What to read after "Book of Proof?"

[Rijad Hadzic]

Hi since U.S. education is shite, I've decided that I'm going to learn math from the ground up by myself. My goal is to reach graduate level mathematics in 2-3 years.

I'm currently reading Book of Proof, what should I read after this? My end goal is to be proficient in applied math/ physics.

 

[MidgetDwarf]

Have you seen linear algebra?
A good start would be a proof based linear algebra brook.

You can try Spivak Calculus.

You can maybe learn some intro number theory.

 

[MidgetDwarf]

Since you wAnt to do applied math, I think Apostol calculus would be better, than Spivak.

 

[Rijad Hadzic]

Have you seen linear algebra?
A good start would be a proof based linear algebra brook.

You can try Spivak Calculus.

You can maybe learn some intro number theory.

I've taken a linear algebra course but it is literally just learning to do matrix operations and had laughable proofs. The "application" problems are laughable too, just plug in chug type problems. No real thought going on. Would you be able to recommend me a book?

By the way, would I be ready for Apostol's calculus book, if I have only read the Book of Proof by Hammack, and have taken basic calculus 1-3 in the shitte American education system?

 

[Rijad Hadzic]

Also no offense to anyone of my compatriot's, to put it simply I am just in rage at how we weren't taught mathematics like certain European countries, and I have to go back and learn this crap myself because Texas would rather spend its budget on crap like anti-abortion laws and worrying if the pledge of allegiance should say "under God," instead of giving us a decent education.

Personally I am religious myself, but I’m not going to support stupid use of our state budget just because I am religious.

 

[Dragon27]

I've taken a linear algebra course but it is literally just learning to do matrix operations and had laughable proofs. The "application" problems are laughable too, just plug in chug type problems.

And you're sure that you've mastered this basic stuff?

Would you be able to recommend me a book?

Have you tried Linear Algebra Done Right or Linear Algebra Done Wrong?

 

[MidgetDwarf]

It would still be challenging. Maybe Spivak is gentler, but the problem with Spivak is that their are virtually no applications.

Both are good, and it doesn't hurt to try.

If you read Book of Proofs, I read it, and I think it's a good book with challenging exercises, then you should be ready.

But when you say reading. Did try to prove why such and such is true. Do you understand the different proof methods. Relations? What does it mean to have an equivalence relation. Definition of a partition, equivalence classes. How the collection of all the equivalence classes forms a partition on a set.

What about the function chapter?
What a function is. Definition of image and inverse image etc.

Can you do most of the problems without looking at the solutions?

If yes.

Then a good first book in linear algebra would be Friedberg, Insel,Spence: Linear Algebra.

Axles is good. But it can be a little difficult if you are not used to proof theorem. Even if you can't fully understand it, I think it's worth having it on your bookshelf.

A nice book that is gentle but well written: Pinter: A book on Abstract Algebra. I'm reading this book for preparation for my algebra course. I like it. I also read his set theory book.

You can also try your hand at geometry. Kisselev Planimetry, Moise geometry. Good way to practice proof writing on things you seen before...

 

[Rijad Hadzic]

Thank you MidgetDwarf. Great reply bro I appreciate it.

 

[MidgetDwarf]

Thank you MidgetDwarf. Great reply bro I appreciate it.

No problem. I also have homework exercises from the intro proof class I took. Some of the problems are quite challenging. Pm your email if you are interested.