Math 471-10              Topology                 Spring 2006
Instructor	Office	Phone	Hours
Jimmie Lee Johnson	Auditorium Campus Chicago, Illinois Room 407	(312) 341-3552 Voice Mail	M 5:00-6:00pm and by appointment.
M 6:00-8:30pm Classroom Aud 401			.
	E-mail:  jjohnson@roosevelt.edu Web Page:  http://faculty.roosevelt.edu/jjohnson/

Text: Beginning Topology, Sue E. Goodman, Brooks/Cole, 1st ed. 2005 ISBN 0-534-42426-0.

Prerequisite: Grades of B or better in Math 352 Analysis and Math 300 Linear Algebra or consent of the instructor.

Class will consist of oral reports, quizzes, examples, theorem proving and the answering of questions. Prior to each class, you must do the assigned reading or you will be lost; make notes of topics you feel need elaboration in class. For each class, be prepared to give a short explanation of a definition or proof of a theorem orally, at the chalkboard. You are responsible for all assigned reading even if it is not discussed in class.  Class will usually include
     1. a short quiz each week;
     2. now and then, a short oral presentation of current material by selected students;
     3. discussion of new material via examples and the proof of new theorems.

Quizzes will be given each week beginning January 30th, except for the weeks of the exams. The quizzes will be closed book, and will count for 10% of your grade. The two lowest quiz grades will be dropped. No make-ups; a missed quiz will count as one of the dropped grades.

Homework will be collected, discussed, graded and returned; please leave the assignment on the instructor's desk whether I ask for it or not. Homework, along with oral presentation scores, will count for 20% of your grade. Late homework may be downgraded, if it is later than a week, but it is still worth more than no credit at all.

Maple10 will be discussed, and its application to problems in finite set theory and topology will be used in the course. See the following link to http://www.maplesoft.com/applications/ for a number of applications, including several to topology: Maple 10 will be available in the PC labs, but not on the Macs. You may download the programs dealing with finite topology from the Maplesoft website. For more information, see the instructor. You may be able to buy a copy of Maple 10 at a reduced price, if you so desire.

Exams will be given on March 6th and April 10th. These will be closed book. Their average will count for 35% of your grade. No make-ups except for excused absences with advance notice. The grade on the subsequent exam will be used for both.

Final Examination will be given on Monday, May 8th, closed book and comprehensive. It will count for 35% of your grade.

Grades: Regulations covering grades (especially I and W) are on pages 264-265 of the 2004-2006 Undergraduate Catalog or on pages 203-205 of the 2005-2007 Graduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination (including most of the homework) but misses the final exam because of an excused absence with advanced notice. The last day to drop a class (with a grade of "W") is Friday, March 24, and the drop form must be submitted to the Registrar's Office. Anyone registered after that must be graded solely on academic performance.

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Objectives: In this survey course a variety of topological concepts are presented. The student is expected to learn to: a.) prove many of the basic theorems dealing with continuity in a more general topological space. b.) classify a variety of surfaces and to calculate the genus and the Euler characteristic. c.) prove some coloring theorems, such as on the sphere and various graphs. d.) prove several theorems dealing with vector fields. To this end, the completion of a variety of homework problems and the occasional oral presentation are expected of each student. For assessment purposes, copies of some graded homework assignments and exams of each student will be placed in a file in the school office. Further review of these materials for assessment purposes will not affect the student's standing.

Syllabus

Date	Sections	Topics -  changeable
January 23	1.1-1.2	Open and Closed Sets. Continuous Functions
January 30	1.3-1.4	Topological Properties. Dimension.
February 6	2.1-2.2	Surface. Connected Sum.
February 13	2.3-2.4	Plane Models. Orientability.
February 20	2.5-2.6	Nonorientable Surfaces. Classification.
February 27	3.1-3.2	Euler Characteristic. Triangulations.
March 6	Exam #1	Chapter 1, 2, Sections 3.1-3.2.
(March 13)	No Class!	Spring Break.
March 20	3.3-3.4	Genus. Regular Complexes.
March 27	3.5-4.1	b-Valent Complexes. Maps and Map Coloring.
April 3	4.2-4.3	Five Color Theorem. Graphs.
April 10	Exam #2	Chapter 3, Sections 4.1-4.3.
April 17	4.4-4.5	Graphs in Surfaces. Embedding and Coloring.
April 24	5.1,5.2,5.3	Vector Fields. Index. Limit Sets.
May 1	5.4-5.5	Critical Points. Vector Fields on Surfaces.
May 8	Final	Comprehensive.

This page is at http://faculty.roosevelt.edu/jjohnson/Spring2006/M471S06.htm and was last revised March 27, 2006.