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 in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use 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
  • Mary Pugh | University of Toronto
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University



Showing 1 - 5 of 95 result(s)

Model Theory of Valued Fields

An introduction to applications of model theory to valued fields including the results of Ax-Kochen and Ersov and the model theory of the field of p-adic numbers.

David Marker · University of Illinois at Chicago · Date posted: October 18, 2019

Send feedback to the author(s)

On Cohomological Stochastic Dynamics of Higher Dimensions

Here is one of the best and the more recent books on Complex Dynamics in Higer Dimension. Here, we develop a calculus on positive closed currents of arbitrary bidegree on compact K{\"a}hler manifolds after
recalling a notion of super-potential associated to such currents by using deformations in the space of currents. We define in particular the intersection of such currents and the pull-back operator. We apply the theory of super-potentials to construct Green currents ...

Armand Azonnahin · Instituto de Matemática e Estatística da Universidade de São Paulo · Date posted: October 18, 2019

Send feedback to the author(s)


These are the notes of a two-hour one-semester course on CAT(0) cube complexes which I taught in Muenster during winter term 2012/2013.

Topics covered are for example: Basic CAT(0) geometry, Gromov's link condition, half-space systems and Sageev's cubulation method, cubulating Coxeter groups and the Tits alternative.
Since most of the students neither had a strong background in metric geometry nor in group theory I tried to keep the material as elementary and selfcontained as possible.

Petra Schwer · Otto von Guericke University · Date posted: October 18, 2019 · Date revised: October 20, 2019

Send feedback to the author(s)

Free Probability Theory

This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material here was presented in the winter term 2018/19 at Saarland University in 26 lectures of 90 minutes each. The lectures were recorded and can be found online at

Roland Speicher · Saarland University · Date posted: September 4, 2019

Send feedback to the author(s)

Combinatorics: The Art of Counting

This is a preliminary version of a book which I intend to publish with the AMS. My editor is Ina Mette

Bruce Sagan · Michigan State University · Date posted: September 1, 2019 · Date revised: September 2, 2019

Send feedback to the author(s)


Showing 1 - 5 of 95 result(s)