Hey nerds, I’m planning on going back to school in a few years and want to smash the math proficiency test so I don’t have to spend years relearning things that will probably only take me a few months at most. What books do you all recommend to get me from college algebra to Calc II or III?
Bonus points for stats and physics recs, as well.


For the advanced calculus (depending on your university, usually either linear equations and ordinary differential equations or multivariate calculus is calc III) I learned multivariate calculus from Marsden and Tromba Vector Calculus. I don’t remember the other textbooks I used for calc in undergrad, but I found trying to search for what the textbook I used that UC Berkley has one of their ODE textbooks free online. Can’t verify the quality, but since it is free, you could just look and see if you find it useful.
EDIT: I found that I used Stewart Calculus books for my Calc I and II classes. They were alright. Also, Kline’s calculus book is one I heard of other universities using and that is now a Dover book. I never used it, but it is a common introductory book and would be cheaper than others for a physical copy.
For stats and physics I have a bit better recommendations. (I don’t recommend using the provided Amazon links to buy them, but just so that you have the relevant info)
Eisberg and Resnick is the entry level lower division optics and quantum mechanics text book (https://www.amazon.com/Quantum-Physics-Molecules-Solids-Particles/dp/047187373X)
And there is the entry level (freshman science major) mechanics and electromagnetics books with Resnick as the first author. The other authors change with editions, but my Dad used those books when he was in college, so you should be able to find very cheap old editions. I did actually use the Eisberg and Resnick book, so I assume the other Resnick books should be good.
Griffiths Quantum mechanics and electrodynamics would be the next step, but that is getting into ~3rd year (junior year) levels (https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/1107189632 and https://www.amazon.com/Introduction-Electrodynamics-David-J-Griffiths/dp/1009397753/140-6128986-2705400?psc=1)
Edit: If you are interested, Kittel and Kroemer’s Thermodynamics is a common ~2nd year introduction to thermodynamics and statistical mechanics. I used it and thought that it was decent (https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp/0716710889)
Also, broadly, I would say that if you are looking for a book on a particular subject, a good place to start is Dover books (https://store.doverpublications.com/pages/math-science). They buy a lot of books from other publishers and print them very cheaply. And so they sell very highly regarded books on their topics for very cheap. Many grad school classes used their textbooks and also I still use several of their books as references currently in my job.
For statistics, I have briefly used Mandel’s The Statistical Analysis of Experimental Data, which I remember being very introductory. And I see Kolmogorov https://store.doverpublications.com/collections/math-probability-and-statistics/products/9780486821597 being cited and used as an introductory text book. But I have never read that one myself.
And of course, most of the books I mentioned, including the Dover catalog, will likely be found on libgen or annas-archive.
Griffiths QM is kinda meh. It’s the one I used in my courses, but later while trying to relearn, I found Shankar’s Principles of Quantum Mechanics to be pedagogically superior. From the intro,
Shankar’s lectures are on YouTube as well.
A QM book is probably beyond the immediate need of the OP, but this might be useful to someone.
It is better, but because of going more fully into the mathematics immediately, it is a bit more advanced. My undergrad university used Griffiths for upper division QM and Shankar for Graduate level. Which is why I recommended it earlier for self training. But there is value in just immediately diving into the full mathematical framework right away.
I use amazon to get the ISBN and then download from Anna’s Archive lol