Topology

Description

Introduces students to abstract analytic structures and their applications. Familiar concepts from real analysis such as open and closed intervals, limits, and continuity are extended to the more general settings of metric and topological spaces; this greatly expands the scope of their applicability. The material lies at the heart of many developments in modern mathematics and provides a perfect example of the breadth and unity of mathematics.

Availability

Callaghan Campus

  • Semester 1 - 2015

Learning Outcomes

1. An awareness of the breadth of mathematics as well as an in-depth knowledge of one specific area.

2. An ability to communicate a convincing and reasoned argument of a mathematical nature in both written and oral form.

3. An understanding of what constitutes a rigorous mathematical argument and how to use reasoning effectively to solve problems.

Content

  1. Metric spaces
  2. Continuity
  3. Completeness
  4. Compactness
  5. Connectedness
  6. Topological spaces

Assumed Knowledge

MATH2320 and MATH2330

Assessment Items

Written Assignment: Assignment questions

Project: Project

Formal Examination: Exam

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term