Customer Reviews

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

5 star:		(5)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

"How to Read and Do Proofs" is a magnificent introduction to mathematical thought processes. If you have always wanted to understand how to read and do your own proofs, this book will definitely provide you with the tools. This book is very thorough, and after having mastered it you will feel very comfortable about your abilities to read and construct proofs. Solow covers what he calls the "foward-backward" method first to give the reader a general understanding of how direct proof works. He then explains direct proof of existential quantifiers (there exists...), direct proof of universal quantifiers, proof by contradiction, proof by contrapositive, mathematical induction and more. He also has added 4 appendices pertaining to Modern Albebra, Analysis, Number Theory, and Linear Algebra. Many answers to exercises are provided either in the book or on-line. An excellent rescource for anyone wanting to learn the methods of mathematical proof.

This is a great book, and one of my favorite math books. Like the other reviewer, I also wanted to learn how to read and write proofs. I am an engineer, (many years ago), and not a mathematician, (but really enjoy math). The author communicates clearly, and provides lots of good examples. But the heart of the book is the problem sets for each chapter. Most books on proofs spend way too much time on Logic, (or geometry), and not enough on "math" proofs. The book provides problems from a wide variety of math areas. The latest edition added a lot of new material. I struggled at times, since I went through the whole book without an instructor, and worked on all of the problems. So having most of the possible answers in the back of the book, or on the internet helped as a check on my understanding. This book would make a great gift.

I wish this book was out when I was an undergrad! It is clear and concise. It covers many of the basic areas of math and gives a tremendous amount of insight on which style of proof fits a particular situation. Every example is presented in a very clear way, which gave me confidence in my ability to write proofs. This book should be used by ALL professors who teach an introductory analysis course.

This is an excellent book because if one follows the text and does the work in the exercises, one cannot but attain a competence in constructing proofs and improve one's ability to understand them.

So why do I feel I have been conned? I already had the second edition of this book, and decided that it was so good I would invest in the latest (4th) edition. In the Preface the author states that "The exercises in the body of the text have not changed .... As before, all exercises with a B have answers in the back of the book." This statement is false, which is especially irritating in a book that claims to teach truth tables and the other essentials of mathematical proof. One example of why this claim is false is that in the Second Edition, Ex. 1.9.b has an answer in the back of the book, but this is not the case with the fourth edition. What seems to have happened is that the missing answer has been cut from the book and placed on the publisher's website. Given the massive price increase between the two editions, this seems a somewhat idle approach to creating content for the website; it would have been more reasonable to have created new content for the website. However, the fact is that there are fewer answers provided to Ch. 1 in the fourth edition than there were in the second edition.

It feels disappointing that such a great author and teacher and such a great publishing house should seem to sail so close to the wind. Perhaps a fifth edition will make up for these oversights.

This text is recommended by Harvard University for a course entitled "Introduction to the Theory of Computation". The text is designed to give its reader, in a concise manner, the toolset required to read and write like a mathematician, provided that you have some knowledge of basic algebra and geometry - the writer is concerned with mathematical proofs as they relate to discrete mathematics(so no calculus).

I believe the text is an excellent tool for learning how to solve problems and think logically. I think that anyone who is comfortable with algebra and geometry should read this text to broaden their understanding of mathematics - regardless of age.

This book was very helpful when I was starting to learn how to write mathematical proofs. The only other time I have written proofs before was in Geometry and this book really broke down some of the different techniques. I got an A in the class and I do not know if I could have done it without this book.

This book does a great job of guiding you through the process of developing mathematical reasoning. I used it alongside my transition to higher math course this year and would not have done as well in the course without it.

I will not disagree with the previous reviews, except to say that the author while pretty clear and straight-forward in explaining things, has a stilted style that doesn't always flow or read well. I suspect though for many people, particularly many novice, and some professional, mathematicians will never really notice it or find it problematic.

This book is pretty useless to me. I only bought it because my professor recommended it and because my company covers all my school expenses. I have opened the book exactly one time and it was not much help. But I suppose, as far as books on 'How to read/do proofs' go, this one is probably good. I just don't see a need for this subject in general.

It should be noted that I am an engineer and have no use for this subject all together. I am just taking it to satisfy my course requirements.