Advanced mathematics

[Bombadil]

I’m home schooled so I’ve been teaching myself math. Right now I’m doing calculus out of the book calculus one and several variables 6th edition and I’ve also been starting to do some linear algebra. The problem is that I’m coming to the end of the calculus book and I’m having some trouble figuring out what book to do next and would like some ideas or suggestions as what I should go into next.

[Fatstep]

Try this; Vector Calculus Linear Algebra Differential Forms: John H. Hubbard

[Jay-qu]

Differential equations would be a good step after you have done calculus. It depends on if you want to follow on or do something different. Non-Real number analysis, the math of uncertainty (probability) and computational (numeric) maths are three areas that are of interest to me.

[Erasmus00]

I’m home schooled so I’ve been teaching myself math. Right now I’m doing calculus out of the book calculus one and several variables 6th edition and I’ve also been starting to do some linear algebra. The problem is that I’m coming to the end of the calculus book and I’m having some trouble figuring out what book to do next and would like some ideas or suggestions as what I should go into next.

 

It depends on what your interests are. I think before you move on to more mathematics, you should consider learning how to apply calculus to real world problems (i.e. physics).

 

Kleppner and Kolenkow's Introduction to Mechanics is a very good, very calculus based textbook. It also has some very good problems.

 

Ed Purcell's book Electricity and Magnetism is another good calculus based physics text. The subject material is great for applied multi-variable calculus.

-Will

[Bombadil]

I’m doing some physics and Iv been planning on getting into something more on electricity and magnetism. I’ve got fundamentals of electricity and magnetism by Arthur F Kip but I don’t know where I got it or how good a book it is if there is a better one I’d consider getting it instead.

As far as what I’d like to get into, I think that theoretical physics would be an interesting thing to learn. Although I don’t know what all the different mathematics go into.

[Sajuuk]

After doing elementary differential equations and vector calculus you'll have to get into complex analysis and special functions to tackle quantum mechanics. I suggest the book by Butkov for this (it's called Mathematical Physics).

 

I learnt the basics of differential geometry in "A first course in general relativity" by Schutz, I think it serves as a good introduction text (it teaches you the maths and then the physics).