MHB Book Recommendations for Proofs

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For those seeking a solid introduction to undergraduate or graduate mathematics with exercises and clear explanations, "Elementary Number Theory" by David M. Burton is highly recommended. It provides insight into various proof techniques not typically encountered in high school math. The discussion emphasizes that undergraduate and graduate math is categorized into specific subjects like linear algebra and abstract algebra, which are essential for understanding proofs. A strong mathematical background may be necessary for tackling advanced topics directly. Additionally, a MathOverflow thread offers a curated list of books focused on proofs.
kanderson
I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.
 
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kanderson said:
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.
 
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.
 

Thread 'A variant of the Monty Hall problem'

There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...
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