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 205 result(s)

Affine noncommutative geometry

Introduction to noncommutative geometry, or rather to the "simplest" such geometries, namely those using operator algebras, and coordinates, and with emphasis on "free geometry". Consists of 4 parts, 100pp each, with each part corresponding to material for a 1/2 semester graduate course: (1) Abstract geometries (2) Free manifolds (3) Intermediate geometries (4) Free coordinates. Everything printer-friendly, all components having length multiples of 4.

Teo Banica · Univ. Cergy-Pontoise · Date posted: May 19, 2022

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Quantum permutation groups

Introduction to quantum permutation groups, which are beautiful mathematical objects, expected to be useful in several branches of modern physics. Consists of 4 parts, 100pp each, with each part corresponding to material for a 1/2 semester advanced graduate course: (1) Quantum permutations (2) Analytic aspects (3) Quantum reflections (4) Matrix models. Everything printer-friendly, all components having length multiples of 4.

Teo Banica · Univ. Cergy-Pontoise · Date posted: May 19, 2022

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Blue Book of Mathematics for Elementary School Teachers

In these lectures, we review elementary mathematics within the larger picture of modern mathematics. The main audience of the course are students with prospective careers in elementary school education.
The topics include: sets, properties of arithmetic operations, culture of calculations, exponents, decimal and non-decimal base systems, historical numeration systems, GCF(a,b) and LCM(a,b), prime factorization, divisibility tests.
Each chapter includes definitions, examples, exercises.

Natasha Rozhkovskaya · Kansas State University · Date posted: April 24, 2022

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Complex Variables II: Conformal Mappings, Laplace and Fourier Transforms: Complex Variables II

This manuscript comprises the course notes for MATD34 (Complex Variables II), a fourth year undergraduate course which was taught at University of Toronto Scarborough in January-April 2021.

Lisa Jeffrey · University of Toronto · Yasin Mobassir · University of Toronto · Bonnie Yam · University of Toronto · Date posted: April 10, 2022

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Numerical Mathematics I

Introductory course on Numerical Mathematics: Includes Landau symbols, operator norms, condition, polynomial interpolation over general fields, spline interpolation, numerical integration, Cholesky and QR decomposition for linear systems, Newton's method, numerical methods for eigenvalues and minimization. Appendix includes floating point arithmetic, rounding errors, discrete Fourier transform, fast Fourier transform, trigonometric interpolation, and derivative-free minimization.

Peter Philip · LMU Munich · Date posted: April 7, 2022

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Showing 1 - 5 of 205 result(s)