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 177 result(s)

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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Extremely Advanced Calculus: Multivariable Analysis, Vectors, Forms, Metric

The book is about differential and integral calculus in several variables. The first part on Analysis is mainly about calculus on an open subset of R^n. The second part on Smooth Geometry is about calculus on a manifold modeled on an open subset of R^n. This part has an emphasis on how to draw pictures. not only of vector fields, but also of differential forms and twisted differential forms. The third part on Metric Geometry includes an additional structure: the metric tensor.

William Faris · University of Arizona · Date posted: January 24, 2021

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Category, measure, and forcing: Set theory lecture notes

Notes based on a graduate course in set theory. The first part covers measure, category, the continuum hypothesis, and cardinal characteristics of the continuum. The second part introduces the method forcing, and concludes by showing how forcing can prove independence results about the continuum hypothesis as well as the values of the cardinal characteristics.

Samuel Coskey · Boise State University · Erik Holmes · University of Hawaii · Date posted: January 22, 2021

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Geometric Structures on Manifolds

An invitation to locally homogeneous geomtric structures on manifolds.
Particular attention is paid to affine and projective structures in low dimnsions

william goldman · university of maryland · Date posted: January 22, 2021

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Showing 1 - 5 of 177 result(s)