MA323 - Topology, Fall 2023

  • Here is the midterm exam.
  • Assignment 12, required but not collected.
  • Assignment 11 due Friday, Dec. 29: [Y] Sec. 4.1 #5, 6, 7, 8.
  • Assignment 10 due Friday, Dec. 22.
  • Supplementary readings
  • Assignment 9 due Friday, Dec. 15. (Mislabeled question corrected Dec. 12, thanks Weitong!)
  • Visualizing the Hopf map
  • Assignment 8 due Friday, Dec. 8: [Y] Sec. 2.5 #1, 5, 6; Sec. 2.6 #3, 4; Sec. 3.2 #8, 9, 10, 14. (Updated Dec. 4)
  • Assignment 7 due Friday, Dec. 1: [Y] Sec. 2.4 #4, 5, 8, 10.
  • Office hours on Tuesday, Nov. 21 are canceled due to instructor's travel plans.
  • The midterm exam on Friday, Nov. 17 covers [Y] Secs. 1.1–1.3 and 2.1–2.3.
  • Examples of compact spaces: higher-dimensional spheres
  • Assignment 6 due Friday, Nov. 10: [Y] Sec. 2.3 #1, 2, 4, 5, 6, 7, 9, 11, 16, 18, 19.
  • Assignment 5 due Tuesday, Oct. 31: [Y] Sec. 2.1 #5, 6, 12, 14, 18; Sec. 2.2 #3, 4. [M] Sec. 33 #3; Sec. 35 #7b.
  • Office hours on Tuesday, Oct. 24 are canceled due to instructor's travel plans.
  • Assignment 4 due Friday, Oct. 20: [Y] Sec. 1.3 #3, 4, 6, 8.
  • Assignment 3 due Friday, Oct. 13: [Y] Sec. 1.2 #2 (also show that the subspace topology is in fact the coarsest topology on B for which the inclusion i is continuous), 4, 5, 6, 9, 10, 12, 13.
  • Assignment 2 due Sunday, Oct. 8: [Y] Sec. 1.1 #7, 8, 13, 15; Sec. 1.2 #2 (also show that the subspace topology is in fact the coarsest topology on B for which the inclusion i is continuous), 4, 5, 6, 9, 10, 12, 13.
  • Assignment 1 due Friday, Sept. 22: [Y] Sec. 1.1 #2, 3, 4, 5.
  • Topology: intuitions, examples, and connections

Instructor

朱一飞 ZHU Yifei

College of Science M705

zhuyf@sustech.edu.cn

Office Hours: Tuesdays 10:20 am–12:10 pm

Grader: 梁嘉诚 LIANG Jiacheng

Prerequisites

Abstract Algebra (MA214/219) or consent of the Department.

Objectives

This course introduces basic notions and examples in general topology and algebraic topology, with a view towards more advanced analysis, (algebraic and differential) geometry, and topology studies, as well as applications.

An approximate schedule and references

[Y] 尤承业，基础拓扑学讲义，北京大学出版社，1997. (The main textbook, minimum requirement; good organization.)

[M] James R. Munkres, Topology, Prentice Hall, Inc., Upper Saddle River, NJ, 2000, Second edition of [MR0464128]. MR3728284 (A classic textbook; many in-depth, elaborate discussions and examples; somewhat old-fashioned; mostly optional reading on selected topics and exemplary mathematical exposition in general.)

[BBT] Tai-Danae Bradley, Tyler Bryson, and John Terilla, Topology—a categorical approach, MIT Press, Cambridge, MA, 2020. MR4232168 (A new textbook; supplementary with categorical perspectives.)

[B] 包志强，点集拓扑与代数拓扑引论，北京大学出版社，2013. (A relatively recent textbook; supplementary with selected topics.)

[A] Mark Anthony Armstrong, Basic topology, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1983, Corrected reprint of the 1979 original. MR705632 (For additional perspectives.)

Exams

There will be one in-class midterm exam, on November 17, 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.