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 180 result(s)

Gaussian free field, Liouville quantum gravity and Gaussian multiplicative chaos

These lecture notes are intended to be an introduction to the two-dimensional continuum Gaussian free field, Liouville quantum gravity and the general theory of Gaussian multiplicative chaos.

Nathanaël Berestycki · Universität Wien · Ellen Powell · Durham University · Date posted: March 25, 2021 · Date revised: April 8, 2021

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Partial Differential Equations

This is a graduate course on partial differential equations, on the level of the Lawrence C. Evans PDE text, but shorter, perhaps more explicit in physical interpretations. Topics include: Laplace, heat, wave, and Hamilton-Jacobi equations, conservations laws, Sobolev spaces, spectral theory, energy methods, evolution semigroups, Euler-Lagrange equations, variational methods, fixed points, semilinear elliptic equations.

WILLIAM FARIS · University of Arizona · Date posted: March 17, 2021

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Lectures on Geometry and Topology in the Plane

This course introduces different aspects of geometry and topology, in a series of chapters that
appear in no particular order, other than a general tendency for the later parts to be deal with
notions less familiar to students. The exposition eschews rigor in favor of intuition.

Paul Seidel · MIT · Date posted: March 8, 2021

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Lectures on Partial Differential Equations

This is an undergraduate course on partial differential equations. It treats classical equations: translation, wave, diffusion, Laplace, Schrodinger, along with non-linear variants. Classical techniques include methods for explicit solutions, Fourier series and transforms, spherical harmonics, and Green's functions. Applications topics are varied: conservation laws, Einsteins's formula for diffusion, recurrence and transience, reaction-diffusion, gas dynamics and sound speed.

William Faris · University of Arizona · Date posted: February 22, 2021

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Honors Intro to Analysis

A nets-heavy rigorous course of single variable analysis. It is designed for flipped instruction.

Willie Wong · Michigan State University · Date posted: January 26, 2021

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Showing 1 - 5 of 180 result(s)