Skip to main content
Unit of study_

Topics in Topology - MATH5340

Year - 2020

Topology is the mathematical theory of the "shape of spaces". It gives a flexible framework in which the fabric of space is like rubber and thus enables the study of the general shape of a space. The spaces often arise indirectly: as the solution space of a set of equations; as the parameter space for a family of objects; as a point cloud from a data set; and so on. This leads to strong interactions between topology and a plethora of mathematical and scientific areas. The love of the study and use of topology is far reaching, including the use of topological techniques in the phases of matter and transition which received the 2016 Nobel Prize in Physics. This unit introduces you to a selection of topics in pure or applied topology. Topology receives strength from its areas of applications and imparts insights in return. A wide spectrum of methods is used, dividing topology into the areas of algebraic, computational, differential, geometric and set-theoretic topology. You will learn the methods, key results, and role in current mathematics of at least one of these areas, and gain an understanding of current research problems and open conjectures in the field.

Classes
4-5 contact hours/week comprising lectures, and tutorials or seminars

Assessment
tutorial participation (10%), written assignments (40%), final exam (50%)

Assumed knowledge
Familiarity with metric spaces (e.g., MATH4061 or equivalent) and algebraic topology (e.g., MATH4311 or equivalent). Please consult with the coordinator for further information.

Details

Faculty: Science

Semester 2

03 Aug 2020

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2020
Unit of study level: Postgraduate
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Oded Yacobi
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

To help you understand common terms that we use at the University, we offer an online glossary.