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.

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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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	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)
	Algebraic Fredholm Theory These notes develop, for vector spaces over arbitrary fields, the purely algebraic parts of basic Fredholm theory, emphasizing, (without any mention of topology or continuity) how the Fredholm index describes invertibility and spectra for Fredholm operators. The exposition culminates in a Fredholm-inspired analysis of the spectra of multiplication operators on spaces of holomorphic functions. Joel Shapiro · Portland State University · Date posted: December 19, 2024 Send feedback to the author(s)
	The Story of Statistics: Inquiry based notes for introductory statistics Notes for an introductory statistics course emphasizing the process of statistical thinking. Topics include data collection, graphical and numerical summaries, introduction to probability, random variables, sampling distributions, confidence intervals, hypothesis testing, and simple linear regression. A common investigation is woven throughout the notes to provide continuity and hands on activities are used to introduce new concepts. Lindsey Bell · Coastal Carolina University · Nicholas Pritchard · Coastal Carolina University · Douglas Weathers · Coastal Carolina University · Date posted: December 16, 2024 Send feedback to the author(s)

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