A First Taste of Algorithms

Going Deeper

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A short, opinionated shelf — where to go when this book runs out. It is arranged the way the book was: the friendly first steps, then the standard references, then the machines that learn, then the edge of the map. Nothing here is required, and none of it is a textbook you must finish. All of it is an invitation.

Read next — and now

• Brian Christian and Tom Griffiths, Algorithms to Live By (2016). The gentlest possible sequel: the very ideas of this book — searching, sorting, when to stop looking, how to guess well — turned on everyday life, from packing a closet to choosing an apartment. No code, no equations, all intuition. Read it the month you finish this one.
• Grant Sanderson, 3Blue1Brown (videos, free online). The Essence of Linear Algebra and Neural Networks series are the clearest moving pictures of the mathematics under Chapters 8 and 9. Watch the neural-network series the week you finish Chapter 9, and the descent of Chapter 8 will turn from words into a thing you can see.

The standard references — for the reread at 17

• Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein, Introduction to Algorithms (4th edition, MIT Press, 2022). The book the whole field calls CLRS — the comprehensive reference for everything in Chapters 1 through 7, with every proof in full. This is the MIT algorithms book; when a university course says “the algorithms textbook,” it means this one. We kept ours to a first taste on purpose. This is the full meal, and you are now ready to sit down to it.
• Steven Skiena, The Algorithm Design Manual (3rd edition, 2020). Warmer and more practical than CLRS, full of “war stories” of real algorithms meeting real problems. The best companion for someone who wants to use this material, not only prove it.
• Charles Petzold, The Annotated Turing (2008). Walks line by line through Turing’s 1936 paper — the halting-problem argument of the epilogue, in the original. Demanding, and worth it once the epilogue has made you curious about where the wall came from.

The machines that learn — further into Chapter 9

• Andrej Karpathy, Neural Networks: Zero to Hero (video course, free online). Builds, from nothing, exactly what Chapter 9 builds: a tiny automatic-differentiation engine (micrograd) and then a small language model (makemore, then nanoGPT). If Chapter 9 was your favorite chapter, this is the next thing to do with your own hands.
• Michael Nielsen, Neural Networks and Deep Learning (free online book). Derives backpropagation from first principles, with the clearest explanations of why it works that exist anywhere.

The edge of the map — years from now

• Avi Wigderson, Mathematics and Computation (Princeton University Press, 2019; free PDF from the author). Wigderson — winner of both the Abel Prize and the Turing Award — is among the deepest living authorities on the P-versus-NP question and on the role of randomness (Chapter 7’s coins) in computation. The book is written for mathematicians; treat it as a mountain to keep in view, not one to climb yet. That the epilogue’s open question has a living literature this deep is itself the point.
• The P vs NP Problem, Clay Mathematics Institute. The official statement, by Stephen Cook, of the epilogue’s great open question — one of seven Millennium Prize Problems, with a million-dollar prize unclaimed. Short, precise, and exactly as unsolved as the day you read it.
• Scott Aaronson, Quantum Computing Since Democritus (2013), and the blog Shtetl-Optimized. The most candid, funny, and deep writing anywhere on what computers can and cannot do. Start with the blog; read the book when the mood for the deep end strikes.

One closing word, the book’s own. Every title on this shelf was written by someone who refused to do most of the work and then proved the refusal correct — and who left the door open behind them. Go in.

All 32 chapters of A First Taste of Algorithms · Foundations · All courses