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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20. Listed in the Popular books section, aimed at a general audience rather than students.
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.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. The page carries a footnote: "Some of the companies listed above have sponsored 3Blue1Brown videos in the past, but the recommendations here are not sponsored or advertisements in any way." He does not say which companies, so every commercial learning platform on the page is labelled as a disclosed relationship.
Also, and I'll admit I'm biased because it was built by friends, the act of actually writing math questions on Itempool is a delight
Post sharing the software and hardware setup he used for a run of 10 live-streamed math lectures, written for teachers moving classes online. He discloses in the quoted sentence that Itempool was built by former Khan Academy coworkers of his.
It's an online graphing calculator that makes it very simple to whip up surprisingly complicated graphs. I found it abundantly useful for live presentations over a stream, and what's nice is that you can share the links of what you build so that students can play with them.
Post sharing the software and hardware setup he used for a run of 10 live-streamed math lectures, written for teachers moving classes online. The tool being described here is Desmos, named in the preceding sentence and heading.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20. Listed in the Popular books section, aimed at a general audience rather than students. The commentary opens by linking his Math With Bad Drawings blog.
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.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20. Listed in the Popular books section, aimed at a general audience rather than students.
Leave it to Matt Parker to write an entire book about making mistakes in math.
His Book recommendations page, introduced as "a small list of textbooks I've thoroughly enjoyed at some time in the past, with the added condition that each one stands out in some way from the surrounding body of math texts". The cover images link to Amazon through amzn.to short links that resolve to URLs carrying the affiliate tag 3b1b04-20. Listed in the Popular books section, aimed at a general audience rather than students.
I know a few of the people there, and I can vouch for the fact that they are extremely thoughtful about what makes for good learning. It shows in the product. Rather than putting lectures and videos front and center, problems and puzzles take precedence, all presented in a structured progression.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. The page carries a footnote: "Some of the companies listed above have sponsored 3Blue1Brown videos in the past, but the recommendations here are not sponsored or advertisements in any way." He does not say which companies, so every commercial learning platform on the page is labelled as a disclosed relationship.
Mathigon is a very beautifully done set of interactive articles on all sorts of fun topics in math. The experience sits somewhere between reading and playing a game, with a really wonderful blend of artwork, technology and pedagogical clarity.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. The page carries a footnote: "Some of the companies listed above have sponsored 3Blue1Brown videos in the past, but the recommendations here are not sponsored or advertisements in any way." He does not say which companies, so every commercial learning platform on the page is labelled as a disclosed relationship.
They are probably most famous for the videos Sal does, but arguably the site is most valuable as a source of problems you can drill on, starting from the very basics if necessary. I may be biased, though, given that I used to work there!
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. He discloses in the quoted sentence that he is a former Khan Academy employee. The page carries a footnote: "Some of the companies listed above have sponsored 3Blue1Brown videos in the past, but the recommendations here are not sponsored or advertisements in any way." He does not say which companies, so every commercial learning platform on the page is labelled as a disclosed relationship.
Half of the appeal here comes from the delightful bits of math this channel covers, often with novel ways of presenting otherwise extremely complicated topics to make them easier.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
I'm guessing if you're here, you already know about Numberphile. If somehow you don't, it's a great channel full of interviews with mathematicians.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
This channel is more whimsical and comedic, but that's not to say there isn't a lot of serious math it covers.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
She covers ideas from physics and math explained simply and unusually honestly.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
this channel is full of high production quality and well-written videos. There are also several series on machine learning, the topics underlying self-driving cars, so this is certainly one of the more applied math channels out there.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
If you like seeing how to work out integrals in all sorts of crazy ways, boy is this the channel for you. Steven is a math teacher, and the videos have a feeling of being in office hours, honestly working through problems with a very skillful and enthusiastic teacher. Many of the problems covered are the kind you might come across in school, and many or just for fun.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
If you want good, honest worked examples of practice problems, especially for calculus, it's hard to find a deeper well of examples than what this channel provides.
His Recommendations page, "Other places online to explore math", a companion to his book recommendations post. From the Other YouTube channels section; these are individual creators, not the companies the sponsorship footnote refers to.
In OBS you can set up keyboard shortcuts, so I set up a few to associate certain keys under the lefthand of my keyboard with different scenes so that I could switch between them easily
Post sharing the software and hardware setup he used for a run of 10 live-streamed math lectures, written for teachers moving classes online. OBS did the heavy lifting for the streams.
USB Audio Interface to take the feed from the mic to the computer (Focusrite Scarlett Solo)
Post sharing the software and hardware setup he used for a run of 10 live-streamed math lectures, written for teachers moving classes online. From the equipment list; the gear was lent to him by Ben Eater.
A lav mic (More specifically a Rode Lavalier Lapel Omni-Directional Condenser Microphone)
Post sharing the software and hardware setup he used for a run of 10 live-streamed math lectures, written for teachers moving classes online. From the equipment list; the gear was lent to him by Ben Eater.
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