Book Recommendations for Proofs

[kanderson]

I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.

 

[caffeinemachine]

I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.

I have never seen any book titled "Intro to undergrad math". Maybe there are such books but I don't know.
"Elementary Number Theory by David M Burton" is an excellent book. If one wants to start reading non High School math then I guess this is a good place to start. You will get to know numerous proof techniques not used at all in high school. It has a lot of exercises too.

 

[Evgeny.Makarov]

Undergraduate, and especially graduate, math is divided into subjects: analytical geometry, linear algebra, abstract algebra, calculus, discrete mathematics and so on. I personally never studied any generic higher math or proof methods per se; I studied the subjects above and in the process I learned how proofs work.

That said, when I started college I already had a good background in math, so starting abstract algebra directly may not work for everyone. This thread on MathOverflow seems to have a nice selection of books about proofs.