Resources for math and physics
Tags: Math, Learning, Resources, Science

I seem to keep recommending a similar list of books that are the ‘standard’ to people, along with some assorted websites and YouTube videos. Someone suggested I make an article, so here we are. This article will probably be updated occasionally.

I should make a disclaimer that I’m a highschool student. There’s a reasonable percentage of these books that I have not read, or at least not read in their entirety. This is compiled from what has clicked with me as I’ve jumped from subject to subject, and what I’ve heard others reference and mention over and over again. Sometimes, you just need a place to start, and I’m hoping to help provide that. I’ve also included links to some other recommendation lists in this list, and you should feel free to mention sources you like in the comments.

The first thing that’s really important when trying to learn something on your own is this: if you can’t figure something out from one resource, try a different one. Odds are, it’s the resource, not you. Of course there are times when you’ll need to just buckle down, but there’s no point bashing your head against a brick wall when you could bash it against a wall made of marshmallows.

The other thing to note is how to obtain these books. First, check your local used bookstore. Even if the books you find are not ‘well known’ or ‘standards’, there can be some real gems. (I also personally prefer print to online for reading.) Next, try googling it. Odds are there’s a pdf out there. Then, check libgen. If it’s not on there, you’ll probably have to pony up the money, so hopefully it’s a really good book.

Math

For math up through precalculus, the standard recommendations are the YouTuber PatrickJMT and, even better, Khan Academy. Practice until you know it, and then practice a little more. I also like the ‘1000 practice problems’ and ’workbook’ books by For Dummies — just lots of problems with fully worked solutions. I got one of those after a took algebra, and that’s what made factoring a breeze for me. Beyond precalculus is when it starts getting interesting.

Calculus

3blue1brown’s excellent video series

Spivak, Spivak, Spivak. Did I say Spivak? (Not to be confused with his textbook Calculus on Manifolds, which I’ve heard is also good, but is definitely not single variable calculus.)

Apostol is a common text, and some may like it, but I found it rather…dry. I like math books that are able to give an intuitive sense of where we’re going and why, and Apostol fits the more standard format of theorem, proof, theorem, proof, oh look a lemma, theorem, proof. It does have the advantage of covering pretty much everything.

Paul’s Online Math Notes are another pretty well known source, but again — not a huge fan. A lot of people like them, though, so check it out!

Silvanus Thompson’s book, available free on Project Gutenberg

Gonick’s Cartoon Guide to Calculus is fun. Anything with cartoons gets my vote.

Burn Math Class has some nice explanations for calculus (and also has some nice explanations of precalculus material and the thought process that goes on behind mathematics, mixed in with some ranting about how the math education system in America is currently set up)

Vector calculus — Div, Grad, Curl, and All That

Multivariable — The guy behind 3blue1brown has a good playlist, but associated with Khan Academy instead of his normal account.

Differential equations — you guessed it, 3blue1brown

Linear algebra

3blue1brown (honestly, just watch all of his videos) has a fantastic series called The Essence of Linear Algebra. Watch this and do problems and you’re pretty much good to go for practical applications. If you want to do pure maths, you should probably read a textbook too.

Gilbert Strang’s book is considered a classic

I own Elementary Linear Algebra by Larson and Edwards and like it. I picked it up cheap at a used bookstore and it has served me well.

Higher math

Set theory — Naive Set Theory by Paul Halmos. So good.

Credits to Abstruse Goose

Analysis — Baby Rudin, followed by Papa Rudin, then Grandpa Rudin

Topology — the classic text is Munkres’ Topology, but there’s a really great YouTube playlist here (the creator of which has some really good math videos in general…and also some really good medicine videos, if that’s your shtick)

Abstract Algebra — I’ve heard that the classic is Artin’s Algebra, but I’ve never even snuck a glimpse at it. I have a book by Durbin called Modern Algebra that seems decent, but of all the math books I’m recommending here, this is possibly the spot I feel least qualified to give a recommendation.

General

This has almost everything — it is called the Infinite Napkin

Look up lecture notes. Seriously.

Check MIT OCW

Did I mention 3blue1brown?

Math Stack Exchange (if you’re looking for a book/resource on something, check through their [resource-recommendations] tag)

If you’re really into high level math, Math Overflow is cool

I feel like if you’re into math, it’d be really nice to read through a history of mathematics, but I’ve never found a very good history of math (admittedly, I haven’t looked very hard).

Chicago math books list

This cool website also gives recs

In the spirit of the previous one, see also this website

How to Solve It — never read it, but I’ve heard over and over that it’s a classic

List of unsolved problems in maths

Physics

General

Young and Freedman — a classic college physics text. We’re using it in my Physics C class.

Halliday, Resnick, and Walker — another classic college physics text.

Physics Hypertextbook

Arnold’s Mathematical Methods of Classical Mechanics

How to become a good theoretical physicist, according to Gerard t’Hooft

Chicago book list

Landau & Lifshitz — their books are considered classics, but also very dense. Go after them at your own risk. If you work through them and understand what is in them, you will be very good at physics.

Classical mechanics

Kleppner & Kolenkow — good introductory mechanics textbook.

Goldstein — an advanced and difficult mechanics textbook.

Spivak’s Physics for Mathematicians: Mechanics I — different take on the subject if you’re more of a math person

Hamiltonian Dynamics, by Kilmister — old (I think it might be out of print), but short and to the point.

Susskind’s The Theoretical Minimum. Quite possibly one of the better and more to the point books I’ve gotten ahold of. Covers the relevant maths as well, so very self contained.

Susskind’s Special Relativity and Classical Field Theory. The third book in his theoretical minimum series. Neither topic is classical mechanics, yes. I didn’t quite know where to put this one.

Electromagnetism/circuits

Jackson — well known for its exceedingly difficult, but also well written, problems. I bear no responsibility for any pain and late nights.

There should be more here. I am not qualified to recommend stuff here, but Jackson is a name I hear over and over.

Forest Mims III has a bunch of good books for learning about circuits. Make also has two nice books on electronics.

General Relativity

Zee — called Einstein Gravity in a Nutshell, though it’s quite long for a nutshell (he wrote another book about QFT titled similarly that is actually a nutshell). In spite of this false advertising, it is an excellent book that covers quite a lot in a way that is feasible for a reader that knows some calculus/linear algebra and some highschool physics.

Carroll’s Spacetime and Geometry — another introductory book, but harder than Zee.

MTW — aka, Misner, Thorne, and Wheeler, aka Gravitation, aka the phonebook. Bow down before this masterpiece. Don’t learn from it; use it as a reference. Or, you know, google.

This list (also has good math recommendations)

String theory and M theory by Becker and Schwarz is a name I’ve heard a bit.

Quantum mechanics

Susskind’s Quantum Mechanics — the second book in his theoretical minimum series.

Griffiths’ Introduction to Quantum Mechanics — the textbook most physics students learn with. I have a copy, and it seems like a decent introduction, but I know a couple physicists who curse it and swear by Shankar.

Shankar — longer, more thorough, covers linear algebra as well, fantastic writing. It makes sense why the aforementioned physicists swear by it.

Dirac — Yes, the P.A.M. Dirac. He, unsurprisingly, wrote a text on QM.

Sakurai has a graduate level text on QM.

Quantum field theory

Zee — Quantum Field Theory in a Nutshell.

QED, by Feynman.

Again, there should be more here.

Quantum computing

Nielsen and Chuang — literally the bible of quantum computing. Colloquially referred to as Mike and Ike. If you’re interested in quantum computing, this is your text.

Quantum Computing Since Democritus, by Scott Aaronson. This has been on my wishlist for awhile; I’ve heard it’s quite good.

Michael Nielsen’s videos (yes, the Nielsen of Nielsen & Chuang)

quirk —one of the better simulators out there.

Other notes

LaTeX is really useful if you type up math (and physics). Resources include

I also tend to use overleaf (which merged with ShareLaTeX) because it’s an easy, online, cross-device way to type this sort of thing up. Many people use stuff like texmaker/texlive instead. If you’re creating a website that will have math on it, look into MathJax.

There’s something to be said for reading blogs on interesting new developments on math and science. Here are some nice ones (feel free to suggest ones you like in the comments):

Shtetl Optimized — Scott Aaronson

Terence Tao’s blog

Tim Gowers’ blog

At some point, you’re going to have to start reading scientific papers. Here’s what you should know.