Mathematic preliminaries ======================== Typical prerequisites for statistics and econometrics are: - linear algebra - calculus - probability They usually take 2-4 semester in college. Linear algebra is fully covered by [VMLS][VMLS], and [Gilbert Strang][GS] lectures are highly recommended. Probability is exposed in [PSC][PSC], even though it is a compact reference, not formally a textbook. [Scipy lectures][Sci] are a great one-stop resource for numerical computing basics. Linear Algebra -------------- - [Vectors, Matrices, and Least Squares (VLMS)][VMLS] [VMLS]: http://vmls-book.stanford.edu - [Gilbert Strang lectures on linear algebra][GS] get vocal [acclaim from the former students](https://twitter.com/ryxcommar/status/1199677021816799233), as a kind of course that helped students gain a lot of confidence in the subject. [GS]: https://ocw.mit.edu/faculty/gilbert-strang/ See also: - [Computational Linear Algebra](https://github.com/fastai/numerical-linear-algebra) repository from *fast.ai*. Calculus -------- I do not have a one single source to recommend for calculus yet. Maybe it is a basic subject with no reason for a new basic textbook to appear in. However, renewed interest for differentiation problems cames from deep learning subject area. *The Matrix Calculus You Need For Deep Learning* by Terence Parr and Jeremy Howard is a prime resource for matrix calculus, it is accessble as: - [arxiv preprint](https://arxiv.org/abs/1802.01528) - or as an nicely designed [web page](https://explained.ai/matrix-calculus/index.html). Authors recommend [Khan Academy differential calculus course](https://www.khanacademy.org/math/differential-calculus) as a starter, but it is not a single downloadable reference. *fast.ai* also has a [calculus intro](http://wiki.fast.ai/index.php/Calculus_for_Deep_Learning), going rather quickly from one-arg function derivatives to deep learning. Probability and statistics -------------------------- - [Probability and Statistics Cookbook (PSC)][PSC], concise reference [PSC]: http://pages.cs.wisc.edu/~tdw/files/cookbook-en.pdf - [Introduction to Probability](http://pi.math.cornell.edu/~web3040/amsbook.mac-probability.pdf) by Charles M. Grinstead and J. Laurie Snell - [An Introduction to Probability Theory and its Applications (Volume 1)](https://archive.org/details/AnIntroductionToProbabilityTheoryAndItsApplicationsVolume1) by William Feller See also:

5 must-haves for any #Probability library:

Technical: Feller-Volume 1
Classic: Kolmogorov-Foundations of Prob
Real world: Taleb-Antifragile @nntaleb
Application: Grosjean-Exhibit CAA (alt. Jacobson-AAP)
Bio: Thorp-Man for all Mkts

What did I miss? RT/reply w your 5

— Harry Crane (@HarryDCrane) January 10, 2020
Numerical computing -------------------- - [Scipy lectures: one document to learn numerics, science, and data with Python][Sci] [Sci]: http://www.scipy-lectures.org Machine learning-related ------------------------ - [Mathematics for Machine Learning](https://mml-book.github.io/) by Marc Peter Deisenroth, A Aldo Faisal, and Cheng Soon Ong - [A Beginner's Guide to the Mathematics of Neural Networks](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.3556&rep=rep1&type=pdf) by A.C.C. Coolen, HT [@iamtrask](https://twitter.com/iamtrask/status/1165911962053677057) Other ----- - [140 unsorted formulas with a bit of Portugese](https://drive.google.com/file/d/0B0RLknmL54khQlhGUzFUWEtncTA/view), nice for a bulk review. Prepared by [Rubens Zimbres](https://github.com/RubensZimbres).