Basic information
Welcome to Topology I!
This course is the first half of a year long introduction to topology. In this first half of the course, we will primarily discuss point set topology. The main part of the course will cover most of chapters 2-4 and chapter 9 of Munkres' textbook and parts of chapters 0-1 of Hatcher's book, including: basic definitions and examples of topological spaces and continuous functions, properties of topological spaces used to distinguish between shapes (such as connectedness, compactness, separability), deforming one space into another ("homotopy"), the fundamental group, and applications. The central learning objective of the course is to develop skills in logical reasoning and reading and writing proofs.
Course expectations: Attendance is expected, as much as possible, but please do not attend class if you are feeling ill. By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner's attitude, and to encourage your fellow students to do the same. Regular class attendance and participation, and working through the homework, are your best methods for insuring that you will keep up with the material, and to make sure that you understand all of the concepts.
You are encouraged to work on the problem sets together in groups, or discuss them with me; you should however write up your own solutions. You are also encouraged to use our course materials while working on the problem sets, especially our class notes. See our course syllabus for the AI policy for this class.
Office Hours: Mondays 5 – 6 pm and Fridays 10:30 – 11:30 am.
Apart from these notes, the primary textbooks for the class are
Munkres' Topology, Second Edition
Hatcher's Algebraic Topology, available electronically on the author's website
Final Problem Set 1: due Tuesday, September 1 (tex)
Lecture 1 (Monday, August 24): What is a topology?
Lecture 2 (Wednesday, August 26): Worksheet 1: Topologies
Lecture 3 (Friday, August 28): Bases for a topology
Lecture 4 (Monday, August 31): Examples of bases.
Worksheet 1: Topologies (Solutions)
University of Nebraska-Lincoln
This course is the first half of a year long introduction to topology. In this first half of the course, we will primarily discuss point set topology. The main part of the course will cover most of chapters 2-4 and chapter 9 of Munkres' textbook and parts of chapters 0-1 of Hatcher's book, including: basic definitions and examples of topological spaces and continuous functions, properties of topological spaces used to distinguish between shapes (such as connectedness, compactness, separability), deforming one space into another ("homotopy"), the fundamental group, and applications. The central learning objective of the course is to develop skills in logical reasoning and reading and writing proofs.
Course expectations: Attendance is expected, as much as possible, but please do not attend class if you are feeling ill. By enrolling in this class, you are agreeing to be an engaged student, to come to class with a learner's attitude, and to encourage your fellow students to do the same. Regular class attendance and participation, and working through the homework, are your best methods for insuring that you will keep up with the material, and to make sure that you understand all of the concepts.
You are encouraged to work on the problem sets together in groups, or discuss them with me; you should however write up your own solutions. You are also encouraged to use our course materials while working on the problem sets, especially our class notes. See our course syllabus for the AI policy for this class.
Office Hours: Mondays 5 – 6 pm and Fridays 10:30 – 11:30 am.
Course notes
Here are the Course notes. I will be updating these throughout the semester. If you find any typos at all, however small, please let me know.Apart from these notes, the primary textbooks for the class are
Problem Sets
Instructions: You are welcome to work together with your classmates on the problems, and I will be happy to give you hints or discuss the problems with you, but you should write up your solutions by yourself. You will submit your work on gradescope; your submission should be a pdf file, but you are not required to type your solutions. If you prefer to handwrite your work on paper, there are apps like Scannable or Genius Scan that can scan your work into one pdf. See our course syllabus for the AI policy for this class.Schedule
Worksheets
Exams
We will have three midterms and a final, on- Monday, September 28, 5:30–7:30 pm
- Monday, October 26, 5:30–7:30 pm
- Monday, November 23, 5:30–7:30 pm
- Wednesday, December 16, 1–3 pm
Resources
Here are some other resources of potential interest:- A list of some of our favorite topologies
- Terry Tao's public lecture at the ICM, on Mathematics in the Age of AI