Ask HN: Best books or courses to self study undergrad math subjects? | Hacker News Reader

Ask HN: Best books or courses to self study undergrad math subjects?

27 pointsnewsoul17 comments

For someone out of touch in mathematics and done undergrad in electrical engineering and currently working as a programmer I want to relearn/learn mathematica again. I have done calculus in the past and some matrix algebra and probability in college. But I remember those topics very foggily.

I want to learn undergrad math properly again. Books or courses are my friend in this journey.

I ask you all HNers who have had similar experiences or have suggestions please suggest a path I should follow.

P.S.: Being an electrical engineering grad I know boolean logic and all. But have never formally learned or written mathematical proofs. I want to learn that too.

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If you want thickness:

https://www.cis.upenn.edu/~jean/gbooks/geomath.html

If you want proofs:

https://cseweb.ucsd.edu/~gill/CILASite/

If you want dictionary:

https://press.princeton.edu/books/hardcover/9780691118802/th...

If you want usefullness:

any mathematical physics book will do

https://www.cis.upenn.edu/~jean/gbooks/geomath.html

Approx. 2188 pages

Holy %@^&, you weren't joking about that thing being thick! Imagine a print copy. You could prop your car up on it to change a flat tire or something.

TBF that's probably a few courses bundled together.

Would love to see a thick book for math for General Relativity. I'm thinking about something from Calculus, Algebra to Differential Geometry and Tensor.

As a bonus it should have plenty of exercises to satisfy 20 years of free time for a domestic middle aged male.

Like this

https://www.amazon.com/Mathematical-Methods-Physicists-Compr...

Yup, thanks man!

I won't recommend any specific books, as I don't consider myself enough of a maths expert to have any standing to do so. But what I will suggest is to give the Youtube channel "The Math Sorcerer"[1] a look. He does a LOT of book reviews, talks a lot about self-study, and most of his book reviews include a pretty big focus on which books are or are not really good for self-study.

[1]: https://www.youtube.com/@TheMathSorcerer

I really like MIT's Open Courseware offerings (available on youtube).

From HN, @optbuild shared some math-stuff, e.g.,

- Fourier Transform (https://news.ycombinator.com/item?id=35858725)

- Mathematical Problem Solving (https://news.ycombinator.com/item?id=35858763)

So did @__rito__ (https://news.ycombinator.com/submitted?id=__rito__).

I am also a fan of Complexity Explorer (which @__rito__ shared). Can't say enough great things about Santa Fe Institute.

Chartrand - mathematical proofs (if you don’t have background with proofs)

Then-

Baby Rudin - analysis (first 8 chapters is good)

Dummit Foote - algebra (as much as you can read, groups, rings, fields, even more if you can)

Needham - complex analysis

Friedberg - linear algebra

After that you can go in many directions

Many other interesting courses

Number theory

Representation theory

Probability -> stochastic processes

Statistics

Spivak and Apostol are the two classic intro texts. Apostol is used more in programs that eventually get into physics, while Spivak is used more as a lead-in to analysis.

In my youth, I once wrote a paper just on how Apostol's proof of the fundamental theorem of calculus was more beautiful than Spivak's, and that they were both way better my school's textbook, rofl. In my old age, I recognize that Spivak teaches you incredibly powerful and useful tools in its kinda obtuse approaches to things

Springer literally has a book series called "Undergraduate texts in mathematics". The quality varies from book to book, but overall I would highly recommend taking a look.

Back in university the honor students use Rudin to learn real analysis. My university is a peasant comparing to MIT/Berk but I guess it says something.

A very similar Ask HN post title asking for books and courses for college math was posted less than a day before your post. Why do requests for math courses come up so often?

It's a popular topic around here for sure. Not that that's a bad thing. But one does sometimes wish that people would search first instead of posting the 3,741,231,440'th iteration of more or less the same question. :-)

That said, repeats aren't the worst thing in the world. New members join, or people happen to be on at the right time to catch certain posts where they may have missed the previous one(s), etc.

see also this question asked a couple hours before you asked yours: https://news.ycombinator.com/item?id=35854717

Also consider that this question, or a close variant of it, gets asked about once every 2-3 weeks or so. Using the search feature and searching for "math book" or "math study" or something similar should turn up loads of previous discussion on this topic.

https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

I don't think I've ever seen it repeated so close before (not that I check every day ... but still: when someone's asking a question that's practically identical the the most-recently-asked Ask HN ... you'd think they wouldn't ask :)

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