The University of Newcastle, Australia
Available in 2019

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.


Availability2019 Course Timetables

Callaghan

  • 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

MATH3180TopologyIntroduces 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.FSCITFaculty of Science724School of Mathematical and Physical Sciences1030005940Semester 1 - 2019CALLAGHANCallaghan2019MATH2320 and MATH2330 Metric spaces Continuity Completeness Compactness Connectedness Topological spaces YOn successful completion of this course, students will be able to:1Demonstrate knowledge of the theory of topological spaces and its role within modern mathematics2Communicate a convincing and reasoned argument of a mathematical nature in both written and oral form3Solve problems in topological spaces using rigorous mathematical reasoning. Written Assignment: Assignment questionsProject: ProjectFormal Examination: Exam CallaghanLectureFace to Face On Campus3hour(s)per Week for0Full Term0


Assessment items

Written Assignment: Assignment questions

Project: Project

Formal Examination: Exam


Contact hours

Callaghan

Lecture

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