Skip to Main Content

Open Math Notes

Resources and inspiration for math instruction and learning

Home Submit FAQ Contact My Notes

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 235 result(s)

A Careful Introduction to Thermodynamics & Statistical Mechanics - with mathematics in mind

The aim of these notes is to provide a carefully reasoned presentation of the basic ideas of the subject so that they may be more appealing to mathematics students than is often the case.

Ivan Wilde · King's College, London (retired) · Date posted: December 30, 2023

Send feedback to the author(s)

Abstract Functional Analysis: Course Notes in Functional Analysis

A self-contained introduction to Functional Analysis and C*-algebras.
Including: Finite Dimensional Spaces, Hilbert Spaces, Hahn-Banach Theorem, Open/Closed/Uniform Boundedness Theorem. Gelfand-Naimark Theorems, Compact Normal Operators

Warren Moors · The University of Auckland · Date posted: December 28, 2023

Send feedback to the author(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

Send feedback to the author(s)

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

Send feedback to the author(s)

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

Send feedback to the author(s)


Showing 1 - 5 of 235 result(s)