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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	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)
	Foundations of Statistical Theory We focus on the elements of probability required for statistics, sampling distributions, parameter estimation and hypothesis testing. Len Meas · Royal University of Phnom Penh · Date posted: December 15, 2024 Send feedback to the author(s)
	Commutative Algebra A self-contained introduction to the theory of Commutative Algebra, at a level that is accessible to students or researchers who have already completed a standard two-semester Introduction to Abstract Algebra course. Topics include fundamentals of rings and modules, an introduction to Homological Algebra, integral extensions, primary decomposition theorems, Krull dimension, derivations, differentials, normal rings, regular rings, divisor class groups and classical ideal theory. Timothy Ford · Florida Atlantic University · Date posted: October 3, 2024 Send feedback to the author(s)

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