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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



Showing 1 - 5 of 233 result(s)

Calculus - Essential University Mathematics: Calculus

This is a much enhanced set of lecture notes presented as part of the mathematics programme in the Mathematics Department of King's College, London. The aim here is to offer a clear exposition of many of the essential results from calculus. The student is expected to be both curious and willing to persevere. This is not intended to be a cookbook of recipes but rather to present not just the what but also the why.

Ivan Wilde · retired - Maths Dept, King's College, London · Date posted: October 23, 2023

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Foundation of Number Theory

This book is on the presentation of the fundamental concepts in the number theory:
divisibility, greatest common divisor, Euclidean algorithm, congruences, diophantine equations. The three classical theorems: Wilson’s theorem, Fermat’s Little theorem and Euler’s
theorem together with its applications are also presented.

Len Meas · Royal University of Phnom Penh · Date posted: October 9, 2023

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Lectures on Statistics

This is a course on the theory of statistics at the advanced undergraduate (or beginning graduate) level. The goal is to prepare students to use probability to understand statistical inference. Some more advanced topics include decision theory and its relation to Bayes procedures. There is also material on order statistics and on the bootstrap.

William Faris · University of Arizona · Date posted: October 2, 2023

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Ordinary Differential Equations

Introductory course: Includes elementary solution via separation of variables and change of variables, general theory (Peano existence theorem, uniqueness of solutions, maximal solutions, continuity in initial conditions), linear ODE (existence, uniqueness, vector space of solutions, fundamental matrix solution, variation of constants, higher-order, Wronskian, constant coefficients), qualitative theory (stability at fixed points, phase portraits, Lyapunov's theorem, linearization, limit sets).

Peter Philip · LMU Munich · Date posted: August 9, 2023

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Martingales and Random Fluctuations: The Gambling Metaphor in Probability Theory

Part I is an intermediate level probability course given at the Independent University of Moscow. The unusual feature is an emphasis on discrete-parameter martingales. The development using examples based on gambling schemes makes no mention of conditional expectation.

Part II is a more systematic review of basic theory, leading up to the common definition of martingales in terms of conditional expectation.

William Faris · University of Arizona · Date posted: August 8, 2023

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Showing 1 - 5 of 233 result(s)