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

contact

  or  

Showing 1 - 5 of 198 result(s)

Ordinary Differential Equations: A First Course

This volume is an elementary textbook on ordinary differential equations that most students in science and engineering faculties take in their second year. All topics in this book are organized into chapters, sections, and subsections. There is at least one solved example for each subject in the book, and most of them are accompanied by graphs and drawing to illustrate the main point visually. The book is self-contained. The appendix chapter summarizes the essential pre-requisite for the course.

Mohammad Niksirat · University of Alberta · Date posted: November 14, 2021 · Date revised: December 4, 2021

Send feedback to the author(s)

Partial Differential Equations: A first course

The submitted work is prepared as an undergraduate textbook on partial differential equations for students who take a course on that subject. The text covers one-semester materials on linear first and second-order equations.

Mohammad Niksirat · University of Alberta · Date posted: November 2, 2021 · Date revised: November 4, 2021

Send feedback to the author(s)

Anosov representations: Informal lecture notes

Informal lecture notes on Anosov representations based on a graduate course given by the author at the University of Michigan in Winter 2020.

Richard Canary · University of Michigan · Date posted: November 2, 2021

Send feedback to the author(s)

Linear Algebra I

First part of two-semester course on Linear Algebra: Starting with the basics of propositional calculus and set theory, we then introduce functions, relations, and proofs by induction. After proving necessary facts regarding groups, rings, and fields, we study Linear Algebra's core
subjects, i.e. vector spaces, linear maps, matrices,
and linear systems. Appendix includes an introduction to axiomatic set theory and the axiom of choice.

Peter Philip · LMU Munich · Date posted: October 20, 2021 · Date revised: October 21, 2021

Send feedback to the author(s)

Linear Algebra II

Second part of two-semester course on Linear Algebra: Affine geometry is introduced as well as duality, multilinear maps, determinants, and eigenvalues. Via characteristic and minimal polynomials, we obtain the Jordan normal form. We study vector spaces with inner products, including orthogonality, adjoint maps, as well as Hermitian, unitary, and normal maps. Appendix includes an existence proof for algebraic closures.

Peter Philip · LMU Munich · Date posted: October 20, 2021 · Date revised: October 21, 2021

Send feedback to the author(s)

  or  

Showing 1 - 5 of 198 result(s)