An Introduction to Mathematical Reasoning: Numbers, Sets and Functions

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 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.

Eye-opening.

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

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.

This is an excellent text, and perfect for my needs, with clear prose and lots of example problems and puzzles to work through. However, the binding on my copy is simply atrocious. A large amount of force is need to keep the book open, making it hard to use pen and paper while looking at the open book. Extremely heavy weights would be needed to hold it open. Worse, several pages have fallen out of the front and back within the first few days. At this price, the publisher has truly done an embarrassingly bad job with this excellent book.

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.

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.

Bought this for a uni course. A good introductory book into the world of pure maths, and I would recommend it to anyone who wants to know more about infinity and what it means from a mathematical standpoint. That being said this is a text written by a University professor, for 1st year university students, so bear that in mind.

Sobran las palabras. Es un mágnifico libro para cualquier amante de las ciencias en general. y de las matemáticas en particular

Well written, covers classical fundamentals of advanced mathematics. Contains answers to all exercises, which is a big advantage compared to other textbooks on the subject.

Necessary for course

Basics introduction