Customer Reviews

Mathematical Reasoning: Writing and Proof (2nd Edition)

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

 

 

This book was very helpful. I have a better understanding of how to construct a proof and what proofs are best in each situation. The book also gave plenty of examples of proofs of theorems so you had something to compare your proof too. It also give some answers and hints to selected problems in the back which were a great help.

Of all the other reviewers, only mathgirlie seems to understand the purpose of this book: to teach one how to *WRITE* proofs in upper-level mathematics.

As such, it is the only one of its kind in existence, period. No other so-called "intro to proofs" textbook understands that writing proofs is a skill that anyone capable of thinking logically can learn. And there's only one way: write, edit, rewrite, re-edit, rewrite, re-edit, etc., with constant feedback from a competent instructor.

If you're one of the talented few, you won't need this or any other book of a similar ilk. The rest of us need exactly what this book offers: a stepwise process to get an idea and turn it into a sketch, an outline, a first draft, and finally, after enough rewrites and thorough edits, a finished proof that reads professionally.

Having taught how to write better proofs for over 20 years now, I've found it takes beginners about 6-8 drafts to get a reasonable "beginners proof." After two or three semesters, most are able to produce professional results in two or three drafts. (That's about what it takes experienced research mathematicians to produce something ready to submit to a journal.)

Sundstrom seems to be the only author who understands that this is the real process that the vast majority of math majors undergo.

As one of my students told me, it's the only way proofs should be taught. But most profs don't want to expend the time, energy, and effort it takes to teach proofs this way. Thankfully, Sundstrom does.

It's very easy to say you hate this book when you are barely transitioning from a period when math was just plug and chug to a stage when math becomes a more rigorous and highly technical. This book provides a very easy transition between those two stages and I believe that if you were to jump right away into the upper level mathematics (which I mean higher than multi-variable calculus) you would be eaten alive. Fortunately this book is here to help and help it does. After you program your brain to do these logic checks, jumping into a real analysis proof becomes tolerable and fun.

Unfortunately this book does have it's drawbacks. There are plenty of errors all around this book and the introductions to the sections can get really frustrating - especially when you're bogged down on time and just need a quick few examples to get started on the section. While I do love the way the introduction to each section forces you to read and think for yourself before you start doing any real math - there comes a point when it just gets tiring because you just want to "get to damn point" as my professor would have said.

All in all, good book, if you're having trouble with it just remind yourself:
1. Yes real mathematics is entirely rigorous and abstract.
2. No these stupid logic games don't go away later, they just get much tougher.
3. It's logic, pure and straight logic, no magic, no wizardry, just logic. Think harder!

Enjoy your time as a math student!

I did not like this book. It was very confusing. It has lots of preview activities and exercises but no solutions to them. I would not recommend this book to anyone trying to learn theorems.

The format of the book is kind of bad. Lack of practice problems. However, if you do spend a lot of time in it, you probably can master writing proof with just this book. I wouldn't say this book is that bad.

I expected better from a college textbook with so many editors and reviewers, my classmates and I found errors in pretty much every lesson, typos that made it near impossible to get the answers are professor wanted turned in, and we did less than half the problems in the half of the book we went through! It was an easy to understand book, I probably could have taught myself the subject with this book, if it weren't for all the errors...also, a lot of questions were on the bottom of the right hand side, and the exercises were at the top of the other side, not exactly the easiest, especially when you're trying to share books.

I can't even begin to illustrate my frustration with this book. With several colleges backing Dr. Sundstrom's work, I find it sadistically humorous that there are so many topographic errors and scatterbrained thoughts contained within it. The only thing I can postulate about colleges that chose this book is either a) they're getting money back for endorsing it, or b) there was a mathematical conference that overinflated this book.

Each chapter starts with throwing the reader into the deep end without explaining the necessary details. I can't get over the fact that this book was patronizing its reader in every chapter. I understand the concept of exemplary demonstration, but the examples are placed at the forefront of every section, rather than in the middle, meaning the reader has to sit back and guess for each of the problem, or jump a few pages ahead just to get past the opening section. This is fine for a reference manual, but this is unacceptable for a textbook designed for learning.

Problems frequently host topographical errors which tells me that no one proofread the print before sending it off for publication. Sure, an error here and there is something that every publisher has to live with, but this book has at least three errors in every section. If you're with an instructor that knows the material, this is doable, but the real problem is that this is, at core, a mathematics book. A simple typo means the entire problem changes, often times making the problem impossible to solve.

All that said, Dr. Sundstrom does a nice job explaining the particular elements of proofs, but some of the problems written are downright cruel to the student, giving problems that transcend the book's target audience. Still, most of those elements are defined in a confusing, but understandable way.

Also, it should be said that while there are answers to select problems in the back of the book, most of these are hints, and nearly none are completed proofs. If you're looking to learn by example, don't expect the exercise problems to help you.


All in all, I have to say that this is one of the worst math text books I've seen. Both under and overscoped, condescending, and full of errors; I can only warn those that read this with a big fat BUYERS BEWARE.