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Mathematics 441

MATH 441
TOPOLOGY

Catalog Entry

MATH 441. Topology
Three hours lecture (3).

Prerequisites: MATH 252

An introduction to point-set topology, with emphasis on the study of functions and the real line.

 

Detailed Description of Content of Course

The following topics will be covered:

a) An introduction to basic set theory including Cartesian Products and DeMorgan's Laws
b) An introduction to functions and countability
c) A study of topological spaces with an emphasis on the real line and the plane
d) A consideration of bases, subbases and the product topology
e) A consideration of continuous functions
f) An introduction to separation axioms, connectedness, compactness, metric spaces, and convergence

 

Detailed Description of Conduct of Course

Most instructors will present the course material in lecture format. Students may be required to prepare and present problems for class discussion. Students are expected to develop an understanding of the material by working exercises.

 

Goals and Objectives of the Course

1. To develop a knowledge base and problem solving skills which will serve the student well in future mathematics courses, particularly graduate school analysis courses.
2. The student is expected to develop a deep understanding of the concept of continuous function.
3. The student is expected to improve skills of presentation including proof writing and possibly oral presentations.

 

Assessment Measures

Graded tasks may include tests, quizzes, homework exercises, and class participation.

 

Other Course Information

None.

 

Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair