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 in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use 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 119 result(s)

Hamiltonian Mechanics

These are the lecture notes for the Hamiltonian Mechanics (WIYHM-12) course at the University of Groningen. The notes provide an excursus on the main ideas in Newtonian, Lagrangian and Hamiltonian mechanics. The main focus is on the discovery of the underlying geometric structure, with a strong emphasis on classical integrability and perturbation theory. The notes are full of exercises and provide plenty of external references for the interested students.

Marcello Seri · Bernoulli Institute, University of Groningen · Date posted: October 13, 2020

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From Linear Algebra to Algebraic Groups: An exercise based approach to matrix groups

This is a collection of exercises which could be useful for anyone wants to learn about linear groups, algebraic groups and finite simple groups.

Anupam Singh · IISER Pune · Date posted: October 13, 2020

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The Mathematics of Game Shows

Notes for a course I developed on The Mathematics of Game Shows. Develops concepts from probability, combinatorics, and modeling in the context of game show strategy. Suitable for freshmen, for non-math majors, and for motivated high school students.

Frank Thorne · University of South Carolina · Date posted: September 22, 2020 · Date revised: September 23, 2020

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Introduction to Abstract Algebra

This textbook is intended for a first course in abstract algebra at the undergraduate level, mainly written during the summer of 2019. It is borne of a desire for more open source textbooks, to introduce group actions in a beginning algebra course, and out of not having a course to teach during that semester and wanting a project.

Jaree Hudson · Florida Atlantic University · Date posted: September 8, 2020 · Date revised: September 20, 2020

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Spectral theory and asymptotic methods

Lecture notes with some exercises. Topics include: unbounded (differential) operators, sesquilinear forms, classification of spectra, perturbations, min-max principle for eigenvalues. Schrödinger operators and Laplacians in open sets are considered as main examples. More advanced topics include decay estimates for eigenfunctions (Agmon-type estimates), semiclassical asymptotics for potential wells, Laplacians in some unbounded domains (incl. waveguides).

Konstantin Pankrashkin · Carl von Ossietzky University of Oldenburg · Date posted: September 8, 2020

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Showing 1 - 5 of 119 result(s)