100 books like Linear Algebra Done Right

I like Prof. Cohen's book because it includes computational examples based on Python and NumPy to illustrate each concept. This is the way I like to think about linear algebra concepts.

Yes, it's important to understand the formulas and theoretical ideas, but applying linear algebra operations in the real world will always involve some computational platform and not pen and paper. This is the only book I know that shows readers the practical computational linear algebra in parallel with the theory.

The author provides computational notebooks for each chapter on GitHub, which makes it easy to explore all the material from a code-first computational perspective.

Prof. Strang has been teaching linear algebra at MIT for more than 60 years! This wealth of experience shines through in his book, which covers all the standard concepts using clear and concise explanations that have been polished through time and contain just the right amount of details.

The book is accompanied by a whole course of video lectures available through MIT OpenCourseWare or via YouTube. I learned a lot from Prof. Strang's approach to teaching; in particular, I appreciate the visualization of the fundamental theorem of linear algebra and his explanation of the matrix-vector product from the column picture and the row picture.

If you want to learn linear algebra, you can't go wrong with this classic.

This book has been a bit of an inspiration for me, and I use it regularly as a reference.

First of all, the content is complete and covers all the standard topics, including complete proofs. I like Heffron's book particularly because of the comprehensive exercises with complete worked solutions. It's hard to over-emphasize the importance of solving problems when learning, and this book has A LOT of them, which makes it an excellent choice for anyone learning on their own.

The author also provides lots of bonus material through his website, including slides, homework assignments, and a video lecture series. Last but not least, the entire book is released under an open license, allowing instructors to adapt and customize the material.

This is a good example of a book that makes a complicated topic accessible and easy to understand. Strictly speaking, this is not a linear algebra book, but quantum computing is so closely linked to linear algebra that I'm including this gem.

Prof. Wong covers all quantum computing topics in a straightforward and intuitive manner. He goes out of his way to prepare hundreds of examples of quantum circuits that made my life easy as a reader. What I like particularly about this book is that it explains all the derivations and all the details without skipping any steps.

I can recognize the work of a true master teacher: whenever I ran into a confusing concept, it was explained a few lines later, as if reading my mind.

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

Oakley is best known for her co-instruction of Learning How to Learn, one of the most popular Coursera courses that has had millions of students. This book offers a science-driven perspective for how to get good at math. Oakley walks her talk too, specializing in linguistics she only became a professor of engineering later, despite some difficulties with math.

For decades, the most famous opening chord in rock and roll was an unsolved problem, since no one could reproduce it. But in 2004, Jason Brown, a professor at Dalhousie University, used mathematics to recreate the opening chord of the Beatles hit song, “A Hard Day’s Night”. I remember when newspapers around the world reported on Jason’s findings, as I was at Dalhousie at the time, as one of Jason’s Ph.D. students.

Jason’s Beatles story serves as the final chapter in this wonderful book, a collection of short vignettes about how mathematics relates to every aspect of our lives, including garbage pickup routes, grocery shopping, political polling, and social networks. The book’s thesis is that as we understand mathematics better, our lives become more meaningful. I couldn’t agree more.    

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.

Having read or browsed many books dedicated to the mathematics of options and other derivative instruments, I unquestionably consider Neftci’s book as by far the best choice.

Starting with the fundamentals, it goes much further than a simple “introduction”, and typically fits with the needs of a “quant” specializing in options, with a good balance between pure theoretical, mathematical developments (such as Partial Differential Equations, Girsanov theorem, Markov processes, etc) and practical applications on option pricing. 

Have you ever been to a mathematics lecture where the speaker wore a tuxedo and baffled the audience with his mystifying knowledge of numbers? Well, I have and the speaker was Arthur Benjamin, who combined mathematics and magic. He even displayed this knowledge with Stephen Colbert on his earlier show The Colbert Report. It is our good fortune that he describes much of this mathematical wizardry in this fascinating book.