An Introduction to Mathematical Reasoning: Numbers, Sets and Functions

This was an excellent mathematical reasoning book, written at a very appropriate level for an undergraduate with a budding interest in more rigorous mathematics beyond what most people learn up to and including college level calculus.I already knew the basics of proof by contradiction, proof by contrapositive, and induction. They gave a few examples about strong induction, but I wish there was more of a focus on this concept since it is such a powerful and important concept. The sections about number theory were the most interesting, especially the Euclidian algorithm and its use in solving linear diophantine equations.Many solutions are also nicely worked out, something I wish there were more of in upper division level textbooks.

Just as the other reviews describe, this is an excellent book that introduces proofs and mathematical reasoning. The major advantage of this book is the excellent writing, which provides some entertainment and keeps your interest high. Most of he proofs must of course be read carefully, and followed with a pen and paper. The problems with solutions are moderately difficult. I have a mediocre math background, a little exposure to formal math but was able to do most of the problems from the first three units with effort. If you don't get a proof or a problem, put it aside for awhile and look at it again.

The explanations are clear and concise. Exercises are challenging, but there are solutions so you can work out how the problems are solved.

I needed a book that covered fundamental background information behind mathematical proof techniques for an undergraduate univeristy level linear algebra class.With this book, I was able to truly learn and understand the major concepts behind mathematical logic and proof. This text brings a whole new meaning to teaching the reader about being precise; and I mean the author does an extremely terrific job of doing just that. Wow!Seriously, the focus here is on content so you won't find any sexy graphs or anything. The content is so good that I often felt that just by reading it I was propelled into a quasi- pseudo-lecture meeting.After following this text, I can say that I now appreciate the act of being precise to the point that is required for mathematical proof. If you want to extend the knowledge of your 'white board' then just buy this thing. I am so glad I did.BTW, I only needed the content from the first five chapters, I can't say much about the rest of the text. However, taking an inductive approach, I must assume that the other chapters are also very excellent. Yess, see it worked!

This is hands down the best introduction to logic and mathematical reasoning in my current library. I highly recommend this to anyone who needs to learn the basics of mathematical proofs because the author takes great care to motivate each concept with plenty of down to earth examples. This book was the only reason I breezed through all my abstract math classes.

This online version was about half the price of the hard copy, but the formulas were inserted as graphics which did not enlarge, making them very tiny and hard to read sometimes.Also, there were some significant typos (some minus signs instead of =, a 6 instead of a b), that were confusing.This book need a good proofread, and get the formulas inserted with equation editor.

Does a great job of introducing an inexperienced reader to the language of mathematical proofs. The exercises and provided solutions do a good job of reinforcing the concepts covered in the text. The author provides numerous examples throughout the text.

I agree with almost everyone else that the book is a great introduction to the topic. There's one problem with the Kindle version, though: The text appears to have been scanned in using OCR (optical character recognition) technology, and there are a number of typos in the Kindle text as a result.For example, the phrase "a, b and c" often becomes "a, band c." Sometimes, the equals sign ("=") gets replaced with a hyphen ("-"). Most of these errors are just distracting, but it's annoying to have this occur in a book that's about how to write rigorous mathematical proofs.