The University of Newcastle, Australia
Not currently offered
Course code

MATH3180

Units

10 units

Level

3000 level

Course handbook

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

Not currently offered.

This Course was last offered in Semester 1 - 2019.


Learning outcomes

On successful completion of the course students will be able to:

1. Demonstrate knowledge of the theory of topological spaces and its role within modern mathematics

2. Communicate a convincing and reasoned argument of a mathematical nature in both written and oral form

3. Solve problems in topological spaces using rigorous mathematical reasoning.


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