COURSE SYLLABUS

Course Number: MATH7760
Course Title: AN INTRODUCTION TO ALGEBRAIC TOPOLOGY I
Credit Hours: 3
Prerequisites: MATH 7510 or departmental approval.
Corequisite: 

Objectives: 
To provide students with the elementary theory and common applications of singular homology theory.  To prepare students for further study in the areas of both geometric and algebraic topology.

Course Content:
The major goal of  MATH 7760 is to establish a homology theory for a reasonable class of spaces and equip students with the knowledge and techniques which will enable them to use the material in standard applications, such as degree theory for maps of spheres, separation and invariance properties in Euclidean spaces, and fixed point theorems.  One possible development of the material is the following:

    Homology of chain complexes (2 weeks).
    Chain complexes arising from spaces and simplicial and/or CW complexes. (2 weeks).
    The axioms of homology and their verification (3 weeks)
    Computations of homology groups. (3 weeks).
    Applications. (4 weeks). 


Possible textbooks and/or references: 
Algebraic Topology, Edwin H. Spanier, 1966, Springer-Verlag New York, Inc.
Lectures on Algebraic Topology, 2nd ed. Albrecht Dold, 1980, Springer-Verlag New York, Inc.
Elements of Algebraic Topology, James R. Munkres, 1984, Addison-Wesley Publishing Co., Inc.
Topology and Geometry, Glen E. Bredon, 1993, Springer-Verlag New York, Inc.

Sample Grading and Evaluation Procedures

A graduate student is expected to creatively engage the mathematical material of the course.  The student will be given problems to solve; these problems may include the derivation of proofs to theorems.  These solutions may be presented in class on the blackboard or be written up to be handed in to the instructor. Extended projects may also be assigned.  

Grade Calculation
Presentation of solutions to problems/theorems, homework:				40%
Midterm exam or midterm project:							25%
Final Exam or culminating project:							35%

There may be variations in these procedures depending on the individual instructors and the nature of the specific material.
Sample Statement Re: Accommodations
	Students who need accommodations are asked to arrange a meeting during office hours the first week of classes, or as soon as possible if accommodations are needed immediately.  If you have a conflict with my office hours, an alternate time can, be arranged.  To set up this meeting, please contact me by E-mail.  Bring a Copy of your Accommodation Memo and an Instructor Verification Form to the meeting.  If you do not have an Accommodation Memo but need accommodations, make an appointment with The Program for Students with Disabilities, 1244 Haley Center, 844-2096 (V/TT).  (Note: Instructor office room, office hours and email address will be made available on the course syllabus and on the first day of class.)

JUSTIFICATION FOR GRADUATE CREDIT

	This course is part of a modified semester version of a 600-level sequence under the quarter system.  Under the quarter system it was specifically designed as a graduate course.  It was approved as part of our graduate program and has been a traditional part of our graduate program offerings.  Outside of modernization, the standard of the course remains at the same graduate level that the department has maintained in the past. The course demands considerable mathematics background and a degree of mathematical maturity traditionally found at the graduate level.  The 7000-level course will inculcate the same analytical skills and depth of understanding previously demanded by the comparable 600-level quarter course.  In order to successfully complete the course the student will have to demonstrate an ability to creatively examine and apply the mathematics presented in the course.