This is a collection of open courses and learning resources for topics in mathematics and statistics.
In terms of scope, this collection includes topics across mathematics and statistics, up to and including topics in machine learning and data analysis. However, it does not cover deep learning, for which there are other available resource lists.
The following are general (introductory) resources for learning math & statistics.
The following resources are primarily focused on having text and animation based explainers.
'Better Explained' is a collective of lessons on topics in mathematics that focus on explaining intuitive examples and explainers.
'3Blue1Brown' is a collection of explainers on mathematics, using animations.
'Seeing Theory' is a visual introduction to probability and statistics.
The following resources are primarily focused on having video-based resources.
'Khan academy' is an educational organization that creates online resources for many topics, including math and statistics.
Steve Brunton, on the Eigensteve youtube channel makes videos explaining topics across math, statistics, and physics.
This section covers mathematics.
The following are openly available courses and online textbooks on mathematics.
The 'Introductory Linear Algebra' class, by Gilbert Strang, is freely available through MIT's OpenCourseWare. The materials include lecture videos, selected readings from Strang's books, and problem sets.
This is a newer course on Linear Algebra's applications in data analysis and machine learning, also available from MIT's OpenCourseWare.
The following resources introduce mathematical topics and concepts using code-based examples and exercises.
This openly available book and exercises introduces core topics in mathematics, organized for people who already have experience with programming. It includes code examples, in Python.
The scipy lecture notes offer tutorials on the scientific Python ecosystem.
This resource, including an online textbook, PDF, and examples in Python, covers numerical methods for differential equations with Python.
This resource covers doing matrix computations accurately and efficiently in Python.
This section covers statistics.
The following are openly available courses and online textbooks on statistics.
'Statistics 110: Probability' is a class by Joe Blitzstein, who is a professor in the department of statistics at Harvard University. He has made his textbook, course syllabus, practice problems (with solutions!), and openly available.
'Statistical Rethinking', by Richard McElreath is a great resource for scientists with moderate background in univariate statistics and inference who want to learn more about statistics and modelling, with a focus on a Bayesian approach to statistical inference.
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).
The freely available textbook An Introduction to Statistical Learning provides a 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 - Online Course - Textbook
'Frequentism and Bayesianism' is a 5-part series by Jake VanderPlas that outlines and explains the distinctions of frequentist vs bayesian statistics.
The following are resources on specific topics within statistics.
The following are resources on key concepts in statistics:
The following are resources on statistical testing:
- An overview of statistical tests as linear models, by Jonas Kristoffer Lindeløv
- A visual explanation of permutation tests, by Jared Wilber
- A reference collection related to common statistical myths
The following are resources related to p-values:
- What is a p-value video, by Daniel Lakens
- Common misconceptions about p-values blog post by Daniel Lakens
- Comparing p-values and s-values
This section covers Machine Learning.
The following are openly available courses and online textbooks on machine learning.
'Mathematics of Machine Learning', by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ung, covers the basic necessary mathematical concepts for machine learning. It is available for purchase as well as as a free PDF.
This 'crash-course' by Google provides an overview of fundamentals and core concepts for machine learning.
The 'Machine Learning Glossary', by Google, is a glossary that defines terms in machine learning.
This set of cheatsheets, by Shervine and Afshine Amidi, provides summary overviews of key topics in machine learning.
'Distill' was scientific journal that focused on clear and dynamic explainers in machine learning. The journal is now on indefinite hiatus, but previous articles are still available.
The following are resources on specific topics within Machine Learning.
The following resources provide overviews of specific algorithms:
- A complete guide to k-nearest-neighbors
- An introduction to random forests
- An explainer of Kalman filters
The following resources provide overviews of dimensionality reduction:
- An overview of dimenstionality reduction techniques
- An introduction to principal component analyses
- The bluffers guide to PCA video
The following resources cover other topics in machine learning:
- An overview of how physics connects to machine learning, by Jaan Altosaar