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# Book of Proof

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This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Alth
...more

Paperback, 314 pages

Published
May 31st 2013
by Richard Hammack
(first published 2009)

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**Playing with Numbers**

22 June 2018 - Sydney

Well, what do you know, a university textbook that doesn’t actually break the bank. In fact a University text book that actually costs you absolutely nothing. I’m definitely going to give this book some good marks for that. Yeah, I remember the last time I was at Uni and the most expensive aspect of it was the books (well, yes, the fees, but the government technically pays for that). In fact when I did Law you could be assured that the yearly boo ...more

Very little is assumed of the reader at the beginning, which surprisingly is not a given for such a text. There is a potentially useful chapter on combinatorics - basic stuff (multiplication principle, factorials, Pascal's triangle, a little inclusion-exclusion) that we can't necessarily assume our students have seen in high school. Standard techniques including proof by contradiction and mathematical induction are well-represented. The material on cardinality (at the end of the book) is nice.

Two things stand out about

*Book of Proof*, compared not only to other free books, but compared to any other books for a "proofs" or "transitions" course: first, the proofs presented herein are not all presented in a finished form; Hammack develops them in a way that reflects the thought process. Second, there are

*tons*of completely written-out proofs in the answers section at the back.

I contend that these are very significant things, and that they are sufficient for anyone teaching a course of this nature to consider adopting this text. I see no reason not to at least add it as a supplemental text - not just in the "transitions" course, but for other courses where students will be struggling with the same issues, eg. Discrete Math. ...more

I can confidently recommend this book to autodidacts. I studied it in my personal study hour in the morning before work.

Richard Hammack is clearly an adept teacher; he masterfully structured this book with a range of student exposure to the material in-mind. From the complete beginner (as in my case, I only had highschool algebra with some non-rigorously, self- ...more

The theories are explained with Proofs, described in a clear and concise way, with sufficient exercises at the end. I went thru the exercises, and took me awhile to finish, but it was enjoyable.

Topics include: Sets, Logic, Counting, Relations, Functions, Set Cardinality

Proof methods include: Direct, Contrapositive, Contradiction ...more

It has a specific job, to teach basic proofs. At that job, it is the best book available. You can get the PDF for free on Prof. Hammack's website, but I bought the physical copy. So before you start your Real Analysis course with Baby Rudin or your graduate economics course ...more

May 28, 2014
Ramesh
marked it as to-read

Thus far, the most accessible illustration of the implication operation's logic table......

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“Mathematics is filled with such instances where it is important to regard one set as a subset of another.”
—
1 likes

“Sets are fundamental because every mathematical structure,

object or entity can be described as a set. Logic is fundamental because it

allows us to understand the meanings of statements, to deduce information

about mathematical structures and to uncover further structures.”
—
0 likes

More quotes…
object or entity can be described as a set. Logic is fundamental because it

allows us to understand the meanings of statements, to deduce information

about mathematical structures and to uncover further structures.”