100 books like Linear Algebra

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.

In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.

My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.

The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.

I highly recommend this book as a second book on linear algebra.

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.

I used this book for several years starting in 2013 when the first edition came out. It absolutely holds up today. Learning the Python language (the syntax) is one thing. Learning how to design programs using this syntax is another. We need both but, unfortunately, many books forgo the latter for the former. Not this book! I like the Problem Solving and Worked Example sections: they help learners apply a disciplined, step-by-step strategy to programming projects. There are multiple, varied contexts here as well, which helps capture a broader base of learners. Bonus feature: the Computing & Society boxes.

The biggest challenge to setting out a worldview within a universe is describing the detail about entities that imbues the feelings associated with living as those entities within it. Banks manages the sensation of living beings masterfully, where they are so alien and so abstract your pure imagination is put to the test. What would life be like for you as a jelly blob that flies around a gas giant? Pretty damn good thanks to Iain, and it's something I tackled in my book too with not nearly as much success it seems, at least yet.

Readers of this list may be surprised that there are no books by Benoit Mandelbrot, the father of fractals. I found his books fascinating but frustrating. Feder’s book, by contrast, was readable and usable.

This book taught me how to do fractal analysis. While Feder’s book has nothing to do with markets, it has everything to do with applications. While I reuse much of Feder’s methodology in my books, readers will find it useful to see other practical applications of fractal analysis.

From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.

But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.

She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).

A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.