Metric Spaces (Advanced) (MATH3961)

UNIT OF STUDY

Topology, developed at the end of the 19th Century to investigate the subtle interaction of analysis and geometry, is now one of the basic disciplines of mathematics. A working knowledge of the language and concepts of topology is essential in fields as diverse as algebraic number theory and non-linear analysis. This unit develops the basic ideas of topology using the example of metric spaces to illustrate and motivate the general theory. Topics covered include: Metric spaces, convergence, completeness and the contraction mapping theorem; Metric topology, open and closed subsets; Topological spaces, subspaces, product spaces; Continuous mappings and homeomorphisms; Compact spaces; Connected spaces; Hausdorff spaces and normal spaces, Applications include the implicit function theorem, chaotic dynamical systems and an introduction to Hilbert spaces and abstract Fourier series.

Our courses that offer this unit of study

Further unit of study information

Classes

Three 1 hour lectures and one 1 hour tutorial per week.

Assessment

2 hour exam, assignments, quizzes (100%)

Faculty/department permission required?

No

Unit of study rules

Prerequisites and assumed knowledge

12 credit points of Intermediate Mathematics units with average grade of at least credit

MATH2961 or MATH2962

Prohibitions

MATH3901, MATH3001

Study this unit outside a degree

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 underake cross-institutional study in one or more units of study at the University of Sydney.