{"id":964,"date":"2023-01-18T18:46:30","date_gmt":"2023-01-18T18:46:30","guid":{"rendered":"https:\/\/math.hmc.edu\/su\/?page_id=964"},"modified":"2025-09-24T16:01:17","modified_gmt":"2025-09-24T16:01:17","slug":"math147-spring2025","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/su\/math147-spring2025\/","title":{"rendered":"Math 147: Topology Spring 2025"},"content":{"rendered":"
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sphere eversion<\/a><\/figcaption><\/figure>\n<\/div>\n\n\n

Professor Francis Su<\/strong>
Spring 2025
MW 1:15pm in Shanahan 3485<\/p>\n\n\n\n

My Office:<\/strong> Shanahan 3416
My Email:<\/strong> (my last name) at math.hmc.edu
My Drop-In Hours<\/strong>:
Wednesdays 2:30-4pm or by appointment.<\/p>\n\n\n\n

Grader:<\/strong> Shreya Balaji (sbalaji) at g.hmc.edu<\/p>\n\n\n\n

Prerequisites:<\/strong> Math 131 (analysis).  Math 171 (algebra) is recommended as a co-requisite.<\/p>\n\n\n\n

Topology is the study of properties of objects pre\u00adserved 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.<\/p>\n\n\n\n

Inquiry Based Learning<\/h2>\n\n\n\n

This course will be taught in an IBL (inquiry-based learning) format. This is a guided discovery process, which can 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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Text<\/h2>\n\n\n\n

The text for the course is Topology through Inquiry<\/em> by Michael Starbird and Francis Su. The publisher sells a hardcopy and e-book version here<\/a>. Or compare here<\/a>.<\/p>\n\n\n\n

Course Structure<\/h2>\n\n\n\n

NO OUTSIDE SOURCES:<\/strong> 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 solutions that you encounter while doing work for other courses.] The fun of the course is learning how to wrestle with challenging ideas. Consulting outside sources stifles the development of your own creativity.<\/p>\n\n\n\n

NOTEBOOK:<\/strong> You should create a notebook (a loose-leaf binder works well for this). As you prove theorems in this course (or see them proved in class), you will write up these proofs and add them to this 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. More importantly, a nice notebook will be something you can be very proud of years from now, as you look back on your experience.<\/p>\n\n\n\n

HOMEWORK:<\/strong> Though you should be attempting the proof of many theorems, you will be asked to write up 5 selected problems to be handed in weekly via Gradescope<\/strong>. Therefore it will be important to pay attention to proofs presented in class, as you will write them up for credit. Homeworks will be due Thursdays at 5pm<\/strong>.<\/p>\n\n\n\n

EXAMS:<\/strong> There will be no midterm, but there will be a final examination.<\/p>\n\n\n\n

GRADES:<\/strong> I\u2019d 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:<\/p>\n\n\n\n

– Make class presentations at least 12 times (roughly once\/week).
– Participate in class discussions at least 12 times (roughly once\/week).
– Share a story of a “productive failure” in class at least 3 times (e.g., lessons you learned from trying things that didn’t work out).
– 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.<\/p>\n\n\n\n

Homeworks (30%) and Final Exam (20%) will count the remaining portion of your grade.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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!<\/p>\n\n\n\n

Honor Code<\/h2>\n\n\n\n

The HMC Honor Code applies in all matters of conduct concerning this course. Cooperation is encouraged. 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.<\/p>\n\n\n\n

You can expect this course to be challenging and 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!<\/p>\n\n\n\n

Homework Assignments<\/h2>\n\n\n\n

Due on Gradescope by 5pm<\/strong> on the assigned day, generally Thursdays.<\/p>\n\n\n\n

You may find these LaTeX files of all the theorems<\/a> in the book handy.
(The main tex file in this folder is topology-thms.tex.)<\/p>\n\n\n\n

There’s also a PDF of all theorem statements: one per page<\/a>, or all together<\/a>.<\/p>\n\n\n