I want to self-study proofs. I need something with lots of exercises and solutions to exercises since I will be doing it alone. Is Book or Proof or Discrete Math by Rosen better for self-studies? I want a book that will ready me for a rigorous first course in Abstract Algebra, Real Analysis.
I want to teach myself proofs. Rosen or Hammack better?
You just jump into algebra or real analysis and stop being a brainlet. Undergrad analysis books are meant to introduce you to rigorous proofs anyway
Hammack or Laczkovich
Only if you read a brainlet analysis or algebra book that barely covers the subject.
Thanks for the recommendations. Hammacks book is much shorter than Rosen's. I'll go with that first and then move onward to Analysis/Algebra.
I've just finished Velleman, took a while but did all the excercises. Wonder what's your opinion on the book?
Artin, Aloffi and Tao are brainlet textbooks then. None require reading a book on proofs because that'd be retarded unless it's proof theory or whatever. But informal mathematical reasoning? Just quit math if you need a book for that
I haven't really looked at it. I started Rosen and read every page, did all the exercises with solutions and it took a very long time to get past chapters 1 and 2, with chapter 1 spending an incredible amount of time on logic, it bored me. Chapter 2 was better with sets, but the pace of Rosen is incredibly slow.
Hammack's is less than 300 pages. So I figured it has to move quicker ad get to the point with less words.
What is your opinion on Velleman? How long did it take you to do and does his book have solutions to odd problems?
this book has solutions to maybe a half of the problems. It goes through logic at the beginning which you can skip optionally, then some set theory. chapter 3 is an introduction to "proof techniques": contrapositive, contradiction, p->q, etc, goes through how to separate givens, how to frame problem in quantifiers and what quantifier tells you about the goal etc. probably the most usefull part. Then there are other chapters about some parts of abstract algebra, relations on tuples, functions. Induction is cover later in a book and closing chapter covers infinite sets. Overall, at the beginning you have every proof for every theorem explained, as you go later you are expected to figure out more by yourself. A lot of excercises which generally require you to do previous chapters, which was kinda cool, so you do not forget previous concepts. In particular, selection of certain topics seems artificial but I guess you have to practice on something. I feel however there is quite a leap somewhere inbetween chapters 5-7, when proofs become more notably complex than before. In effect, on some parts you spend a lot less time on than on the others in no particular order. Some excercises are labeled as more demanding but for me I haven't found it to correspond with my situation. There is also a link to some proof designer software but I do not know if it works.
Some cool excercises are examples of proofs requiring you to spot some inconsitencies.
And for the anwsers, there is really a lot less than I would like them to be, especially for the later parts. i used blog of this guy for help inchmeal.io
I feel much more confident with just simple epsilon delta proofs now than I did before, I do not think however whole book was required for that goal
it took 3 weeks counting the days i did exercises
Great thank you! Does this site have all the solutions to every problem in the book?
some solutions are left out in the very last chapter, just so. Carefull though, occasional errors.
Hammack is the best for exercising
Velleman is the best for the theory behind proofs
Solow is the best for explaining the thought processes behind a proof.
Also try A Transition to Advanced Mathematics, it's cool and it's free on the web
Chartrand is also good.
I don't care if she's an SJW, I would cum deep inside of her in a heart beat.
literally a meme, should be burnt
She is a national socialist.
Like I said, I don't care if she's an SJW I would still ejaculate inside of her.
This one (free/creative commons) is a really good intro to pure math for anybody who did 3 semesters of Stewart and didn't do anything rigorous infinitedescent.xyz though above anons are correct if you jump into some real analysis text or even Hoffman & Kunze Linear Algebra text you'll eventually learn the same 'reasoning' by doing enough excersizes.