Product Description

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This textbook will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarise students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed ‘scratchwork’ sections to expose the machinery of proofs about the natural numbers, relations, functions and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Product Details

• Amazon Sales Rank: #445779 in Books
• Published on: 1994-11-25
• Original language: English
• Number of items: 1
• Binding: Paperback
• 309 pages

Review
'… we can warmly advise this excellent book for those who need to get acquainted with or must teach course on formalism and proof techniques.' Acta Scientiarum Mathematicarum

From the Author
Related software available
Macintosh software that helps you learn to write proofs using the methods explained in this book can be downloaded from my homepage at:
http://www.cs.amherst.edu/~djv

Customer Reviews

MUST OWN!!!
I first purchased this book two years ago and became really excited when I found that I had it in me to write proofs. The truth be told, I have NOT STOPPED writing proofs since being inspired by this book. It is a masterpiece and I think ANY student approaching the writing of proofs for the first time couldn't possibly go wrong with an investment in a copy of this book. I also think that professors teaching a first class in abstract mathematics would be doing a service to their students by either requiring the book or giving it serious recommendation. AWESOME!!

Wonderful into to rigorous mathematics
I agree with Usispaul's comments.

I only want to add that this is a wonderful introduction to mathematical thinking. It is completely engaging, and not like other textbooks. [This is a rigorous math book (not a book about math) and covers the material of first course for mathematics majors, logic, sets, relations, functions.] There are exercises (do them!) and examples.

I took math in college, but this book made me want to know MORE about mathematics.

Engaging book on producing mathematical proofs
The emphasis of Vellemans book on the difference between manufacturing a proof and the proof's final presentation speaks directly to the confusion of the uninitiated to proofs. It meets the (perhaps frequent) naive expectation of an invariable and immediate recognition of a polished proofs rhyme and reason. It consequently points to the often necessary autonomous efforts of the student to independantly unravel the proof of a theorem or definition. The book moves rapidly from the necessary setential logic and truth tabels (a Wittgensteinian invention) to the chapters on proof writing and follows with chapters on functions, relations, closures, and more.