Open Math Notes

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)

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)

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)

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)

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)