This is a collection of open courses and learning resources for topics in mathematics and statistics that are highly relevant to cognitive science.

MIT OpenCourseWare is the best! Gilbert Strang's introductory Linear Algebra Class is available for free online, as is a newer course on Linear Alebra's applications in data analysis and machine learning. The courses include lecture videos, selected readings from Strang's books, and problem sets.

Linear Algebra - Matrix Methods in Data Anlalysis, Signal Processing, and Machine Learning

Harvard's Joe Blitzstein has made his textbook, course syllabus, practice problems (with solutions!), and awesome lectures openly available to the public.

Homepage - Textbook - Lectures on YouTube

Richard McElreath's Statistical Rethinking is an awesome resource, particularly for scientists with moderate background in univariate statistics and inference who are looking to take the next step. He is a fantastic teacher and his target audience is scientists who are eager to get better at statistics and modelling. McElreath teaches a Bayesian approach to statistical inference, so this is a great entry point for those looking to get into Bayesian data analysis. While the full textbook itself is not free, there's a wealth of free online resources, including a full set of lecture videos and slides with problem sets and code examples in R (plus conversions to Python and Julia).

Videos - GitHub

It's hard to beat the freely available textbook An Introduction to Statistical Learning if you want a good primer on machine learning methods (and intuition!). It's one of the most popular textbooks for teaching statistics in formal university settings as well, and has well-developed examples in R with publicly available datasets. The more recent second edition (2021) adds modern topics like Deep Learning and Bayesian Additive Regression Trees.

Homepage - edX course - PDF