There are many ways you can study Mathematics with Computer Science, Computer Engineering or Software Engineering at UNSW.
In the first year, the science programs have almost identical studies. You will study the core mathematical and computer science topics that any student at UNSW needs if their degree involves mathematics or computing. You may choose your elective courses from several other Schools so that you can follow or cultivate other interests. In later years you have the opportunity to focus your mathematical and computing skills in an area of your choice. The engineering programs include many of the same courses but also others with a more engineering slant.
To find out the formal requirements (in terms of courses that you must study), see the corresponding pages in the Programs and Courses, and see 3789 - Science/Computer Science and 3778 - Computer Science in the UNSW Handbook.
Mathematics can be studied at the Ordinary level or at the Higher level depending on your interests and abilities, but study at the Higher level is recommended (and is compulsory if enrolled in the Advanced Maths or Science programs) and may be necessary for certain courses in later years.
In the final year of the Advanced Maths or Science program, or if you do the extra fourth (Honours) year of the Science Program or the combined degree in Computer Science, you will do some course work but will also spend time writing a thesis. The aim of the thesis is for you to become involved in an active area of research of your choice. You could even discover something new, which is not as uncommon as you might think!
If your interest is mainly in Computer Science and you wish to include substantial Mathematics, then take the three-year Computer Science degree with a second major in Mathematics.
If your interest is in Mathematics and you wish to add some Computer Science skills, then take the three-year Science degree with a major in Mathematics and add electives in Computer Science.
If you want to study Mathematics together with Computer Science or Computer Engineering or Software Engineering in full, then take the appropriate Combined Degree. This option would also be advisable if you are not sure which you prefer, as it may be possible to transfer out of a combined degree into either of the single degrees.
It is possible to transfer between degree programs without reapplying for admission, see the Internal Program Transfer page on the University web site.