**Professor Francis Su**

Spring 2023

MW 2:45pm in Shan 2440

**My Office:** Shanahan 3416**My Email:** (my last name) at math.hmc.edu**My Drop-In Hours**:

Mondays 4-5pm (in person, right after class)

Also available by appointment via Zoom on Thursdays or Fridays

**Graders:** Clay Adams and Elizabeth Lucas-Foley (ccadams, elucasfoley)

**Prerequisites:** Math 131 (analysis). Math 171 (algebra) is recommended as a co-requisite.

Topology is the study of properties of objects preserved by continuous deformations (much like geometry is the study of properties preserved by rigid motions). Hence, topology is sometimes called “rubber-sheet” geometry. This course is an introduction to point-set topology with additional topics chosen from geometric and algebraic topology, including: topological spaces, separation properties, compactness, connectedness, and the fundamental group.

## Inquiry Based Learning

This course will be taught in an IBL (inquiry-based learning) format. This is a guided discovery process, which I expect will be one of the most rewarding mathematical experiences you’ll have. We learn best when we discover things for ourselves. The book contains theorems, definitions, examples structured so that you’ll naturally discover things. Your goal is to prove a collection of theorems in collaboration with classmates and with guidance from me.

You will take turns presenting proofs of theorems in class, while other students will determine if it is correct. I will provide perspective on the material, and motivating examples if you get stuck.

## Text

The text for the course is *Topology through Inquiry* by Michael Starbird and Francis Su. If you don’t yet have the book, check here for access to the first chapters.

## Sakai

All course notes and other private information for the course will be posted on the course Sakai page.

## Course Structure

**NO OUTSIDE SOURCES:** As is customary in any IBL course, you are forbidden from consulting any outside sources, including textbooks, the internet, or artificial intelligence to solve these problems. [Exceptions are sources that you are required to use for other courses.] The fun of the course is in struggling with ideas and enjoying challenging problems that will stretch your mind.

As part of your grade for the course, these notebooks will be evaluated. More importantly, a nice notebook will be something you can be very proud of years from now, as you look back on your experience.

**HOMEWORK:** Though you should be attempting the proof of many theorems, you will be asked to write up 5 selected theorem proofs to be handed in weekly via **Gradescope**. Homeworks will be due **Tuesday evenings at 10pm.** The **first 3 homeworks will be group assignments **(I will assign the groups, you’ll turn in one assignment for the group via Gradescope). The purpose of group assignments to: get to know others and learn from one another and to discuss and agree what you will included in your solutions. I encourage you to meet with your group on Thursday or Friday to work on problems together. **After the first 3 homeworks, you are encouraged to continue working in groups of your own choosing.**

The learning you are doing in this class takes place in a larger framework of school and life. Even if I am excited about teaching and you are excited about learning, work is not the most important thing, and sometimes life can take precedence. I can be somewhat flexible in accommodating requests for homework extensions and absences for other important events. Please make these requests 24 hours in advance, if possible.

Similarly, ‘success’ by whatever measure is not the most important thing in this course either. Every assessment of your work in this class is a measure of progress, not a measure of promise. Joy, wonder, productive struggle, having your mind expanded—these are more important!

**EXAMS:** There will be no midterm, but there will be a final examination.

**GRADES:** I’d rather you not worry about grades. I hope you will concentrate on learning. But since we must, grades will be determined in the following ways. 50% of your grade will be specifications-based. This means that you must meet each of the following specifications to pass the course:

– Present in class 6 times over the course of the semester.

– Contribute 12 questions/comments in class over the course of the semester.

– Among presentations/comments: 5 should be “productive failures”: such as lessons learned from trying things that didn’t work out.

– Contribute or edit 12 proofs in the Common Solution Set [which will be sent via email].

– Keep a well-organized notebook, which will be turned in 2/3 of way through the semester, these will be graded exceptional pass/pass/no pass.

**[The number 12 basically means once per week, and 6 means once every 2 weeks.]**

Homeworks (30%) and Final Exam (20%), will count the remaining portion of your grade.

## Honor Code

The HMC Honor Code applies in all matters of conduct concerning this course. Cooperation is encouraged. On group assignments, all members should be actively engaged in producing written work (and we will discuss the best way to approach group work).

You may not consult outside mathematical sources without my permission, unless required for some other course. Your solutions should acknowledge the assistance of other people or resources of any kind.

Expect this course to be challenging, but also very rewarding. The value of the IBL format is that when you prove theorems by yourself, you will never forget the proofs you came up with, and you will gain confidence in your abilities as mathematicians!

## Homeworks

Due on Gradescope on** Tuesdays at 10pm**. For group assignments only one person needs to submit, but you must tag the other people in your group.

You may find these LaTeX files of all the theorems in the book handy.

(The main tex file in this folder is topology-thms.tex.)