Playing with Infinity: Mathematical Explorations and Excursions by Rozsa Peter (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 well done. a Math book that is actually readable.

⭐The book shows a number of ways the concept of Infinity has benefited us as mathematicians.

⭐The author invites the curious reader on a tour of various mathematical topics. I hope her stated goal of sharing mathematics with those whose background is elsewhere is achieved. As someone whose career is in this field, I learned a great deal from insights mentioned almost as afterthoughts. Two examples:You and a bunch of friends are points on the plane. Under what conditions can you take a small step that will simultaneously bring you closer to all your friends? (From the introduction)What is it that makes the axiom about parallel lines different from all the others? (From Chapter 18)Although the author is not concerned here with politics or history, occasional references to the fate of her pupils and their parents remind us that this masterpiece was created in occupied Hungary during the Second World War. In an understated way, it is a tribute to the human spirit.

⭐The author, Rozsa Peter, is a lady mathematician (or is one not supposed to notice?) who shares with George Gamow and Richard Feynman a flair of making the complicated seem simple. The preface states that the book is written for “intellectually minded people who are not mathematicians.” The book explores various ways in which the concept of infinity enters into mathematics – and the dangers it poses. Along the way other concepts, drawn from topology and non-Euclidean geometry, are snuck in. While these are only peripherally concerned with infinity, they constitute some of the most appealing material. The “seven bridges of Koenigsberg problem” is an example. Perhaps the very best part of the book is the last chapter, devoted to Goedel’s “unprovability” theorem.My general impression of this book is that of a mathematical counterpart to Gamow’s, “One, Two, Three … Infinity” — but not quite as good. Of course Gamow’s work is such a masterpiece that “not quite as good” still leaves lots of room. And that is why this book is a gem in its own right. I recommend this book especially to high school students with a strong interest in mathematics.So, why is the book not quite as good as Gamow’s? For one thing it does not quite have the breathtaking sweep of Gamow. The other is that in the process of making things simple, Rozsa overdoes it at times. Concepts that great minds struggled with for centuries appear as child’s play. The image of little ten-year-old Eva rediscovering the irrationality of the square-root-of-two all by herself seems a little strained. But then again — maybe she did do it!

⭐This book is a gem. I read it as a highschool student, and itplayed an important role in enticing me to become amathematician. Its emphasis is not on practical applicationsor on solving funny problems: instead, it is an inspiringintroduction to some of the greatintellectual challenges in the history of mathematics.

⭐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.

⭐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.

⭐A very interesting, well written, book, I’ll always remember that the best teachers I had would present / explain things in different ways to enable a greater understanding of them. This book certainly does that.

⭐It used to be my favourite maths book in Hungary, and now I`m happy that I found the English version for a friend. It`s like a tale about the world of mathematics. Easy to understand and provides a fantastic grounding in maths.

⭐It is interestingly written, however most people with an interest in mathematics will not learn anything from it. They will, however, learn how best to communicate it.(Very good value, too)

⭐Excellent book.

⭐I think it is a great introduction book to the wonderful world of mathematical logics. The book was in much better quality than I expect, shipping was reasonable and I enjoyed the book.

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