Lecture time and location

MW 1:30-2:45 in MH 233

Prerequisite

Math 131A with a grade of ”B” or better or instructor consent.

Office hours

Online via Zoom Tuesdays 2:00-3:00 PM, Thursdays 10:00-11:00 AM, 15 minutes before and after each class (in-person), and by appointment. The Zoom links will be posted on Piazza.

Textbook

Michael Starbird and Francis Su, Topology Through Inquiry, AMS/MAA Textbooks Volume: 58; 2019

Format

The format of this course will be Inquiry Based Learning (IBL). I will provide weekly assignments consisting of a list of theorems and exercises from the textbook. Your goal will be to do the assignments (prove all the theorems and solve all the exercises) by yourselves in a guided discovery process, with collaboration of classmates and guidance from me. You will take turns presenting proofs of theorems in class, while other students will determine if they are correct. I will provide perspective on the material and motivating examples.

No outside sources

As is customary in any IBL course, you are not allowed to consult any outside sources, including textbooks or the internet, to solve these problems. (The exceptions are sources that you are required to use for other courses.)

Notebook

You should acquire a loose-leaf binder, in which you will save all course notes. As you prove theorems in this course (or see them proved in class), you will write up these proofs and add them to your Notebook. In a sense, you are writing your own book on the subject, filled with your own proofs. As part of your grade for the course, these Notebooks will be evaluated.

Homework

You will be asked to write up selected theorems to be handed in weekly. Thus it is important to pay attention to proofs of theorems presented in class, since you will write these up for credit.

Homework will be due on Wednesdays.

(HW1) Reading for the week of 1/23: Sections 1.1, 1.2 and 1.3. Sections 1.4 and 1.5 are recommended but optional.

Homework due 1/25: Exercise 1.3, Theorems 1.12, 1.13, and 1.16.

Target for 1/25: be prepared to present Theorems 1.12, 1.13, and 1.16.

Carefully write up the proofs and solutions of the target theorems and exercises, and submit your assignment via a private note on Piazza the week after (no strict deadline).

Honor code

Cooperation is encouraged, but solutions should be written up individually. You may not consult outside mathematical sources without my permission, unless required for some other course.

Exams

There wil be no exams.

Expository paper

Each student will be required to write a short expository paper on a topic related to the course. A list of potential topics will be posted later. Papers need to be typeset in LaTeX.

Presentation

Each student will be required to present her/his expository paper at the end of the semester. Presentations will be 10-15 minutes long with a few minutes for questions.

Grading policy

Homework 20%, notebook 20%, participation 20%, expository paper 30%, presentation 10%

Piazza

To handle questions posed outside of class, we will be using Piazza. Piazza is a free online gathering place where students can ask, answer, and explore 24/7, under the guidance of their instructors. On the class dashboard, students can post questions and collaborate Wikipedia-style to edit responses to these questions. I as an instructor can also answer questions, endorse student answers, and edit or delete any posted content.

Instead of emailing me math questions, I encourage you to post them on Piazza.

Each student will be invited to join Piazza by email. Please join it as soon as you can, as I plan to use Piazza extensively.

Greensheet

Course greensheet