Grant Sanderson
Mathematician and creator of the 3Blue1Brown YouTube channel and the Manim animation library.
An Introduction to Thermal Physics by Daniel Schroeder
Despite my aim to keep this list purely about math books, I cannot help but include this one in the list. Simply put, it's one of the most enjoyable textbooks I've ever read, giving a very satisfying first-principles understanding of what thermodynamic concepts like temperature and entropy really are, and how we can to understand them.
on 3blue1brown.com · 1 Jun 2020
Change Is the Only Constant: The Wisdom of Calculus in a Madcap World by Ben Orlin
I feel like Ben Orlin solved what was previously an unsolved problem with this book: Teach calculus in a way that is as enjoyable to those unfamiliar with the topic as it is to experts who use it every day. I, for one, was laughing from page 1.
on 3blue1brown.com · 1 Jun 2020
Chaos: Making a New Science by James Gleick
This is one of my all-time favorite books, closely followed by everything else Gleick has written. It gives an inspiring look at the birth of a new field, and unlike many popular science books, it manages to talk substantively about the math that was being discovered.
on 3blue1brown.com · 1 Jun 2020
Fourier Analysis: An Introduction by Elias Stein and Rami Shakarchi
Not only is this a wonderful foundation for Fourier analysis, with a surprising and satisfying application to prime numbers given in the last chapter, but it's also a good starting point for analysis as a whole. Stein and Shakarchi have a series of four excellent books on the foundations of analysis, based on a now-famous series of lectures given at Princeton.
on 3blue1brown.com · 1 Jun 2020
Humble Pi: A Comedy of Maths Errors by Matt Parker
Leave it to Matt Parker to write an entire book about making mistakes in math.
on 3blue1brown.com · 1 Jun 2020
Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz
This is another wonderful book aiming to popularize calculus (2019 was a good year for that goal). What I enjoyed about this one is how broad a view Strogatz takes of the origins of calculus, ranging from the clever proofs Archimedes was developing up to Fourier's study of heat.
on 3blue1brown.com · 1 Jun 2020
Information Theory, Inference and Learning Algorithms by David MacKay
Information theory has a way of shaping the way you view many things in math, computer science, physics, and beyond. It's one of those fields that takes ideas that you wouldn't think of as being quantifiable or rigorous and makes them so.
on 3blue1brown.com · 1 Jun 2020
Nonlinear Dynamics and Chaos by Steven Strogatz
Steven Strogatz is one of the most well-known math communicators, and for good reason. He has a way of making you love a problem before diving into telling you how it's solved. Chaos is an incredibly fascinating field, which has only emerged relatively recently in the history of math. This is the well-deserved gold standard for understanding what it's all about.
on 3blue1brown.com · 1 Jun 2020
Ordinary Differential Equations by Vladimir Arnold
If you want to understand differential equations, but more from the pure math side of things, Arnold gives a wonderful picture of what the field is all about, with a mixture of high-level intuitions and low-level details, with a satisfying focus on visual and physical intuition along the way.
on 3blue1brown.com · 1 Jun 2020
Primes of the Form x^2 + n y^2 by David A. Cox
This might seem like a bizarrely specific question to write a whole book about, but that's actually the charm. It covers deep and general ideas, such as class field theory and elliptic functions, which are usually only taught to graduate students, but Cox approaches it all from an extremely concrete question which Fermat thought about.
on 3blue1brown.com · 1 Jun 2020
Proofs from the book by Martin Aigner and Günter Ziegler
If you like clever proofs, this is the book for you. It's filled with some of the most elegant arguments in math, taken from combinatorics, geometry, graph theory, analysis, set theory, and more. I can't think of any other books with a higher density of "aha" moments.
on 3blue1brown.com · 1 Jun 2020
The Art Of Probability by Richard Hamming
Hamming was a practitioner, spending much of his career in Bell Labs, so unlike many books on probability, this stays grounded in the kind of intuitions that come up a lot in solving practical problems. It has countless helpful puzzles and problem-solving tricks which are organized in such a way as to give a sense of the deeper theory underlying probability and statistics.
on 3blue1brown.com · 1 Jun 2020
The Art of Problem Solving by Richard Rusczyk
The original Art of Problem Solving book by Richard Rusczyk, by the way, was one of the things that made me fall in love with creative math as a young student.
on 3blue1brown.com · 1 Jun 2020
The Cauchy-Schwarz Master Class by J. Michael Steele
The strength of this book is the central role it places on problems. Its aim is to teach you about inequalities, which are the backbone of analysis. But it's all too easy to teach the statement of an inequality without conveying the intuition for when and how you'd use it. By focusing on well-chosen puzzles, this book does an admirable job circumventing that risk and leaving you with the feeling of having trained a skill, rather than having learned a list of facts.
on 3blue1brown.com · 1 Jun 2020
The Princeton Companion to Mathematics by Timothy Gowers (and many, many others)
Books can never replace the intuition available if there's a professor down the hall whose door you can knock on to start asking questions. However, this book gets pretty close.
on 3blue1brown.com · 1 Jun 2020
Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John Hubbard and Barbara Burke Hubbard
This is what I wish I learned from in my freshman year of college. The part of it about linear algebra is one of the best linear algebra resources out there, and remainder shows you how those tools apply to non-linear mathematics.
on 3blue1brown.com · 1 Jun 2020
Visual Complex Analysis by Tristan Needham
As the title suggests, this offers a highly pictorial introduction to complex analysis. I would not use this as the only text to learn about complex analysis, but Needham does a marvelous job of conveying the beauty of the subject, with numerous helpful intuitions for otherwise famously tricky ideas.
on 3blue1brown.com · 1 Jun 2020
Visual Group Theory by Nathan Carter
Another text with a titular promise to focus on pictures, this one tackles a subject which is more commonly taught purely symbolically. One of the most important things for any student learning about groups to understand is just how many different ways there are to think about a group, and how different views might be helpful in different contexts. Again, I wouldn't use this as the only book to understand the topic, but it offers a refreshingly different perspective on the topic from most others out there to help arm your arsenal of intuitions.
on 3blue1brown.com · 1 Jun 2020
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