Open Math Notes

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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.

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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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	Macdonald Polynomials and Operators, and Catalan Combinatorics Our main aim with these notes is to introduce the combinatorial and symmetric function tools that relate to the description of the Poincar´e polynomial of the triply graded Khovanov-Rozansky homology of torus links, a.k.a. the (reduced) “superpolynomial” of these links. These where written in the context of the AIM Research Community on Link Homology. François Bergeron · University of Quebec in Montreal · Date posted: April 18, 2025 Send feedback to the author(s)
	A First Course in College Calculus A first course in calculus/analysis, the first part of the course motivates the study of sequences and their convergence through problems involving calculating the area under a graph and the slope of the tangent at a point on a graph. The second part draws on observations from the first about structural differences between the reals and the rationals, and starts with some axioms for the reals. These axioms are then used to study continuity and properties of continuous functions on the reals. Tulsi Srinivasan · Azim Premji University · Date posted: April 17, 2025 Send feedback to the author(s)
	Special Relativity, Einstein Velocity Addition, and Gyrogroups: An Introduction In these notes we give an introductory united treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocity addition, and gyrogroups and gyrovector spaces. An effort has been made to present the material in a manner that is accessible to non-specialists and graduate students, and may even serve as the basis for a graduate course or seminar. Jimmie Lawson · Louisiana State University · Date posted: March 11, 2025 Send feedback to the author(s)
	Asymptotic and Perturbation Methods Extended lecture notes for half-year course APM441 "Asymptotic and Perturbation Methods" for students who are specializing in mathematics, physics, astronomy.. Victor Ivrii · University of Toronto · Date posted: February 6, 2025 Send feedback to the author(s)
	Mathematical Notes - from measures to stochastic analysis: Mathematics of stochastic analysis These notes are based on lectures designed to provide a gentle but rigorous route from measure theory on to stochastic processes, martingales, the Wiener process and stochastic integration. Ivan Wilde · King's College, London (retired) · Date posted: December 30, 2024 Send feedback to the author(s)

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