Mathematics

When I teach a course entitled "Fundamentals of Arithmetic and Logic" I constantly emphasize the fact that the basics of mathematics is all about the use of more sophisticated and abstract patterns. For example, I use the following argument to demonstrate why the commutative law of addition holds: 1) Positive integers can be considered shorthand representations for piles of sticks. 2) If you have two piles of sticks, which pile you move on top of the other has no affect on the number of sticks you have. While this is simplistic, the students find it easy to understand and they do remember it when we move on to other sets of numbers such as the rationals and the reals. In this book, Devlin does an excellent job of taking similar, simple concepts and then abstracting it to an initial general pattern. From this pattern, he then expands it out to more generalized patterns. This is the essence of mathematics and in my experience, one that students find easier to follow when learning. Humans naturally carry out inductive reasoning, taking distinct yet similar experiences and reaching generalized conclusions. In fact, it can be argued that such activities are a signature characteristic of intelligence. Devlin cites many examples of fundamental mathematical concepts that are the basis of mathematics. I try to include as many of them as possible in my basic math courses, because in my opinion together they form the best way for people to learn mathematics. It is natural and consistent with how humans do a large percentage of their learning.

This book helps the lay reader understand the meaning of why we study math. I recommend it to all of my students!

This marvelous book to explains to non-mathematicians the joy, beauty and power of mathematics. Each topic is presented in an original manner with alot of colorful illustrations to delight the eye and mind. Devlin shows how mathematical thinking is critical to our exploration of the world around us. This is one my top ten of all time list

Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The six chapters cover number theory, set theory, calculus, group theory and topology; but to state it baldly like this is to miss the main value of this seductively illustrated book. Devlin titles his chapters innocuously--"Shape", or "Position"--and the initial discussion, couched generally in English, not mathematics, is so clear that a math-phobic can understand it. By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics. And of the dramatis personae, too; one nice feature is the large number of good pictures of mathematicians, including several more recent figures such as Ribet and Thurston.Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics. The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it. The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.The illustrations deserve an extra comment. I've already mentioned the pictures of mathematicians. There are good diagrams, of the quality you'd expect from Scientific American. There are also plenty of pictures of the sort you see in every maths book of this kind--Escher tessellations, Kepler's nested Platonic solids, a Durer perspective drawing. But there are several more that I've never seen (and I've read a lot of these books). Two notable pictures: a cardboard model of an aperiodic tiling of space, by John Conway; and a picture of a set of tiles at a Dutch high school, designed by Escher: I'm an Escher fan and have never seen these before.Potential purchasers should note, by the way, that this book was reworked into Devlin's "Language of Mathematics". In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground."This is a fine book. Strongly recommended.

This book is a brilliant example of mathematics at it's best. It is from Scientific American, so you know you can trust it. And it is written at an understandable level, quite a feat for many very complex topics. The book features incredible illustrations, every concept is laid out in a colorful image. If you like the works of M.C. Escher, you will like this book. It has a lot of substance to it, and it will keep you busy thinking for a long time, and that's time well spent