Customer Reviews

Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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

 

 

I'm using this in an undergraduate introduction to proofs class with a focus on analysis. As a freshman, it seems a bit overwhelming at times - I wouldn't recommend it to most freshmen or even sophomores.
I do feel like this does a more than adequate job preparing me for more advanced math, and goes far above and beyond similar "proofs and problem solving" style books.

This book was an excellent read, and provided some great information. However, as a math text, I feel like it should have provided a bit more examples, and perhaps even a solutions manual.

I understand that the books main focus was on the abstract discussions of mathematics, but I feel like that should merit the writer to put a bit more examples to drive home the theorems before copious amounts of problems are assigned at the end of each chapter. A ton of these problems are classical, and need to be understood, in light of this, why isn't there a solutions manual to better explain these problems?

I greatly appreciated the voices of the writers keeping themselves grounded in pragmatic language. Too often will mathematicians get lofty in their dictions and fuddle the material they claim to understand all too well. This book did a great job discussing simple concepts simply, meanwhile working the more difficult ones with more space.

I ran into the first edition of this book ten years ago when taking courses at George Mason University, and really loved it. I still love it. It covers proofs from all basic "pieces" of mathematics and gives the reader a good feel for the "proofology," both in technique and fundamental nomenclature and results, that a student is expected to know when taking the first analysis and abstract algebra courses. It's not perfect though. I haven't bought the second edition, but in the first edition, Example 2.21, p.27 says: "An integer is even if and only if it is the sum of two odd integers." Obviously, it is easy to show the sum of two odd integers is even by forming the sum (2k+1) + (2l+1) = 2(k+l+1), which is twice an integer and thus even. But, if an integer is even, it can be the sum of two odd integers OR two even integers, so the statement is not complete. If small stuff like that doesn't bother you, this book is for you.

The author gives solutions or hints for one-third to one half the problems depending on the chapter, which is more than enough for self-study. I would disregard the whiny one star review that is posted for this book; it is typical of someone who wants to be spoonfed mathematics.

I originally purchased this book as a text for a math course and quite enjoyed the selections that we worked through in it. It has been about a year since I took that course and I still find myself going back for references in the book. It is a must have for someone who is interested in proofs or will be doing them on a semi-regular basis.

My main problem with this text is the level of understanding it assumes on behalf of the reader. Many reviewers say "great reference" or something of the sort. But this book is a *foundational* text. It's not a book for mathematicians or a mathematically mature reader -- they should already own the techniques presented here. A book of this kind should be suitable for self study and this book fails in that department. Given the amount of math it assumes, I would imagine those at that level are already fairly assimilated to proofs and the like. Hence my critique that the level and function is confused. Note also that this book is *expensive*.

If you want a book on problem solving, go with Zeitz or Engel, or something of "olympiad" character. If you want a book to learn proof techniques, Vellman or Eccles is good; Solow for true beginners.

This is a great book filled with great proofs and just a great amount of information. Whenever I'm unsure of a proof or need confirmation of some obscure factoid of numbers, this is where I look first. Great for building the foundations needed for learning advanced mathematics.

With a disposition towards problem solving, the book was very helpful for someone like myself who needs the mathematical tools but lacks the background. Occasionally the book lapses into the silly notion that you've seen some of the material and concepts before.

I use this textbook in a math 300 class, the textbook is very dry, has little to no examples and illustrations.
The author failed miserably in arousing interest in the subject(based on many similar complaints from my classmates), and i spend about 50% of the time asking myself "why am i learning this kind of useless, twisted thinking?" while reading the text book. Unfortunately i never find an answer to that question.

The book was coming a loose from the center binder. It has a big orange sticker on the front of the cover that is hard to come off.

The material covered does not help you solve the exercises at the end of the chapter. I wish there was a solutions manual available, so I don't have to guess the answer and be left unsure of what to do to solve a problem.