Where can I find resources for learning mathematical proofs from scratch?

[vulpe]

Hey guys, I just recently transferred to the mathematics department at University of Illinois as a junior undergrad and one of the classes I'm required to take this fall is called Mathematical Reasoning and I'm pretty sure it has to do with proofs... Which I know absolutely nothing about! What is a good resource (book, video, website) where I can start learning this stuff from ground 0?

 

[Dmobb Jr.]

I think that the best way to learn mathematical reasoning is to just choose any topic that you find interesting and read rigerous textbooks for that topic.

If you are interested in calculus I would suggest "ISBN: 9780387904597 Elementary analysis : the theory of calculus, Author: Kenneth A. Ross."

If you are interested in Algebra I would suggest "Introduction to Abstract Algebra, by Neal H. McCoy and Gerald J. Janusz ISBN: 9780982263310"

 

[Fredrik]

I would guess that the course covers the basics of logic (notation and truth tables) and set theory. There are many books that cover these things. "How to prove it" by Daniel Velleman seems to be popular. "Book of proof" by Richard Hammack looks good as well, and can be read for free online.

http://books.google.se/books?id=lpt...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
http://www.people.vcu.edu/~rhammack/BookOfProof/

 

[vulpe]

Thank you for the replies guys! Also thanks to the moderator for moving my thread, greatly appreciated :D

I will check out the links to both books and try to get a head start on this subject before fall classes start. I'm worried about the class, a lot :((, I have no experience in this area whatsoever. I did just fine in calculus and differential equations... but they kind of work off one another. This seems like a totally different area of maths.

 

[Fredrik]

Don't worry about it. Just study the definitions carefully and do a lot of simple-looking exercises, and you'll do fine.

 

[JaredEBland]

I just finished a junior level course in mathematical proofs. We used the 3rd edition of this book: https://www.amazon.com/s/ref=nb_sb_...athematical+proofs,aps,1188&tag=pfamazon01-20 . I purchased the 2nd edition to save money, and comparing side-by-side, the two editions aren't that different. It reads relatively easily, and has sections on logic, truth tables, logical equivalence, direct proofs, proof by contradiction, minimum counter example proofs, induction, strong induction. Our class mostly did number theory to focus on the methods of proofs, other professors just into a couple new advanced topics (e.g. rings) and they learn how to prove along the way.

A discrete math text would also be worth looking into for logic, and goodwillbooks.com will probably have one that you can get to your door for less than $5.

 

[Inve]

I would wholeheartedly recommend this book by Abbott. I found it to be a great book explaining the reasoning underlying the tools of calculus.

https://www.amazon.com/Understanding-Analysis-Stephen-Abbott/dp/0387950605

 

[vulpe]

Thank you so much to everyone, I cannot tell you how much this helps and encourages me :D **mr bean style thumbs up** lol

 

[deluks917]

I learned what proving something "meant" by reading Spivak's Calculus and doing the exercizes. Then comparing my solutions to the one's in the solution manuel (I had no teacher).

 

[vulpe]

Has anyone ever used the Demystified series Math Proofs? I'm currently using that book to get started because all the other suggestions are damn hard to follow at the moment. I was wondering if anyone can tell me if I'm just wasting my time with this book?