four subject areas:

- Mathematics
- Statistics
- Financial Mathematics and Statistics
- Data Science (shared with the School of Computer Science in the Faculty of Engineering).

Students eligible to enrol in the Dalyell stream may choose the Mathematical Sciences program, incorporating one of the above four majors.

In each case the requirements for the major include four senior level units (24 credit points) in the chosen subject area, one of which must be the designated project unit for the major (or the Science Interdisciplinary Project Unit SCPU3001). A minor requires two senior level units (12 credit points) in the subject area. Typically each year a student will enrol in units totalling 48 credit, to make up the required total of 144 credit points for the course. So it is typical for students to take eight senior level units in their third year. Thus students taking a minor offered by another school may also enrol in one or two senior level units offered by the School of Mathematics and Statistics, provided they have the intermediate level prerequisities.

Students need to be sure that the units of study they choose to enrol in will satisfy the degree regulations. If required, our Senior Year Coordinators can advise on unit of study selection.

## 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:

- Leo Tzou, Room 613, Carslaw Building, phone 9351 3114, 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:

- John Ormerod, Room 815, Carslaw Building, phone 9351 5883, email: st3.maths@sydney.edu.au

## Summary of Enrolment Advice

- Students who wish to take two of the four majors offered by the School will typically enrol in four senior level units in each semester, two from each of the two chosen subject areas. Either mainstream or advanced units may be chosen. The chosen units must include the project units for both majors.
- Students who wish to take a major offered by the School and also a minor offered by the School will need to take a total of six senior level units in their subject areas, one of which will be the project unit for the major. To make up the standard 48 credit points for the year, two additional units should be chosen; these may be units offered by the School of Mathematics and Statistics, or units offered by another school.
- Students taking a major offered by the School of Mathematics and Statistics and a minor offered by another school will take four units offered by the School (typically two in each semester) including the project unit. They may have scope to enrol in one or two further units offered by the School, to make up the standard 48 credit points for the year.
- Students taking a minor in the School of Mathematics and Statistics and a major offered by another school must take at least two and up to four senior level units offered by the School.
- Students taking a major offered by another school and a minor offered by another school may have scope to take one or two senior level units offered by the School of Mathematics and Statistics, if desired.
- Students intending to do honours in Applied Mathematics should take at least four units (24 credit points) of Senior level Mathematics. At least three of these should come from the list of Applied Mathematics units, and at least two of the three should be Advanced level units. MATH3963 and MATH3978 are strongly recommended for all students.
- Students intending to do honours in Pure Mathematics should take at least four units (24 credit points) of Senior level Mathematics. At least three of these should come from the list of Pure Mathematics units, and at least two of the three should be Advanced level units. MATH3961 and MATH3962 are strongly recommended for all students.
- Students intending to do honours in Statistics should take four units (24 credit points) of Senior Advanced Statistics.

## 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 particularly 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 particularly interested and motivated to do Honours
should see the Pure Mathematics 4 coordinator,
Laurentiu Paunescu
(Carslaw room 715,
email pm4.maths@sydney.edu.au
or phone 9351 2966).

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.