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Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto



Showing 1 - 5 of 239 result(s)

Handbook of Mathematical Proof

This can be used for an intro to proofs course, or a reference in a proof-based course Designing any guide or text on mathematical proof leads to a discussion of sets first or propositions first. We introduce a little of each first, and then constantly bring the discussion back to categorizing what each kind of thing is, with emphasis on mathematical language.

Edward Kim · University of Wisconsin-La Crosse · Date posted: July 11, 2024

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Algebraic Methods in Combinatorics

Lecture notes from a Part III course at the University of Cambridge, UK

Oleg Pikhurko · University of Warwick · Date posted: July 10, 2024

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The Hitchhiker's Guide to Complex Analysis

This book covers an advanced or honors undergraduate course in complex variables and, at the same time, an introductory graduate course in complex functions. It is aimed at a wide population of students with diverse backgrounds, welcoming also those who had no previous exposure to complex numbers. The book is a tool to prepare all of them, in a guided manner suitable for active self-study. It is based on the author's lecture notes for his classes at the University of Texas at Dallas.

Vladimir Dragovic · The University of Texas at Dallas · Date posted: May 21, 2024 · Date revised: May 24, 2024

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Symplectic geometry and topology

These are the lecture notes used for topics courses on symplectic geometry and topology; the only prerequisites are familiarity with smooth manifolds and differential forms. Introductory material includes the geometry of Hamiltonian flows, symplectic linear algebra, almost complex and related geometric structures, and the Moser technique and its applications. Additional topics include Weinstein surgery, Lefschetz fibrations, and generating functions.

Michael Usher · University of Georgia · Date posted: May 15, 2024

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A Careful Introduction to Thermodynamics & Statistical Mechanics - with mathematics in mind

The aim of these notes is to provide a carefully reasoned presentation of the basic ideas of the subject so that they may be more appealing to mathematics students than is often the case.

Ivan Wilde · King's College, London (retired) · Date posted: December 30, 2023

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Showing 1 - 5 of 239 result(s)