9_35 knot

Professor Alexandru I. Suciu

Knotted graph

MTH 3105 Topology I

Fall 2001

* Course Information

Course: MTH 3105 -- Topology I (key # 58356)
Web site: http://www.math.neu.edu/~suciu/mth3105/top1.f01.html
Instructor: Prof. Alex Suciu   < alexsuciu@neu.edu >
Time and Place: Tue. & Th., 7:15 - 8:45 PM, in 544 Nightingale
Office Hours: Tue. 6:15 - 7:15 PM, Th. 4:30 - 5:30, or by appointment -- in 441 Lake
Prerequisites: MTH 3010 (Basics of Analysis)
Textbook: Topology (2nd Edition) by James R. Munkres, Prentice Hall, 2000
Supplement: Algebraic Topology (Chapter 1) by Allen Hatcher, Cambridge University Press, 2001
Grade: Based on problem sets and a final exam

* Course Description

This course provides an introduction to Topology, requiring only some elementary background in Analysis. Time permitting, the following topics will be covered:

* Topological Spaces and Continuous Functions
* Compactness and Connectedness
* The Fundamental Group
* The Seifert-van Kampen Theorem
* Classification of Surfaces
* Classification of Covering Spaces
* Applications to Group Theory

*   The first (shorter) part of the course treats General Topology. The objects of study are metric and topological spaces. The main properties that are studied are connectedness and compactness. We also introduce several constructions of spaces, and study the invariance of various properties under topological equivalence.

*   The second part of the course treats the basics of Algebraic and Geometric Topology. It starts with the fundamental group of a space, methods to compute it, such as the Seifert-van Kampen theorem. It proceeds with the classification of surfaces, and a detailed study of covering spaces. Applications include the Brouwer fixed point theorem, the Borsuk-Ulam theorem, and the Nielsen-Schreier theorem.

For more information, including past exams and class projects, see this older syllabus. You may also want to look at some past qualifying exams in Topology, based in large part on the material covered in this course.

* Homework Assignments

Homework Section Page Problems
1. Section 2.16 Page 92 Problems 3, 4
Section 2.17 Page 101 Problems 11, 12, 13
Section 2.18 Pages 111--112 Problems 3, 10
Section 3.23 Page 152 Problems 2, 5, 9
2. Section 3.24 Page 158 Problems 2, 3, 9, 10
Section 3.25 Page 162 Problems 5, 6, 7
Section 3.26 Page 171 Problems 6, 7, 8
3. Section 2.22 Pages 144--145 Problems 2, 3
Section 9.51 Page 330 Problems 3
Section 9.52 Pages 334--335 Problems 2, 3, 4, 6
Section 9.53 Pages 341 Problems 3, 5, 6
4. Section 9.54 Page 348 Problems 5, 8
Section 9.55 Page 353 Problem 2
Section 9.57 Page 359 Problems 2, 3
Section 9.58 Page 367 Problem 9(e)
5. Section 9.58 Page 366 Problem 2
Section 11.69 Page 425 Problems 1, 3
Section 11.70 Page 433 Problems 1, 2
Section 12.74 Pages 453--454 Problems 1, 2, 6, 7
Section 12.76 Page 457 Problems 4
 
Department of Mathematics  Office:  441 Lake Hall  Messages:  (617) 373-2450 
Northeastern University Phone:  (617) 373-4456  Fax:  (617) 373-5658
Boston, MA, 02115  Email:  alexsuciu@neu.edu  Directions
Home   Started:  September 18, 2001   Last modified:  November 28, 2001.
URL:  http://www.math.neu.edu/~suciu/mth3105/top1.f01.html