COURSE SYLLABUS

Course Number: MATH6500
Course Title: INTRODUCTION TO TOPOLOGY (3). Pr., 
Credit Hours: 3
Prerequisites: MATH3100 or analogous course subject to departmental approval.
Corequisite: 

Objectives: 
To develop basic notions of metric and topological spaces  needed for other areas of mathematics such as analysis, complex analysis, and geometry. To provide background for further study in topology and dynamical systems. 

Course Content:
    Metric spaces.  (3 days)  
    Topological spaces. (3 days)  
    Neighborhoods, closure, interior and boundary. (3 days)
    Continuity, functions and homeomorphisms. (3 days)
    Theory of sets, categories and functors. (3 days)
    Opens covers. (3 days)
    Compactness. (3 days)
    Connectedness. (3 days)
    Components and local connectedness. (3 days)
    Path-connectedness and path-components. (3 days)
    Homotopic paths and loops; simple-connectedness. (3 days)
    Product spaces. (3 days)
    Inverse limit spaces (optional).
    Quotient spaces; constructions by identification. (3 days)

Possible textbook:
Introduction to Topology by Bert Mendelson.

Grading and Evaluation procedures: 
At the discretion of the instructor: tests, written papers, student presentations, and the final exam.

Statement related to policies on unannounced quizzes and class attendance and participation:
Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester.