The best books on mathematical and algorithmic thinking

Steven S. Skiena Author Of The Algorithm Design Manual
By Steven S. Skiena

The Books I Picked & Why

The Art of Computer Programming: Volume 3: Sorting and Searching

By Donald Knuth

The Art of Computer Programming: Volume 3: Sorting and Searching

Why this book?

Knuth’s unique mix of playfulness and rigor came to define computer science as an intellectual discipline: computer science didn’t really have anything to do with computers, but everything to do with a particular way of seeing the world.  Just browse and wonder at the beauty and precision achieved in these books.   

Volume 3 (Sorting and Searching) is my personal favorite, and I encourage you to start there. During the pandemic, I finally got around to reading Volume 4A (Combinatorial Algorithms), which was published thirty plus years after Volume 3. It was the same feeling I had watching the movie The Phantom Menace years after growing up with the original Star Wars trilogy. I had forgotten just how unique and distinctive Knuth’s Art of Computer Programming is.


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Algorithms to Live by: The Computer Science of Human Decisions

By Brian Christian, Tom Griffiths

Algorithms to Live by: The Computer Science of Human Decisions

Why this book?

Thinking algorithmically changes the way one thinks about life. Algorithms to Live By does an amazingly good job of explaining real algorithm design ideas to a general audience in the context of processes optimizing real-life decisions. You will learn why you should wait at least (n/e)th of your potential dating life to select the right spouse (I did ☺).

Searching and scheduling are critical aspects of the human condition, and doing them optimally are classical problems in algorithm theory.  This book will help you do them better in your life, by helping you understand how to solve them best algorithmically.


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How to Solve It: A New Aspect of Mathematical Method

By George Polya

How to Solve It: A New Aspect of Mathematical Method

Why this book?

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.



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How Not to Be Wrong: The Power of Mathematical Thinking

By Jordan Ellenberg

How Not to Be Wrong: The Power of Mathematical Thinking

Why this book?

The world is a complicated place, and it is often difficult to see it clearly. Mathematical tools like logic and proofs let us understand it better. This popular book is a more modern and less technical primer in thinking about the world through a mathematical lens. 

For many readers, it will open the eyes as to why much of that math you learned in school was there in the first place, and refresh your thinking about it. Statistical reasoning is particularly important in today’s data-driven world, and this book will help you realize when someone is lying to you through statistics.


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Adventures of a Mathematician

By S. M. Ulam

Adventures of a Mathematician

Why this book?

This is my favorite autobiography by a mathematician – admittedly a pretty small genre. Stan Ulam was a brilliant theoretical mathematician working in very abstract areas of set theory. But this gentle “theoretician” developed the critical ideas leading to the hydrogen bomb and pioneered the use of computer simulations in science, back in the days when computers were room-sized beasts with less computational power than your cellphone.

I was thrilled to learn that this book was made into a feature film in 2020. I cannot imagine it was easy to get a studio to greenlight this project. I make it a point to contractually retain the film rights for all my algorithm books, but confess my publishers don’t fight me very hard on this. 


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