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 212 result(s)

Symmetric Functions and Rectangular Catalan Combinatorics

These notes where conceived as a complement for a course given on the occasion of the AEC 4th Algorithmic and Enumerative Combinatorics Summer School, 2018, Austria

Fran├žois Bergeron · University of Quebec in Montreal · Date posted: June 22, 2022

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Short Course on Pseudodifferential Operators

In four chapters we present basic material on the theory of pseudodifferential operators and selected applications to PDE. Chapter I: Operators with smooth symbol on R^n. II: Operators with rough symbols and paradifferential operators. III: Layer potentials on domains with uniformly rectifiable boundary. IV: Operators on noncompact manifolds.

Michael Taylor · University of North Carolina, Chapel Hill · Date posted: June 22, 2022

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Partial Differential Equations

The first part of this book is on the presentation of the theory of the transport equation, the conservation laws, particularly for problems involving shock waves.
the second part is on how the Fourier transform and some heuristic techniques can be used effectively to obtain a fundamental solution of Laplace, heat, wave and Schr\"odinger equations. The third part is devoted to the theoretical study of the variational formulation for elliptic boundary value problems.

Meas Len · Royal University of Phnom Penh · Date posted: June 16, 2022

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Probability Theory

This note focuses on the probability space, random variables, expectation and its properties, Limit theorems, Introduction to Markov chain and martingales.

Meas Len · Royal University of Phnom Penh · Date posted: June 16, 2022

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Linear Algebra: Notes and Problems

This set of notes and problems covers a junior-level linear algebra course (following an introduction to proof course) with broad chapter topics of 1) efficiently solving systems of linear equations, 2)vector spaces, 3) connecting ideas (dimension, invertibility, and eigenvalues), and 4) inner product spaces. The approach of these notes is a blend of computational and sense-making problems, as well as an increasing usage of conjecture and proof throughout the course.

Nicholas Long · Stephen F. Austin University · Date posted: May 27, 2022

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Showing 1 - 5 of 212 result(s)