Math464

Course Description form

Faculties and departments requiring this course (if any): Faculty of

    science/Department of Mathematics.

Objectives:  Prefer In points

1-    How to read a mathematical statement and understand it.

2-    How to write a mathematical statement in a correct, clear and short way.

3-    Learn some basics of point set Topology.

Contents: Prefer In points

1. Definition of a topology and a topological space. Some basic examples. Open and closed sets.
2. Closure, interior, boundary, and dense sets.
3. Bases and generating topologies.
4. Subspaces and product spaces
5. Continuous functions and homeomorphisms.
6. Separation Axioms.
7. Metric spaces.
8. Connected and compact spaces.

Course Outcomes:

A-   Knowledge:

    (Specific facts and knowledge of concepts, theories, formula etc.)

    Study the basics of point set topology.

B-Cognitive Skills:

   (Thinking, problem solving )

   Study the application of topology concepts in other branches of Mathematics.

C- Interpersonal skills and responsibilities:

    (group participation, leadership, personal responsibility ,  ethic and moral behavior, capacity for  self directed learning)

     Know how to read a mathematics paragraph and understand it, know how to write a mathematical paragraph in a correct clear and short way.

D- Analysis and communication:

         (communication, mathematical and IT skills)

     Know how to think and discover conclusions.

     Assessment methods for the above elements

Text book: Only one

Paul Long, An Introduction to General topology, Charles E. Merrill Publishing Company, 1971.

Supplementary references

C. Wayne Patty, Foundations of Topology, PWS-KENT Publishing Company, 1993.