Unit of study_

# MATH5330: Topics in Geometry

Geometry, as one of the most ancient branches of pure mathematics, arose from the necessity and desire to describe and thoroughly understand the surrounding world and the universe. The development of geometry substantially contributes to the evolution of mathematics as a whole subject through the concepts and notions of axiom and manifold, which lays the foundation of modern mathematics. Despite the abstract appearance of modern geometry, the objects and problems of modern geometry can usually be traced back to practical situations. A good example is the recent breakthrough in image identification technology, which is rooted in differential geometry. From both a research and an educational perspective, geometry provides perfect opportunities for the implementation and interaction of ideas and techniques from other branches of mathematics like algebra, analysis, topology and probability, and other subjects like chemistry, finance and physics through topics including financial derivatives, Einstein Equations and black holes, which have attracted enormous public attention in recent years. You will learn to approach questions initially through intuition and then make this rigorous using mathematical tools. Through the selection of topics in this unit, you will train your mathematical imagination to discover the geometric framework of a complex problem.

Code MATH5330 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? None None None Familiarity with metric spaces (e.g., MATH4061 or equivalent) and differential geometry (e.g., MATH4068 or equivalent). Please consult with the coordinator for further information

At the completion of this unit, you should be able to:

• LO1. Demonstrate a coherent and advanced understanding of key concepts in geometry.
• LO2. Apply fundamental principles and results in geometry to solve given problems.
• LO3. Distinguish and compare the properties of different types of spaces and maps between them.
• LO4. Formulate geometric problems in terms of invariants and determine the appropriate framework to solve them.
• LO5. Devise geometric solutions to complex problems.
• LO6. Compose correct proofs of unfamiliar general results in geometry.
• LO7. Communicate coherent mathematical arguments appropriately to student and expert audiences, both orally and through written work.

## Unit outlines

Unit outlines will be available 1 week before the first day of teaching for the relevant session.