Description
An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs.
This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision
Great book! I recommend it for anyone who is interested in math. Whether you are a beginner or advanced, you will surely find something in the book that catches your attention.
Even if you already have substantial training in mathematics, this book is worth reading just for the elegance of the proofs.
I was really blown away by this book. Besides the quality of the diagrams and illustrations, which go far beyond any popular mathematics book I’ve ever purchased, the variety and depth of examples of proof techniques is really impressive. All my old favorites (like tiling a checkerboard and the mxn chocolate bar problem), and many that I’ve never seen before (a proof that the number of different infinities is not any of the infinities!) are beautifully illustrated and described in accessible but rigorous terms.
My 7 year old daughter looks over my shoulder when I’m reading this book and asks lots of curious questions. This book has been a great introduction to the beauty and wonder of mathematics for this budding mathematician!
This well-written book by Professor Hamkins has a variety of interesting elementary mathematics. And has many nuggets of wisdom (e.g. the number 1 and prime factorization, the use/mention distinction with fractions and rational numbers, and vacuous truth). It’s an excellent choice for aspiring mathematicians.
Excellent purchase, especially like the “mathematical habits” sections, which will surely cause a moment of reflection and will serve as conversation starters.