What to read after Spivak? And Physics books

[IgnacioMagana]

Hello I am about to finished working though Spivak's Calculus. I am wondering if you guys could give me some recommendations on what to read after I'm done with the book. I am looking for something as rigorous as Spivak.

Also a bit unrelated but I have also worked through an old edition of Calculus by Thomas (before spivak). So I recently bought kleppner and Kolenkow's Mechanics book but I also own a second edition of Halliday and Resnicks Physics for scientists and engineers. I have never formally taken a physics class before and I am wondering which book I should start with. Thank you for taking your time reading my post.

 

[A. Bahat]

For math: do you know linear algebra yet?
For physics: I would just start out with Kleppner/Kolenkow. If it's too hard, you can always switch books and come back to it later.

 

[micromass]

For mathematics, you could now read linear algebra or multivariable calculus. I recommend linear algebra first, since multivariable calculus will go easier with some knowledge of linear algebra.

If you want rigorous books, then I can highly recommend "Linear algebra" by Serge Lang.
For a multivariable calculus book, here are some suggestions, ranked from non-rigorous to extremely rigorous:

"Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by Hubbard
"Analysis on manifolds" by Munkres
"Calculus on manifolds" by Spivak
"Multidimensional Real Analysis" by Duistermaat and Kolk

 

[IgnacioMagana]

Ok I think that's what I'm going to do with Kleppner.

I don't know Linear Algebra, yet. Do you think it will be a good choice to learn Linear Algebra before I begin my study of Multivariable and Vector Calculus at a rigorous level? If so what books would you recommend me to look at? Thanks.

 

[SolsticeFire]

Ok I think that's what I'm going to do with Kleppner.

I don't know Linear Algebra, yet. Do you think it will be a good choice to learn Linear Algebra before I begin my study of Multivariable and Vector Calculus at a rigorous level? If so what books would you recommend me to look at? Thanks.

I'm working on Linear Algebra and have thoroughly researched all the books available.
You should do Lin Alg before Multi Calc.

My Primary Text is: Linear Algebra; A modern introduction. 2nd ed - David Poole (Great section on Markov Chains; pretty rigorous; good depth overall)
Supplementing with: Matrix Analysis and Applied Linear Algebra - Carl D. Meyer (Great problems and depth) and Linear Algebra - Jim Hefferon. (Great optional chapters)

I plan on gauging more depth later using Axler's and Ray, Kunze's texts on the same topic.

Good Luck!

SolsticeFire

PS: I'm working through Spivak right now. Any suggestions?! :)

 

[A. Bahat]

I also recommend you do linear algebra next. Lang's book is good, as is Hoffman/Kunze. Or you could take a non-traditional route and just learn linear and abstract algebra together out of Artin's Algebra.