Exploring the Effectiveness of Proof Books for Students New to Abstract Algebra

[IKonquer]

Has anyone read How to Prove It: A Structured Approach by Daniel Velleman or Introduction to Mathematical Thinking: Algebra and Number Systems by Gilbert and Vanstone?

If so, how well do they prepare a student who has had no exposure to proofs to take classes such as abstract algebra?

Thanks in advance.

 

[anonymity]

I think this will largely depend on how your school approaches the course. I know that my school has what is essentially an intro to proofs class which all students must take before moving on to any pure math such as this, or real analysis, or anything of the sort.

I do know, however, that MIT does not have such a course, and that the only prerequisite for real analysis (a proof based course) is the normal old calculus I and II sequence. Their course (in theory) gives all of the proof-knowledge needed for the course.

That being said, I don't think you can go wrong with Velleman's How To Prove It. I am reading it right now, and it is great.

Check out the comments on amazon, too.

https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

From what everyone says over there it is a great buy and a great asset to an undergrad mathematics student. (This is ultimately the reason I took a chance on it -- and no matter what, it can't hurt. The book is about 400 pages of all proofs, and how to go about solving proofs, and solutions selected proofs. The first two chapters are introductions to some basic math logic stuff, the "language" of proofs, but everything else is proofs. If you go through the whole book, and work the problems, you will most definitely get something substantial out of it.).

Now, whether or not this will be sufficient for your course, I cannot say; for that you will need someone with more experience than I.

 

[Skrew]

I took a proofs course and have a number of proofs books and I found them all kind of boring.

I think it is more interesting to learn proofs while learning a specific math subject.

For example, Analysis with an Introduction to Proofs by Steven Lay appears to be a good book.

I'm sure something similar exists for abstract algebra.