Course Syllabus

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Content: This class is an introduction to point-set and algebraic topology. Topics in point-set topology will include: topological spaces, connectedness, compactness, metric spaces. In algebraic topology, we will mostly focus on fundamental groups, homotopy, quotients and gluing, and covering spaces.  See detailed list of topics below.

Textbook: J. Munkres, Topology (2nd edition).  The international edition is acceptable.

Course staff:

  • Prof. Denis Auroux (auroux@math.harvard.edu): office hours Mondays and Tuesdays 11:00-12:45 in SC 539. (also Thu 12/7, 9am-11am).
  • Gregory Li: office hours Thursdays 3-5pm in Lowell Dining Hall
  • Nico Miller: office hours Thursdays 6-8pm, Math Dept. Lounge
  • Quinn Brussel: office hours Sundays 2-4pm, Mather Dining Hall
  • Emma Cardwell: office hours Saturdays 3-5pm in Quincy Dining Hall
  • Dora Woodruff: office hours Sundays 8-10pm in Quincy Dining Hall
  • Eric Shen: office hours Mondays 9:15-11:15 PM in Leverett Dining Hall (Math night)

Lectures will be held on Tuesdays and Thursdays from 9:00 to 10:15am, starting Tuesday September 5, in Science Center 507.

Assessments: There will be weekly (or near-weekly) homework assignments, a midterm (take-home, open between October 17-23), and a final exam (take-home, December 8-15). Approximate grading weight: homework 50%, midterm 20%, final 30%. One homework score will be dropped for everyone, so you may miss one assignment without penalty, but you are still responsible for working through the material.

Academic integrity policy:

  • You are encouraged to discuss and collaborate with each other on the homework assignments; the use of external resources (including generative AI) is acceptable. However, make sure that you are able to work through the problems yourself. Additionally, you must write up your answers in your own words and in a manner that reflects your own understanding, and you must credit any sources or resources that were used. This is not only a matter of academic integrity, but also crucial for properly learning the material and the problem-solving and mathematical writing skills that this course aims to cover. 
  • For exams, collaboration or consultation of sources other than those explicitly permitted is not allowed.

 

Homework assignments

Direct links to the homework assignments will be posted here as PDF files.  Go to "Assignments" to see the LaTeX source and to submit your solutions.

You are encouraged to discuss the homework problems with other students, and you are allowed to consult external sources. However, the homework that you hand in should reflect your own understanding of the material and be written in your own words. You are NOT allowed to just copy solutions from other students or other sources (including generative AI).

No late homeworks will be accepted (unless circumstances genuinely warrant an extension). However, we will drop your lowest homework score, so you are allowed to miss one assignment without a penalty.

 All homework submissions should be uploaded to Canvas. Handwritten work is welcome, but please upload a readable scan.

 

Lecture topics

The following syllabus is approximate -- we may end up deviating slightly from this list of topics or timetable.  To the extent possible, (usually handwritten) lecture notes will be posted for each lecture.

Course Summary:

Date Details Due
Tue Sep 12, 2023 Assignment Homework 1 due by 11:59pm
Tue Sep 19, 2023 Assignment Homework 2 due by 11:59pm
Tue Sep 26, 2023 Assignment Homework 3 due by 11:59pm
Tue Oct 3, 2023 Assignment Homework 4 due by 11:59pm
Tue Oct 10, 2023 Assignment Homework 5 due by 11:59pm
Tue Oct 17, 2023 Assignment Homework 6 due by 11:59pm
Mon Oct 23, 2023 Assignment Midterm due by 11:59pm
Tue Oct 31, 2023 Assignment Homework 7 due by 11:59pm
Thu Nov 9, 2023 Assignment Homework 8 due by 11:59pm
Tue Nov 21, 2023 Assignment Homework 9 due by 11:59pm
Tue Dec 5, 2023 Assignment Homework 10 due by 11:59pm
Fri Dec 8, 2023 Calendar Event MATH 131: Topological Spaces and Fundamental Group 8pm to 9pm
Fri Dec 15, 2023 Assignment Final due by 11:59pm