Best mathematics books for self study pdf | FREE
Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations.
This is a wonderful, short, easy-to-read book covering a wide variety of techniques applicable to a wide variety of mathematical problems - from making good guesses to evaluating integrals and differential equations. Not only is this book free-of-charge, but there's an accompanying OCW course on MIT, as well as a course offered through edX. The edX course is archived as of writing this, but it can still be an extremely valuable resource! Both courses include video lectures, assignments and solutions. Given that it's just over a hundred pages and that there are accompanying video lctures, as well as solutions for the assignments, it's ideally suited for self-study. Some other aspects of the book that makes it very suitabe for self study are that it doesn't require a lot of prerequisites - some algebra, trigonometry and the basics of single-variable calculus - and that there are several subjects within it, none of which build upon each other. If you dont understand something, skip to the next chapter!
Written by Gilbert Strang of MIT, this is a wonderful introduction for anyone into the world of calculus.
This is an extremely comprehensive introduction to calculus, starting from the very basics and building up to a very advanced level. Not only is professor Gilbert Strang's style of writing very suitable for self study, he and MIT have very generously provided solutions to half of all the exercises in the book (and these are numerous). Not only is the book free for everybody to read, so are the solutions! Gilbert Strang and MIT have also produced video lectures covering the highlights of calculus. I've written more about the book here.
Introduction to Probability
A very comprehensive introfuction to probability, by Dimitri P. Bertsekas and John N. Tsitsikilis.
At almost 300 pages, there's a lot of material that's covered in this book. So why is this one particularly well suited for self study? Well, it doesn't assume much in terms of prerequisites from the reader. It starts with the very basics: sample spaces, basic probability, random variables, expectations, and moves on to the bernoulli and poisson processes, markov chains and limit theorems. In addition to its focus on the fundamentals, MIT has produced video lectures and online exercises that go along with this book. You can find the course on the edX website here.
This is a bit different from the rest of the books on this list, and I was a bit hesitant to include it. Linear Algebra Done Right is a fantastic book to learn linear algebra from, but this is the abridged version. What does that mean? No proofs, no examples and no exercises. So why include it? Well, it's a lot easier to read than a full-fledged math book, and you can still get a lot out of it. Whether you're reading it as a preparation for a real course, or reading it alongside an other more complete book, you can still get a lot out of it. And it's free. And as with many of the other books here, the author has produced videos and is providing them free of charge. You can find them here.
Now that you've covered the basics of linear algebra, it's time to start applying it. Clustering, linear dynamical systems, least squares, validation, feature engineering, classification, multi-objective least squares, constrained least squares, even non-linear least squares.
Mathematics for Computer Science
All of the mathematics you could possibly want to know for computer science. Written by Eric Lehman of Google, F Thomson Leighton of MIT and Albert R Meyer of MIT.
At just under a 1000 pages, this is a tome of a book. It covers proofs - the basics, well ordering principle, logic, infuction, and more. It then goes on to explore structures: number theory and divisibility, direcred graphs, networks, simple graphs, planar graphs and more. After covering structures, it moves on to counting: asymptotes, cardinality rules, and generating functions. Of course, no book on mathematics for computer science would be complete without covering probability and this book does a good job of covering the parts most useful to programming. The last part is about recurrences and I wish it were longer. It's a great book. And, like with many of the other books here, there are accompanying video lectures. The book covers a much wider range and in more depth than the lectures and assignments. You can find all of the accompanying materials here.
This book is about generating functions and some of their uses in discrete mathematics.
This is a wonderful book. I can't do it enough justice here, so please, at least just go and read the preface. It's a free pdf, so it'll only cost you a couple of minutes. It's worth it.
You will learn so much statistics, and a lot of what would be called machine learning nowadays, if you give this book a good go. Roughly, the material in the book can be divided in supervised and unsupervised learning, and the statistical foundations for both. You can find additional materials here, such as data used in the book, errata, R functions and more. You can find the lectures and assignments offered through edX here. Written by Trevor Hastie, Robert Tibshirani and Jerome Friedman. This is the second edition.