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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 225 result(s)

Finite Mathematics

These notes cover matrix algebra, linear programming, probability, counting methods, Markov chains, and game theory. In practice, students work through the notes during class, complete problems in groups, and present their work at the board. Two modules using board games are also included as appendices. The notes can be easily adapted by taking out explanatory passages or examples, based on the mathematical background of the students.

Mindy Capaldi · Valparaiso University · Date posted: May 31, 2023

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Mathematical Logic for the Humanities

A mathematics course designed for students in the humanities. A variety of concepts are covered. Topics will be drawn from the following areas: introductory treatments of sets, logic, number theory.

Ryan Dunning · St. Mary's University · Date posted: May 31, 2023

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Precalculus: An Inquiry-Based Approach

A standard precalculus course covering polynomials, rationals, exponentials, logarithmics, trigonometry, polar coordinates, rate of change, and conic sections. This course may also serve as either College Algebra or Trigonometry simply by choosing the appropriate chapters.

William Mahavier · N/A · Paul Howard · Oklahoma Christian University · Date posted: May 31, 2023

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Lecture Notes on Geometric Group Theory

These notes cover the foundations of geometric group theory, such as Cayley graphs and quasi-isometries, and additionally a selection of topics, such as hyperbolic spaces, CAT(0) spaces, and cube complexes. The style is rather informal, and the goal is often to convey the key ideas rather than the fine details, so they are best used for a course that aims to give an overview of a selection of topics in Geometric Group Theory (or for individual students who want an overview).

Alessandro Sisto · Heriot-Watt University · Laura Ciobanu · Heriot-Watt University · Alexandre Martin · Heriot-Watt University · Date posted: March 20, 2023

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First Order Partial Differential Equations: a simple approach for beginners: First Order Partial Differential Equations

Usually a course on partial differential equations (PDEs) starts with the theory of first order PDEs, which turns out to be quite time consuming for a teacher and difficult for students due to dependence of the proofs on geometry of Monge curves. In this article we present a simpler theory of first order PDEs using only the characteristic curves in the space of independent variables. In addition we discuss existence and uniqueness first with examples and then prove rigorously It has new ideas.

Phoolan Prasad · Indian Institute of Science · Date posted: January 9, 2023

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Showing 1 - 5 of 225 result(s)