High school and undergraduate math textbooks for refreshing my skills

macforlife · Sep 11, 2023

Hi everyone, Im new to the forum and physics in general.

I recently started to dig a bit into popular science on quantum mechanics, cosmology, general relativity etc. and found it super interesting ( as everyone on this forum I assume ). I think the time has come for me to dig a bit deeper into the actual physics behind it ( with math involved ), but beforehand I feel like I would like to refresh my high school mathematics.

Im further planning to get deeper into QC, as Im a software engineer.

Can you recommend me some high school and undergrad mathematics books that would set me up for physics later on?
I prefer smaller books that focus on one subject ( let's say calculus, linear algebra etc. ) rather than those bulky 700 pages books that you can't really take anywhere with you.

I will be glad for any suggestions.

Thank you in advance.
Michal

berkeman · Sep 11, 2023

Welcome to PF.

I did a Google search on undergraduate math textbooks for refreshing my skills and got some good hits. You will get other replies with suggestions in this thread, but here is the Google search hit list:

https://www.google.com/search?clien...extbooks+for+refreshing+my+skills&bshm=rimc/1

One of the first hits on the list is this one, which looks promising:

https://www.edx.org/resources/improve-your-math-skills-with-5-free-online-courses

Frabjous · Sep 11, 2023

@mcastillo356 is working his way on his own through Calculus by Adams. Maybe he can give his opinion.
Stewart and Larson are standard Pre-Calc texts.
BTW, for mathbooks with a large number of editions, there is no problem with not buying the current edition.
The goal is to work a large number of problems so the stuff becomes second nature.

symbolipoint · Sep 12, 2023

What @Frabjous said, post #3 is good. Other alternative authors are likely to be good choices also. Visit a library used-book sale and search what you can find there.

Go based on titles of the books, check some of the contents inside and decide if the contents seem to fit what you need. Titles of books usually keep consistency among the many different authors. ( I mean this for lower division undergraduate and high school Mathematics textbooks.)

macforlife · Sep 13, 2023

Do you guys know any good German books as well? For the sake of optimization i like to improve two skills at once, currently German and math.

macforlife · Sep 13, 2023

Also, what would you say are important parts of mathematics for quantum physics and quantum computing in the future?

Frabjous · Sep 13, 2023

You need to know differential, integral and vector calculus very well. (Assumes knowledge of algebra, pre-calc and geometry).
You need to be comfortable with differential equations, partial differential equations and linear algebra.
You need some knowledge of complex analysis.

You do not need to take the theoretical math version of these topics.

berkeman · Sep 13, 2023

macforlife said:

Do you guys know any good German books as well? For the sake of optimization i like to improve two skills at once, currently German and math.

Paging @fresh_42 @deuteron

fresh_42 · Sep 13, 2023

macforlife said:

Hi everyone, Im new to the forum and physics in general.

I recently started to dig a bit into popular science on quantum mechanics, cosmology, general relativity etc. and found it super interesting ( as everyone on this forum I assume ). I think the time has come for me to dig a bit deeper into the actual physics behind it ( with math involved ), but beforehand I feel like I would like to refresh my high school mathematics.

Im further planning to get deeper into QC, as Im a software engineer.

Can you recommend me some high school and undergrad mathematics books that would set me up for physics later on?
I prefer smaller books that focus on one subject ( let's say calculus, linear algebra etc. ) rather than those bulky 700 pages books that you can't really take anywhere with you.

I will be glad for any suggestions.

Thank you in advance.
Michal

There is a long way to go from high school math to QM and GR math. I have written many insight articles for PF over the years, and about half of them deal with subjects that are useful in this context.

If you want to learn language and mathematics, how about reading the original papers of Einstein, Noether, Heisenberg, Schrödinger, or Gauß? Although the latter was published in Latin, too. This won't probably be the best way to learn physics, but it practices the language and is an interesting read.

In all other cases, you could pick a specific subject, e.g. "Lineare Algebra für Physiker" + pdf, and check the many lecture notes available on university servers.

deuteron · Sep 14, 2023

I usually use English versions of the popular books and haven't really used a book originally in German, but I think it would be easier to find German translations of books that are already established to be fundamental. I used "Principels of Mathematical Analysis" by W. Rubin: https://web.math.ucsb.edu/~agboola/teaching/2021/winter/122A/rudin.pdf
German book on Amazon: https://www.amazon.de/dp/3486578529/

which I found very compact (too compact actually for my taste) and used it usually supplemental to the lectures, but it covers both real and multivariable calculus.

I heard good things about "Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)" by Cummings
(https://www.amazon.com/dp/1077254547/?tag=pfamazon01-20)

You might find https://math.stackexchange.com/questions/129868/german-analysis-texts this question in SO interesting! Good luck!

mathwonk · Sep 14, 2023

i recommend the (original) german editions of books by richard courant, such as methoden der mathematischen physik, and vorlesungen uber differential und integral reichnung:
https://www.amazon.co.uk/Antiquaria...ard+Courant&page=2&qid=1694709654&ref=sr_pg_2

macforlife · Sep 15, 2023

Thanks guys, I'm actually truly delighted that not only there is such a lively forum for physics, but it has also active German community.

Im currently reading Einsteins Spuk from Anton Zeilinger which is rather in popular science section, but quite interesting and well written.

vanhees71 · Sep 15, 2023

macforlife said:

Do you guys know any good German books as well? For the sake of optimization i like to improve two skills at once, currently German and math.

When I started studying physics at the university for all of us the most valuable book to soften the "math shock" was

https://link.springer.com/book/10.1007/978-3-8348-8347-6

Muu9 · Sep 16, 2023

https://fivebooks.com/best-books/quantum-computing-chris-bernhardt/

I don't think you need to know QM to understand QC anymore thsn you need to know classicsl electrodynamics to understand classical computing.

macforlife · Sep 19, 2023

@vanhees71 thanks, its already on its way :)

@Muu9 that's most likely true, but it wont hurt neither

vanhees71 · Sep 19, 2023

Muu9 said:

https://fivebooks.com/best-books/quantum-computing-chris-bernhardt/

I don't think you need to know QM to understand QC anymore thsn you need to know classicsl electrodynamics to understand classical computing.

I'm not an expert in quantum computing, but I can't imagine that you can understand it without knowing the basics of QM. Since it's mostly about many-"qbit" systems, maybe it's sufficient to know just about spin 1/2.

macforlife · Sep 19, 2023

vanhees71 said:

I'm not an expert in quantum computing, but I can't imagine that you can understand it without knowing the basics of QM. Since it's mostly about many-"qbit" systems, maybe it's sufficient to know just about spin 1/2.

I would say we are still in early ages of QC, same as it was with regular computers 50 years ago, so we don't have sufficient abstraction built above the actual quantum layer to be able to skip at least basic knowledge of QM and quantum information theory. At least thats my current understanding. But I'm rather uneducated on the topic at the moment.

WWGD · Sep 19, 2023

For general Math , I suggest books on Advanced Calculus ( many free ones online). To brush up on German online, I suggest you look up Math topics in Wikipediacht, the German Wiki, and follow the links. Once you're more familiar, maybe use books, like those recommended above.

vanhees71 · Sep 20, 2023

A standard German introductory analysis textbook series for the standard analysis course in Germany (Analysis 1-3, unfortunately there's no book for Analysis 4, Complex Function Theory) is

O. Forster, Analysis, 3 Vols. Springer (2016-2023)

High school and undergraduate math textbooks for refreshing my skills

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