MA323 - Topology, Fall 2019

• Final exam on Friday, Jan. 3: Secs. 51-55, 58-60, 67-78, 43-46; Secs. 12-22, 23-29, 30-36, 1-7, 9 & 10.

• Here are solutions to the midterm exam.

• Assignment 12 (required, not collected): Sec. 72 #3; Sec. 73 #2 (enlightening but optional); Sec. 74 #1, 3, 4, 5; Sec. 75 #1; Sec. 78 #2, 3.

• Assignment 11 due Friday, Dec. 20: Sec. 59 #1, 2; Sec. 60 #1, 5; Sec. 67 #2, 4; Sec. 68 #2; Sec. 69 #1; Sec. 71 #2, 3.

• Assignment 10 due Tuesday, Dec. 10: Sec. 53 #3; Sec. 54 #7, 8; Sec. 55 #1, 2; Sec. 58 #5, 9. (We skipped the starred Secs. 56 & 57 and are half-way through Sec. 58. We will wrap up the rest of Ch. 9 after some algebraic preliminaries from Secs. 67-69 for the Seifert-van Kampen theorem to be covered on Friday, Dec. 6. We won't cover Ch. 10.)

• Assignment 9 due Friday, Nov. 29: Sec. 51 #2, 3; Sec. 52 #2, 3, 4, 6, 7.

• Assignment 8 due Friday, Nov. 22: Sec. 43 #8; Sec. 46 #1, 2, 3, 7, 8; read Sec. 47 (optional).

• Assignment 7 due Tuesday, Nov. 12 (The three starred questions are optional and for bonus points): Sec. 35 #2*; Sec. 34 #7; Sec. 36 #4, 5; Sec. 43 #5, 7, 9*, 10*; Sec. 44 #2; Sec. 45 #3.

• Midterm exam on Friday, Nov. 8: Secs. 12-22, 23-29, 30-36, 1-7, 9 & 10.

• Assignment 6 due Friday, Nov. 1: Sec. 32 #1, 6; Sec. 33 #3, 8; Sec. 35 #1, 4, 7.

• Assignment 5 due Friday, Oct. 25: Sec. 26 #1, 8; Sec. 27 #5, 6; Sec. 28 #7; read Secs. 30 & 31; Sec. 30 #1, 4; Sec. 31 #5; read Sec. 37 (optional).

• Assignment 4 due Friday, Oct. 18: Sec. 21 #3; Sec. 22 #2; Sec. 23 #5; Sec. 24 #1, 3, 9; Sec. 25 #7, 9.

• Assignment 3 due Friday, Oct. 11: Sec. 13 #8; Sec. 16 #9; Sec. 17 #6, 19; Sec. 18 #10; read Sec. 20; Sec. 20 #3, 8.

• Assignment 2 due Friday, Sept. 27: Sec. 5 #3; Sec. 7 #4, 6; read Sec. 10; Sec. 10 #7.

• Assignment 1 due Friday, Sept. 20: Sec. 1 #4; Sec. 2 #2, 4; Sec. 3 #2, 3, 13; read Secs. 5 & 6.

• Some motivations:

-- Study of spaces and their shapes: 1, 2, 3, 4;

-- Algebraic geometry: Mumford's treasure map depicting Spec(ℤ[X]), where ℤ[X] is the ring of polynomials in the variable X with integer coefficients;

-- Homotopy theory, differential topology, and number theory: Exotic spheres and topological modular forms;

-- Applied math: Topological data analysis;

-- Physics: Topology in magnetic systems (slides courtesy of Prof. Zi Qiang Qiu).

Instructor

Yifei Zhu

Huiyuan 3-419

8801 5911

zhuyf@sustech.edu.cn

Office Hours: Monday & Thursday 10:00-11:30 am

Grader: 廖文博

Class QQ group: 891307773

Objectives

This course introduces basic notions and examples in point-set and algebraic topology, with a view towards more advanced analysis, (algebraic and differential) geometry, and topology courses. We will cover most of Chapters 1-4, 7, 9, and 11-13 in the Munkres text.

Prerequisites

Abstract Algebra (MA214) or consent of the department.

Textbooks

We will be working from James R. Munkres's Topology, Second Edition.

Useful references include《基础拓扑学讲义》尤承业编著 and《点集拓扑与代数拓扑引论》包志强编著 as well as M.A. Armstrong's Basic Topology.

Exams

There will be one in-class midterm exam, on November 8, and one final exam. Each of these exams is worth 30% of your final grade.

Homework

The assigned problems for each week are due each Friday in-class at 2 pm, listed on this page. Homework is worth 40% of your final grade. Students must make arrangements in advance if they will not be handing in homework on time.

We encourage you to discuss homework problems with your classmates, including strategies for solving different kinds of problems. However, when you actually write up your solutions, you must do this on your own.