Product Description
What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through. ... Read more

Customer Reviews (3)

A wonderful read
I really enjoyed this book and would recommend it to high school students with an interest in studying math in college. Typically, high school students are not exposed to well written proofs. This book would remedy the situation.

The Real Beauty and Exhiliration of Math
This is a superb book, and the best way to first sample the delights of math for its own sake. Don't let the subtitle "Selections from Mathematics for the Amateur" turn you off. True, the math involved is elementary, not going beyond high school algebra and geometry. But the material won't be found in most textbooks, having been chosen with elegance and beauty, rather than utility, in mind (which isn't to say that it doesn't have its important uses). Even the professional mathematician who has already seen most of the contents will profit from studying the book's exemplary treatment of its topics. The authors are some of the best math expositors who have ever lived. Each idea in the book is developed admirably, and strikes the perfect balance between conciseness and lucidity. You probably can't do better in choosing an introduction to prime and perfect numbers, the four-color problem, regular polyhedra, Pythagorean triples, pedal triangles, periodic decimal fractions, Waring's problem, the number 30 (sic!), and many other fascinating intellectual tibdits.

At Dover's low price, this book is a great buy. Get it! If you have more mathematical knowledge, then I also recommend "Proofs from the Book" by Aigner, et al., which is written for mathematicians in a similar style.

An excellent collection of problems at the elementary level
Written by two top-notch mathematicians, requiring the mathematics that a high school student can do, this book takes you on a journey that is easy to follow and yet shows the power of mathematics. It is an excellent bookfor high school enrichement or early undergraduates.

Even if you are amathematician you will be suprized at many of the results and enjoy tryingto solve some of the problems. Many of the problems are quite hard. Eventhough some of the problems are the standard ones, many are off the beatentrack. No matter what your level of expertise, I am sure you will enjoythis book. ... Read more

Product Description

Customer Reviews (5)

A Great Alternative (Pre-War) Look at Calculus
Current calculus books are massive tomes that are geared to 'plug and chug' problems.Once done, the student can then quickly look up the answer in the back of the book.

This book provides a realtively brief introduction the integral and differential using a visual (geometric) approach before getting into the algebra.It takes more time to learn the material this way than simply saying 'the derivative of x^n is nx^n-l :now differentiate x^2'. (I am big on visuals - particularly in real analysis).Rather, Toeplitz goes over the visual idea of differentiation, integration, the fundamental theorem, integration by parts, etc.

You will not learn the whole of calculus from this book.Rather, it is a great tool to have in your back-pocket for Calc I-IV and Rudin's 'Real Analysis'.If you want to have a better appreciation of calculus, you will get a lot of use out of this book.

In an era of calculus textbooks so massive that they can be used in bodybuilding courses, this book is a welcome outlier
In an era of calculus textbooks so massive that they can be used in bodybuilding courses, this book is a welcome outlier. It is small enough to fit in your (large) back pocket, yet contains what can be considered the essence of differential and integral calculus.
It all begins with the fundamentals of the infinite process, the foundation of the subject. Toplitz opens with iterations, summing infinite series, the principle of exhaustion, limits, convergence and infinitesimals. From this, the order is the summation process that leads to the definite integral, followed by differential and integral calculus and then how calculus is applied to motion. The last chapter is also a history lesson, as some of the work of Kepler, Newton and Liebniz in describing motion is covered.
At its' core, the basic principles of calculus can be expressed in less than 200 pages with anything else simply additional ways of doing the same things. Toeplitz certainly expresses a lean form of calculus in this book, something that other authors on the subject should consider. Done right, it is only necessary to say something once, and Toeplitz certainly has done that and done it well.

A relic in another language
Even when translated into English, this book is nearly incomprehensible to the modern reader.It was published in the 1960s, but the author uses turn of the century academic language that is intentionally abstruse.I've read terse mathematical works and been able to penetrate many of them, but I certainly feel for anyone who has to use this unreadable book in their course like I do.

Sad that it didn't quite work
I would find a good "genetic" approach to the calculus extremely valuable, and Toeplitz seems perfect for the job: a big German professor of the classical tradition who says all the right things in the preface, and who throws around quotations in Latin that he expects everyone to understand. So far so good. One is all the more dissapointed then when it turns out that the book simply isn't that good. It covers the calculus from the Greeks and stops after Newton (it seems that there was meant to be a second volume). The topics are the usual ones. Certainly one could learn a lot of calculus from this book, and certainly there are many interesting historical remarks, but the unity of the two does not reach the great heights we had hoped. One can achieve pretty much the same effect by simply pasting together a calculus history book with any old calculus textbook.

Dusseldorf 1926 .. Otto presents the "genetic" method
This translation from the German by Luise Lange is superbly done. The bookcan be appreciated by high school level students who have an interest inmath. I plan to use some of the exampleson my web site which will employmath 101 and Visual Basicprogramming techniques....Leo JL...programmer atlarge ... Read more

Product Description
Der Erwerb des Buches enthält gleichzeitig die kostenlose Mitgliedschaft im Buchklub des Verlags zum Ausprobieren - dort können Sie von über einer Million Bücher ohne weitere Kosten auswählen. Das Buch besteht aus Wikipedia-Artikeln: Nicolas Bourbaki, Felix Klein, Bernt Michael Holmboe, Alexander Witting, Otto Toeplitz, Walther Lietzmann, Hans Freudenthal, Inge Schwank, Martin Wagenschein, Edwin Moise, Morris Kline, W. W. Sawyer, Wolfgang Coy, Karl Seebach, Marianne Franke, Hans-Georg Weigand, Peter Baireuther, Norbert Meder, Robert Kaplan, Hans-Joachim Vollrath, Heinrich Besuden,. Online finden Sie die kostenlose Aktualisierung der Bücher. Nicht dargestellt. Auszug: Felix Christian Klein (* 25. April 1849 in Düsseldorf; † 22. Juni 1925 in Göttingen) war ein deutscher Mathematiker. Felix Klein hat im 19. Jahrhundert bedeutende Ergebnisse in der Geometrie erzielt. Daneben hat er sich um die Anwendung der Mathematik und die Lehre verdient gemacht. Klein, der auch ein bedeutender Wissenschaftsorganisator war, hat wesentlich mit dafür gesorgt, dass Göttingen zu einem Zentrum der Mathematik aufgestiegen ist. Grabstelle in Göttingen Klein studierte in Bonn bei Rudolf Lipschitz und Julius Plücker, dessen Assistent er wurde. Nach dem Tod Plückers übernahm Alfred Clebsch die Herausgabe seines unvollendeten Werkes und übertrug diese Arbeit an den begabten Klein. Klein promovierte 1868 bei Lipschitz mit einem Thema aus der Geometrie angewandt auf die Mechanik. 1869 ging er dann an die Berliner Universität und hörte dort eine Vorlesung von Leopold Kronecker über quadratische Formen. Er nahm an den mathematischen Seminaren von Ernst Eduard Kummer und Karl Weierstraß teil, wo er auch Sophus Lie kennen lernte, mit dem er 1870 zu einem Studienaufenthalt nach Paris ging und befreundet war. Aufgrund des deutsch-französischen Kriegs kehrte er nach Deutschland zurück. Er habilitierte sich 1871 bei Clebsch in Göttingen und blieb 1871/72 als Privatd...http://booksllc.net/?l=de&id=31071 ... Read more