Introduction to Abstract Algebra This textbook is intended for a first course in abstract algebra at the undergraduate level, mainly written during the summer of 2019. It is borne of a desire for more open source textbooks, to introduce group actions in a beginning algebra course, and out of not having a course to teach during that semester and wanting a project. Jaree Hudson · Florida Atlantic University · Date posted: September 8, 2020 · Date revised: September 11, 2020 Send feedback to the author(s)

Spectral theory and asymptotic methods Lecture notes with some exercises. Topics include: unbounded (differential) operators, sesquilinear forms, classification of spectra, perturbations, min-max principle for eigenvalues. Schrödinger operators and Laplacians in open sets are considered as main examples. More advanced topics include decay estimates for eigenfunctions (Agmon-type estimates), semiclassical asymptotics for potential wells, Laplacians in some unbounded domains (incl. waveguides). Konstantin Pankrashkin · Carl von Ossietzky University of Oldenburg · Date posted: September 8, 2020 Send feedback to the author(s)

Fourier Analysis: Second half of a course These are notes for the second half of a Fourier analysis class, written up in spring 2020 after the class was moved online. They somewhat follow the course textbook (Stein-Shakarchi), with the addition of a great deal of material on distributions. Peter Woit · Columbia University · Date posted: September 4, 2020 · Date revised: September 5, 2020 Send feedback to the author(s)

Mechanics for Mathematicians Lecture notes for a one quarter course on mechanics for undergraduate math majors. Jared Wunsch · Northwestern University · Date posted: August 31, 2020 · Date revised: September 15, 2020 Send feedback to the author(s)