Most careers need some sort of mathematical skill, especially those in Science and Engineering but even extending into Medicine and Law. Have you ever sat in a high school maths class and thought "What's the point?" Well at UNSW we aim to make maths more relevant and interesting and will supply you with the analytical skills necessary in the workforce.

Compared to maths at school, university mathematics is more directed towards definite problems, both real-world and abstract ones. It also uses computers with the latest mathematical software, to extend the range of solvable problems well beyond what is possible with pencil and paper and calculators (such as plotting functions like the one on the right).

We offer the usual core first-year classes of Algebra and Calculus. But you also have the option of taking Discrete Mathematics, or a Statistics for Life and Social Sciences course which has proved popular as a single-course option (see below for more on these courses).

The core (6 hours per week of lessons, in each semester) can be studied at three levels:

- Ordinary level MATH1131 in semester 1 and MATH1231 in semester 2 or Summer.
- For students with good HSC results and looking for a challenge, Higher level maths MATH1141 in Semester 1, MATH1241 in Semester 2.
- MATH1011 is a Level I Mathematics course intended for students who are in specific programs (such as Industrial Design), or who do not have sufficient Assumed Knowledge for direct entry into MATH1131, Mathematics 1A.

There is a specialised pair of core courses for student not wishing to major in Maths but their degree requires maths:

- Maths for Life Sciences MATH1031 and Statistics for Life and Social Sciences MATH1041.
- For students enrolled in actuarial studies or finance: MATH1151 and MATH1251.

Each of these courses runs for one semester (half-year). They consist of four hours a week of lectures in large classes, which present the basic material. There are also two hours a week of tutorials in small classes, where problems illustrating the theory are done, and students ask the tutor questions. First-year teaching is done by both leading mathematicians and specialist first-year teachers.

The content of the core courses is about half calculus and half algebra. The calculus is similar to school work, but extends it to both more realistic applications and more depth of understanding. Algebra is more different from school work, dealing with large systems of simultaneous equations and the vectors that form the language used in the mathematical treatment of all modern disciplines from engineering to economics.

For those who want or need to study mathematics beyond the core, Discrete Mathematics is very worthwhile. UNSW has been a leader in providing this contemporary branch of mathematics at first-year level. Discrete mathematics is the mathematics especially relevant to computer science - algorithms, proofs, combinatorics, graph theory, for example. It is thus compulsory for Computer Science and Engineering students, and for Mathematics Majors (students who will specialise in mathematics). For others, it is an attractive and relevant option. Part of the course uses the textbook “Proof in Mathematics: An Introduction”, specially written at UNSW.

Students outside mathematics who are looking for a single widely useful mathematics course should consider Statistics for Life and Social Sciences. Statistics is about describing data, producing data and drawing appropriate conclusions from data. An understanding of statistics is vital for all the sciences. This course does not require a high level of mathematics; rather the emphasis is on the quite sophisticated concepts involved in drawing samples from populations, testing hypotheses, and in making estimations. The course uses Excel, the package standard in business applications.

Please see Advice on Choosing First Year Mathematics Courses for more information on course selection.

Special needs are catered for in many ways. There is a talented students program that involves accelerated progress and extra contact with leading mathematicians. For students who lack the assumed knowledge for courses, there is a bridging course in late January through February to bring students from an HSC "Mathematics" level up to HSC "Mathematics Extension 1" level. For those who have difficulties keeping up with work during the year, there are extra voluntary tutorials and the Maths Student Support Scheme, a scheme where first-year students consult higher-year students at a drop-in centre. MATH1231 is available in Summer Semester so that students who start in mid-year or who fail a course can complete their degrees in minimum time.

With first year over, it's time to look at second year and beyond, where specialised courses lead to the coalface of real research mathematics.