What Are the Best Math Books for Self-Learning?

[tameree]

Hi,

I am looking to develop my mathematical mind as much as possible. The "highest" classes I have taken are Calculus I & II as well as linear algebra. I'd be looking for either a bunch of books or some sort of guide (similar to the guide "How to become a good theoretical physicist" for physics) that ranges from algebra up to topology, complex analysis and partial differential equations.

Basically, I want to master as much of the mathematical field as I can. I'd also be interested in a book (if any exists) that teaches maths at the same time as physics, as I think that learning one reinforces the other. (Is that what's called "Mathematical physics"?)

Thank you.

 

[davesface]

I believe that the standard book for mathematical methods of physics is still "Mathematical Methods in the Physical Sciences" by Boas.

For pure math, check out http://hbpms.blogspot.com/" . Someone posted it a while back, and it seems to be a really comprehensive list of books.

 

[qspeechc]

That link davesface posted list very many books, when you need only two or three books for each subject. And I see it doesn't list some books I would have listed. But it still seems very useful.

tameree, do you know you can search this forum for books? E.g. if you want recommendations for algebra books, search the Science Book Discussion forum for algebra, and you get this:
https://www.physicsforums.com/search.php?searchid=2676705
For example, you will come across this previous thread:
https://www.physicsforums.com/showthread.php?t=102493&highlight=algebra
and many others.

Also, it's a good idea to go to the library and just look through books and see for yourself which books you want to read.

 

[Gingia]

Hi there;

As a first book to go from what you know now to what you're trying to learn, I'd recommend a more theoretical treatment of linear algebra than the one you're familiar with (unless you took a theoretical linear algebra course).

Valenza's book is excellent, and while I haven't read all of it, I think Halmos' book (Finite-Dimensional Vector Spaces) covers similar material.

You may also want to read a theoretical treatment of vector calculus. For this, I recommend Hubbard & Hubbard, as it's a great transition from the more computational to the more theoretical. It's a great complement when read with a dense book like Spivak's 'Calculus on Manifolds'. From there you can dive into topology with Munkres.

 

[tameree]

Thanks for the quick responses guys,

I will definitely take a look into those books you mentioned.

I bought a used copy of "The Road to Reality" on amazon for a few bucks, has anyone read it? How would you rate it in terms of accessibility?

 

[Gingia]

It's a good book, Penrose is a great writer. There's a whole lot of material in it; you'd probably want other books for each subject as well.

 

[tameree]

Thanks Gingia;

That's actually what I'm planning to do, get introduced to subjects with Penrose's book and read specific textbooks when I still feel I want to learn more or certain subjects