MATH5705 is a Honours and Postgraduate Coursework Mathematics course. See the course overview below.

**Units of credit:** 6

**Exclusions: **MATH3570, MATH3611, MATH3610, MATH3620, MATH5645 (MATH3611 jointly taught)

**Cycle of offering:** Term 2

**Graduate attributes: **The course will enhance your research, inquiry and analytical thinking abilities.

**More information: **This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH5705, you can log into UNSW Moodle for this course.

#### Course Overview

Limits and continuity are the central concepts of calculus in one and several variables. These concepts can be extended to quite general situations. The simplest of these is when there is some way of measuring the distance between two objects. Some of the most important examples of these 'metric spaces' occur as sets of functions, so this course looks at ways in which one might say that a sequence of functions converges. Taking these ideas one step further, we look at convergence which does not come from a generalised distance function. These are the ideas of point set topology. The course will include topics such as countability, continuity, uniform convergence, compactness and connectedness. This is not a 'computational' course, but rather one in which you will develop your ability to think and write abstractly, precisely and creatively.