Topology Through Inquiry

Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students.

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From AMS/MAA books: https://bookstore.ams.org/text-58/ or on Amazon: https://amzn.to/34lbNSi

Instructor’s Resource

For those teaching an Inquiry Based Learning (IBL) course, we have an Instructor’s Resource that you may find helpful. In it, we describe the educational philosophy of Inquiry Based Learning, its role in the education of students, practical issues, and tips for how to get started. You should also avail yourself of the many resources, workshops, and conferences for IBL teaching at The Academy of Inquiry Based Learning.

LaTeX files

Students may wish to create their own book of solutions. If so, 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.)

Sample Syllabi

The Preface to Topology Through Inquiry contains an outline of topics suitable for first-semester or second-semester courses. A typical first-semester course covers point-set topology with the possible inclusion of the fundamental group or the classification of surfaces. A typical second-semester course in geometric and algebraic topology would cover simplicial and/or singular homology and other selected topics.

Below are some sample syllabi from those who have used this text in their courses.

Please consider submitting your own syllabus for inclusion here. Write me at “[mylastname] at-sign math.hmc.edu” and include this information:
1. Institution
2. What kind of course you teach [topic, semester or quarter, etc]
3. Who the audience is [general background, prerequisites]
4. A PDF of your syllabus and assignment schedule
5. Link to your public webpage for the course, if you have one.

Harvey Mudd College. Topology (Math 147): first-semester, point-set topology with fundamental groups. Pre-requisite: one semester in real analysis.
This course used a DRAFT version of Topology Through Inquiry, so chapter and theorem numbers may not align with the published text. But you will be able to see the pacing.
Course website.

Harvey Mudd College. Algebraic Topology course: simplicial and singular homology. Pre-requisite: first-semester topology course.
This course used a DRAFT version of Topology Through Inquiry, so chapter and theorem numbers may not align with the published text. But you will be able to see the pacing.
Course website.