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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

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Showing 1 - 5 of 251 result(s)

Group theory

The notes correspond to the bachelor course Group Theory of the Vrije Universiteit Brussel, Faculty of Sciences, Department of Mathematics and Data Sciences.

Leandro Vendramin · Vrije Universiteit Brussel · Date posted: July 8, 2025

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Ring and Module Theory

The notes correspond to the bachelor course Ring and Module Theory of the Vrije Universiteit Brussel, Faculty of Sciences, Department of Mathematics and Data Sciences.

Leandro Vendramin · Vrije Universiteit Brussel · Date posted: July 8, 2025

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A brief summary of polynomials and Galois theory

Notes prepared for a first course in Galois theory inspired by the classical book of Emil Artin.

Shuyang Cheng · University of Michigan · Date posted: June 18, 2025

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Macdonald Polynomials and Operators, and Catalan Combinatorics

Our main aim with these notes is to introduce the combinatorial and symmetric function tools
that relate to the description of the Poincar´e polynomial of the triply graded Khovanov-Rozansky
homology of torus links, a.k.a. the (reduced) “superpolynomial” of these links. These where written in the context of the AIM Research Community on Link Homology.

François Bergeron · University of Quebec in Montreal · Date posted: April 18, 2025

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A First Course in College Calculus

A first course in calculus/analysis, the first part of the course motivates the study of sequences and their convergence through problems involving calculating the area under a graph and the slope of the tangent at a point on a graph. The second part draws on observations from the first about structural differences between the reals and the rationals, and starts with some axioms for the reals. These axioms are then used to study continuity and properties of continuous functions on the reals.

Tulsi Srinivasan · Azim Premji University · Date posted: April 17, 2025

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Showing 1 - 5 of 251 result(s)