Algebraic Topology
MAT215A Fall 2005
Course Information




+Instructor Info

Carlos Barrera-Rodríguez
Office: 481 Kerr Hall
email: carlosbr@math.ucdavis.edu


+Announcements

Welcome. Examination Tomorrow. Posted September 27th 2005, 5:00 am.


+Course Info

Class Time: MTWF 7:00-7:50 AM, Wellman 226. Lectures will take place MTF and the discussion session on Tuesdays.

Office hours: Mondays,Wednesdays from 2-3pm or Fridays 1:00-2:00pm, or by appointment. The TA for the course is Ms. Jane Smith. Her office hours will be Wednesdays from 2:00-3:00pm (473 Kerr). The best way to contact me is via email. Please feel free to ask questions.

Textbooks:
Basic:
Algebraic Topology by Allen Hatcher. An electronic version can be found here
The Knot Book: An Elementary Introduction to the mathematical Theory of Knots by Collin Adams.
Alternative:
Algebraic Topology by Massey.
Topology by Munkres.

Description: The motivation of this course is to encourage people, via the study of Topology and Knot Theory, enriching his mathematical background and learning about the shape of this universe. First, we will begin studying the Fundamental Group of spaces and then we will explore Composition of Knots, Reidemeister Moves, Invariants of Knots(tricoloreability, Unknoting Number, Bridge,Number, Crossing Number), Types of Knots, and Knots Polynomials.The goal of this course is to provide the basic theory to those students who are new in the Topology World and motivate them to continue to explore other related areas of mathematics and to proceed to such topics as Algebra, Differential Geometry and Algebraic Geometry. Here is an overview of the topics we will study:

(5 weeks): Chapters 1-4 of the book Algebraic Topology by Allen Hatcher.

(5 weeks): Chapters 1-8 of the book The Knot Book by Collin Adams



+Prerequisites

Abstract Algebra and Point-Set Topology Notions.


+Grading

The course grade will be based on 4 homeworks (40 points), one midterm exam (30 pts) and the final exam (30 points). The final exam will be comprehensive. I will assign grades based on an statistical curve of points obtained by all students. Please notice that NO LATE HOMEWORKS will be accepted.



+Homeworks

Problem Sets:
HW1: Sect 1.1: 2, 4, 8, 11, 17, 34 ; Sect 1.2: 5, 7, 12, 18 ; Sect 1.3: 1, 2, 3, 15. from Hatcher's book.

Solutions:
No solutions have been posted.


+Sample Examination

Here you have a sample of a examination in this course.