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 188 result(s)

Gaussian Elimination and LU Decomposition

There is more to Gaussian Elimination than meets the eye.This note reviews
Gaussian elimination in various forms from both a computer programming and numerical analysis viewpoint.

gary knott · Civilized Software Inc. · Date posted: July 27, 2021

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Fourier Transforms

The four main types of Fourier transforms are defined and some of their properties and interrelationships are derived. The four types of Fourier transforms are: those defined on periodic functiions defined on R, discrete periodic functions, rapidly-diminishing functions, and linear functionals on rapidly-diminishing functions.,

gary knott · Civilized Software Inc. · Date posted: July 10, 2021

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Ordinary Differential Equations: Lecture Notes

Lecture Notes for MAT 244 “Introduction to Ordinary Differential Equations” at Faculty of Arts and Science, University of Toronto. This is a sophomore class for all but Math Specialist students.

Our texbook “Elementary Differential Equations and Boundary Value Problems” , 11th Edition, by William E. Boyce, Richard C. DiPrima and Douglas B. Meade.

Victor Ivrii · University of Toronto · Date posted: July 10, 2021

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Introduction to Lie Groups

This set of notes on Lie groups is an update of my "Lectures on Lie Groups." The current version is now organized into chapters, the first 7 of which cover the original material, from a first look at Lie groups through basic material on representations of compact groups, with emphasis on the unitary, orthogonal and spin groups. New chapters make contact with harmonic analysis. The final chapter introduces G2. Appendices provide background and complementary results.

Michael Taylor · UNC Chapel Hill · Date posted: June 26, 2021 · Date revised: June 27, 2021

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Complex Variables

Extended lecture notes for half-year course MAT334 "Complex Variables" for students who are not mathematics specialists.

Victor Ivrii · University of Toronto · Date posted: June 25, 2021 · Date revised: June 28, 2021

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Showing 1 - 5 of 188 result(s)