MATH5785 Geometry

MATH5785 is a Honours and Postgraduate Coursework Mathematics course. Its main prerequisite is some mathematical maturity. See the course overview below.

Units of credit: 6

Prerequisites: Core higher second year course or permission of the lecturer.

Cycle of offering: Course not offered every year. 

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

More information: This recent course outline (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 MATH5785, you can log into UNSW Moodle for this course.

Course Overview

We will look at the development of geometry through the ages, starting with the ancient Greek approach to Euclidean geometry (Pythagoras’ theorem and all that), passing through projective geometry (do parallel lines meet at infinity?) to spherical geometry (navigation problems) and hyperbolic geometry (how troubles with the parallel postulate led to the invention of curved space). At the end we will find out why Einstein changed his views on the value of mathematics, and touch on algebraic geometry, the area of geometry where Fields Medals are won.

The approach is geometric, algebraic, combinatorial and computational. Students will be expected to work on problems.

The course will cover the following topics: 

  • Euclidean geometry
  • Projective geometry and fields
  • Spherical and hyperbolic geometries
  • Riemannian geometry
  • Algebraic geometry.