Playing with Numbers 22 June - Sydney Well, what do you know, a university textbook that doesnt actually break the bank. In fact a University text book that actually costs you absolutely nothing. Im 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 book bill would run into the hundreds of dollars. Well, not so with this book, or at least the digital download edition , so well played.
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I have used this as a supplemental text in a few courses, and would totally consider adopting it as the primary text for the right course. Very little is assumed of the reader at the beginning, which surprisingly is not a given for such a text.
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. 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-taught compsci to the This is an excellent book if you want to know how to read and understand proofs or how to derive proofs yourself. His writing is lucid and structured just as well as the book is with sentences that are explicit and clear and consistent.
This book is, honestly, my first encounter with a thorough introduction to rigorous reasoning and argumentation. If the author ever ends up reading this: I wish the exercises had a difficulty ranking e. I also wish critical exercises to understanding that should be done were starred or something.
I also wish there was a bit more history after the critical technical information. I also wish there were a "what to read next" appendix or something for the autodidact. Hammack gently leads the reader through many important mathematic concepts that are taken as understood by the reader in many upper division classes.
This books is a must read for anyone going into upper division math, regardless of major!
Book of Proof
Book of Proof - Third Edition
Book: Book of Proof (Hammack) - under construction