Studying Self-Studying Higher Level Math, Physics & Chemistry: Resources & Textbooks

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The discussion centers on the challenges of self-studying higher-level math, physics, and chemistry subjects, such as real analysis, abstract algebra, vector calculus, quantum mechanics, and electromagnetics. Participants express the difficulty in finding comprehensive textbooks with detailed solutions as one progresses to advanced topics. Recommendations include utilizing college libraries for access to a variety of resources and textbooks used in college courses. Specific textbooks mentioned include Adrian Albert's "Fundamentals of Higher Algebra" and C.H. Sah's "Abstract Algebra," which are available at low prices. Additionally, free online resources, such as notes from James Milne and other educational websites, are highlighted as valuable study aids. The consensus acknowledges that while self-study can be effective, having an instructor for guidance and discussion is often more beneficial for learning complex material.
Simfish
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http://joshua.smcvt.edu/linalg.html/

Something like the above textbook, with plenty of detailed solutions to all of the problems. The thing is, as you go higher in level, you also find fewer solutions manuals and study guides that can make studying higher level subjects far easier.

So does anyone know of any really helpful self-studying textbooks for any of the higher level math, physics, or chemistry subjects? Subjects like real analysis, abstract algebra, vector calculus, basic quantum mechanics and electromagnetics?

And I'm one of those people who does better self-studying the material than taking the courses at college.
 
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In my opinion, you can't beat the college courses where you have instructor feedback and classroom discussion.

I suppose your best bet in learning the material on your own would be to go to a college library. They have a wealth of information and books there.
 
Simfishy said:
http://joshua.smcvt.edu/linalg.html/

Something like the above textbook, with plenty of detailed solutions to all of the problems. The thing is, as you go higher in level, you also find fewer solutions manuals and study guides that can make studying higher level subjects far easier.

So does anyone know of any really helpful self-studying textbooks for any of the higher level math, physics, or chemistry subjects? Subjects like real analysis, abstract algebra, vector calculus, basic quantum mechanics and electromagnetics?

And I'm one of those people who does better self-studying the material than taking the courses at college.
Why not ask the instructors of those courses what textbooks they use?
:smile: Then self-study from those~
 
the best books cost soemthing, but they are cheap, like a adrian Albert, fundamentals of higher algebra, is available sued for $1.

and c.h. sah, abstarct algebra, is available cheap, as is van der waerden modern algebra.


the notes on the webpage of james milne, are free and are excellent in my opinion, in math.

i also like my own notes on my webpage, and there are lots of others. just search the web for free class notes in various topics.

lots of old journal;s are also available free on the web so you might even find papers by einstein and others for free.
 
i agree though that learning from a person who knoiws and will take time to help you and explain to you is far quicker and better than self elarning. i have spent my whole life trying to learn by myself stuff i failed to pay attention to in class or never had.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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