Warning

This may be outdated. Please visit the course Canvas page for the most recent version.

Basic information

MWF 1:30-2:20, Padelford C-038

Instructor: John Palmieri, Padelford C-442, jpalmier@uw.edu. Web page https://sites.math.washington.edu/~palmieri/Courses/2024/Math544/ . Office hours: drop in and by appointment. I expect to be in my office most MWF 11-4ish, also many Tuesdays and occasional Thursdays. I am very happy to make appointments.

TA: Jay Reiter, Padelford C-543, jrreiter@uw.edu. Office hours to be announced.

Textbook

The main textbook is John M. Lee, Introduction to Topological Manifolds . This should be free to download for people affiliated with UW via https://orbiscascade-washington.primo.exlibrisgroup.com/permalink/01ALLIANCE_UW/1juclfo/alma99159971200001452 (follow the "view full text" link) or possibly using the direct link https://link-springer-com.offcampus.lib.washington.edu/content/pdf/10.1007/978-1-4419-7940-7.pdf (you must be logged into the UW system). I will assign problems from this book.

Another option: Oscar Randal-Williams, Algebraic Topology (free PDF download): https://www.dpmms.cam.ac.uk/~or257/teaching/notes/at.pdf . This covers much of the same material.

Different authors will appeal to different people. If you find another resource that you find useful, please let me know! I can add links to the web page, and your fellow students will appreciate having more options.

Approach

This course will be discussion-based. I will spend very little time lecturing. Instead, you will mostly work in groups on the material, either on processing the material (as presented, for example, in the textbook) or on the homework problems.

Goals

• Learn some topology: Chapters 5–13 of the book.
• The best way to learn math is by doing it, so do problems.
• Learn how to read mathematics.
• Learn how to communicate about math "synchronously."
• Learn how to communicate about math in writing.

(If you like, you can replace "learn how to" with "improve/refine your ability to".)

Classroom guidelines

To be developed

Course expectations

• Before each class, do the reading and try to understand it. If you're stuck on something, send me email! (I will try to address these either individually or in class: "several people were confused by ..., so let's talk about it".)

• Before each class, make an attempt on the homework problems.

• Come to class ready to participate in discussions.

Assignments and grading

There are three components to your grade.

Homework

Homework is due at the beginning of class on Wednesdays, although you are welcome to turn it in early. Turning it in electronically would be great — --- upload via Canvas.

You may work with other people on your homework, but you must write your solutions yourself. If you find a solution in a book or some other source, please provide a reference.

You should make an honest and serious attempt at all of the problems. Homework will mostly (90%) be graded based on this ("honest and serious attempt"). One or two problems per week will be evaluated for correctness and exposition, worth 10%. Missing assignments or turning in late assignments will be handled case-by-case.

(If you see an interesting homework problem that I haven't assigned, do it! Let me know about it, and maybe I'll add it to the HW or replace another problem.)

Homework scores of 75-100% will translate to grades of 3.0-3.3.

Homework portfolio

Due December 6, more details provided later. You will pick some of the homework problems that you want to revise and revise them; the goal is to show some of your best work, either the best mathematics or the best exposition (or both). Explain what you changed and why, explain why you chose those problems.

Getting full credit on the portfolio will add 0.4 to your grade.

Final exam

This will likely be oral, and getting full credit will add 0.3 to your grade.

All components are optional, so if (for example) you are happy with your grade just based on the homework, you can skip the portfolio and the final. Of course skipping the homework would be a bad idea.

Mathematical background

You need to know basic group theory, for example as provided by Math 403.

You need to know basic point-set topology. Familiarity with metric spaces is a great start, and it should be enough for the beginning of the course. You should be familiar with:

• open sets, closed sets
• continuous functions
• compactness
• connectedness, path-connectedness

If you've only seen metric spaces, you should familiarize yourself with the following; they are fundamental concepts and any educated mathematician should know them, plus they are likely to come up this quarter:

• topological spaces
• basis for a topological space
• subspaces, product spaces

Other topics from Chapters 1-4 of Lee's book:

• Hausdorff spaces, local compactness, paracompactness, proper maps: pick up as you need them, they are not of central importance right now
• The definition of a manifold: we'll talk about that day 1.
• Quotient spaces and adjunction spaces: we'll talk about those day 1.

Academic integrity

See https://www.washington.edu/cssc/facultystaff/academic-misconduct/ for UW resources. I don't expect misconduct to be an issue for this course, but one thing to watch out for is presenting someone else's work as your own. This is plagiarism, and it is prohibited by the Student Conduct Code.

Access and accommodations

It is the policy and practice of the University of Washington to create inclusive and accessible learning environments consistent with federal and state law. If you have already established accommodations with Disability Resources for Students (DRS), please activate your accommodations via myDRS so we can discuss how they will be implemented in this course.

If you have not yet established services through DRS but have a temporary health condition or permanent disability that requires accommodations (conditions include but not limited to; mental health, attention-related, learning, vision, hearing, physical or health impacts), contact DRS directly to set up an Access Plan. DRS facilitates the interactive process that establishes reasonable accommodations. Contact DRS at https://depts.washington.edu/uwdrs/ .

Religious accommodations

Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW’s policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy ( https://registrar.washington.edu/staffandfaculty/religious-accommodations-policy/ ). Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form ( https://registrar.washington.edu/students/religious-accommodations-request/ ).

And what about the shim-sham?

Hmm?