Playing with Infinity

By Rózsa Péter

Book Overview

This popular account of the many mathematical concepts relating to infinity is one of the best introductions to this subject and to the entire field of mathematics. Dividing her book into three parts -- The Sorcerer's Apprentice, The Creative Role of Form, and The Self-Critique of Pure Reason -- Peter develops her material in twenty-two chapters that sound almost too appealing to be true: playing with fingers, coloring the grey number series, we catch infinity again, the line is filled up, some workshop secrets, the building rocks, and so on. Yet, within this structure, the author discusses many important mathematical concepts with complete accuracy: number systems, arithmetical progression, diagonals of convex polygons, the theory of combinations, the law of prime numbers, equations, negative numbers, vectors, operations with fractions, infinite series, irrational numbers, Pythagoras' Theorem, logarithm tables, analytical geometry, the line at infinity, indefinite and definite integrals, the squaring of the circle, transcendental numbers, the theory of groups, the theory of sets, metamathematics, and much more. Numerous illustrations and examples make all the material readily comprehensible. Without being technical or superficial, the author writes with complete clarity and much originality on the whole range of topics from counting to mathematical logic. Using little algebra and no mathematical formulas, she has written an unusual book that will interest even mathematicians and teachers. Beginning mathematics students and people in the humanities and other fields will find the book particularly outstanding for their purposes.

• Format: Paperback
• Language: English
• ISBN: 0486232654
• ISBN13: 9780486232652
• Release Date: August 2010
• Publisher: Dover Publications
• Length: 288 Pages
• Weight: 1.27 lbs.
• Dimensions: 0.6" x 5.4" x 8.5"

Customer Reviews

Introduction to the great adventure of mathematics for the educated layman

This book is a gem. I read it as a highschool student, and it played an important role in enticing me to become a mathematician. Its emphasis is not on practical applications or on solving funny problems: instead, it is an inspiring introduction to some of the great intellectual challenges in the history of mathematics.

Sweet!

Prof. Peter (whose book on recursive functions is considered a classic among computer scientists) introduces the reader to the beauty that is mathematics by breaking down concepts that might appear intimidating to the neophyte. This charmingly written book takes readers by the hand and explains areas of mathematics that deal with the concept of infinity in a friendly, non-condescending manner, commencing with basic arithmetic and eventually progressing to logic and set theory and the works of Cantor, Hilbert, and Russell. A good introduction to mathematical principles for those looking to get their feet wet, Playing with Infinity is also fun for the more mathematically seasoned reader. Many thanks to Dover for keeping such books available and at such a reasonable price.

Very good general account on infinity..

This book will give you a good general introduction to the concept of infinity. I found the presentation informal and quite easy to follow. Since the book was first written in 1943 and revised in 1960 there are some units that are not used anymore. For example, the coinage of pounds, shillings, and pence is dead. Things like a chapter on "The Charts Get Smoothed Out", may seem round about but still interesting. My favorite chapter is "Mathematics Is One". The derivation of "visual forms" in functions is excellent. Have pen and paper handy because to really enjoy the book I found myself doing some of the "the reader can solve for himself..." stuff. Another point is that you can more or less read the chapters independently and in no particular order and still reap huge benefits from the material.Thank God for Dover which still publishes this book. My copy is a 1976 edition. If you are interested in getting back in touch with things you may have long forgotten get this book.

Explanation of math from the very beginning

This book explains the why's behind math from principles as basic as counting to as complicated as series, geometry, and even some calculus principles. It is written in a conversational tone with lots of pictures (yes, and numbers). Each chapter builds upon the last, and it is easy to follow (though sometimes dense). It was my first "fun" math book and is still by far my favorite. There are other math books that take real situations and relate them to math, but this starts with math and sticks with it. Thus, not for the mathphobe, but great if you want to understand math from the ground up.

Fun intro to Infinity math for older kids and others

Infinity is fun. But most people have never been exposed to the fascinating theory of infinities. This book provides an extremely well presented introduction to the concepts of infinities. The presentation is at times a little forced, however overall it is clearly and simply written, and the basic analyses of enumeration by pairing of elements is explained in a simple and easily understandable manner. The elementary concepts of infinites are not difficult to grasp, and should and can be understood by anyone with an interest in mathematics. This book provides an easy to understand introduction to these concepts. I especially recommend it for parents wanting to study/learn math with their kids in middle and high school. It covers material that will not be covered at school, but is fun and not overly difficult to grasp, and will surely help both the parent and child.