Math 8306 - Algebraic Topology - Fall 2015

Instructor: Anar Akhmedov

Lectures: MWF 11.15am - 12.05pm in Vincent Hall 213.

E-mail: akhmedov@math.umn.edu

Office Hours: Monday 12.40 - 2.20pm. My office is in room 355 of the Vincent Hall.

Prerequisites: Math 8301 or instructor's consent.

Textbook: Algebraic Topology, by Allen Hatcher. The textbook is available at the University bookstore, and also on reserve in the Mathematics Library. Our textbook is also available free online, at http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Other Recommended Textbooks
Title Author(s), Publ. info Location
Topology and Geometry G. Bredon On reserve in math library
Topology from a differential point of view J. Milnor On reserve in math library
Differential forms in Algebraic Topology R. Bott and L. P. Tu On reserve in math library
Algebraic Topology W. Fulton On reserve in math library

Course Outline: This is a first course in algebraic topology. The fall semester we plan to cover Chapters 0 - 3 of the textbook. The main topics are: homotopy, fundamental group, covering spaces, homology, and cohomology.

Web page: http://www.math.umn.edu/~akhmedov/MATH8306.html.

Grading: The course grade will be based on seven homework assignments, in class midterm, and a comprehensive take-home final, with the following weights:

  • 42% Homework
  • 25% Midterm (in class)
  • 33% Take Home Final

    Exams: There will be a comprehensive take-home final examination (which will worth 33% of the final course grade) and in class midterm on October 26 (which will worth 25% of the final course grade). TAKE HOME FINAL
    DUE: by noon Monday, December 21

    Homework: There will be 7 homeworks in this course, each worth 6 points. Homework will be a fundamental part of this course, and will be worth 42 points (42% of the course grade). NO LATE HOMEWORK WILL BE ACCEPTED. The first homework assignment will be due on September 23. Please staple your homework before handing it in. If you have questions about the homework, it is best to ask during my office hours.

    Assignment Problems from the Text
    Homework 1
    due Sept 23     		Chapter 0
    Problems 2, 10, 11, 14, 16, 18, 19, 20, 21, 24.
    Homework 2
    due Oct 7     		Chapter 1
    Section 1.1: Problems 3, 5, 8, 10, 12, 14, 15, 17, 18, 20
    Homework 3
    due October 21     		Chapter 1
    Section 1.2: Problems 2, 3, 4, 6, 9, 14, 16
    Section 1.3: Problems 2, 3, 4, 9, 14, 20, 23
    In class Midterm on Monday, October 26. The Midterm will cover Chapter 0, Chapter 1 Sections 1.1, 1.2, 1.3.
    Homework 4
    due November 11     		Chapter 2
    Section 2.1: Problems 4, 5, 7, 8, 9, 11, 12, 13, 14, 17, 22, 29, 30
    Homework 5
    due November 25     		Chapter 2
    Section 2.2: Problems 2, 4, 10, 11, 15, 21, 22, 23, 24, 36, 38
    Homework 6
    due December 7     		Chapter 3
    Section 3.1: Problems 1, 3, 6, 7, 9, 11
    Homework 7
    due December 14     		Chapters 3
    Section 3.2: Problems 1, 3, 4, 5, 8, 11, 12, 16, 18