Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) [Paperback]

William Dunham (Author)

Book Description

ISBN-10: 0883853280 | ISBN-13: 978-0883853283 | Publication Date: January 1, 1999

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Editorial Reviews

Review

An ideal book for enlivening undergraduate mathematics...he {Dunham} has Euler dazzling us with cleverness, page after page. -- Choice

Mathematician William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Professor Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler's broad shoulders. Such a book has long been overdue. It will not need to be done again for a long long time. -- Martin Gardner

William Dunham has done it again! In "Euler: the Master of Us All", he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham's beautiful clarity and wit, we can follow with amazement Euler's strokes of genius which laid the groundwork for most of the mathematics we have today. -- Ron Graham, Chief Scientist, AT&T

William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler's broad shoulders. Such a book has long been overdue. It will not need to be done again for a long, long time.Martin Gardner

Dunham has done it again! In "Euler: The Master of Us All," he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham's beautiful clarity and wit, we can follow with amazement Euler's strokes of genius which laid the groundwork for most of the mathematics we have today. -- Ronald Graham, Chief Scientist, AT&T

Book Description

Leonhard Euler was one of the most prolific and wide ranging mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more.

See all Editorial Reviews

Product Details

• Paperback: 192 pages
• Publisher: The Mathematical Association of America (January 1, 1999)
• Language: English
• ISBN-10: 0883853280
• ISBN-13: 978-0883853283
• Product Dimensions: 8.9 x 6.7 x 0.5 inches
• Shipping Weight: 10.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #253,360 in Books (See Top 100 in Books)
  • #18 in Books > History > Europe > Switzerland

More About the Author

William Dunham, Koehler Professor of Mathematics at Muhlenberg College, is the author of "Journey Through Genius: The Great Theorems of Mathematics"; "The Mathematical Universe"; and "Euler: The Master of Us All". He has received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.

Customer Reviews

Most Helpful Customer Reviews

69 of 69 people found the following review helpful:

5.0 out of 5 stars An enjoyable mathematical romp, June 7, 2000

By 

Jef Raskin - See all my reviews

This review is from: Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) (Paperback)

I got the book this morning, started reading it, and I didn't know the earth was still rotating until hours later and I had to start the rice cooking for supper. Solid mathematical exposition; historical asides interesting and readable. Very well done except that the puns are too exposed.

Each chapter starts off with a description of the state of some mathematical topic as it was before Euler's work, then it explains Euler's contributions to the topic (take your time to follow along, proofs given!). Lastly, each chapter tells where the work has led since. This is a superb way to present a mathematician's achievements.

The math is mostly pre-calc level: natural logs, complex numbers, and standard trig identities. The occasional derivatives and integrals pose no hazard to a first-year calculus student. But the book is enjoyable even if you skip over some of the math, a credit to the author's clear exposition.

A truly enjoyable mathematical romp.

41 of 41 people found the following review helpful:

5.0 out of 5 stars William Dunham has done it again!, March 24, 2002

By 

Allan Heydon (San Francisco, CA USA) - See all my reviews
(REAL NAME)   

This review is from: Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) (Paperback)

With the publication of this, his third book, Dunham has once more shown himself to be a master himself of mathematical explanation. Unlike his previous two books, The Mathematical Universe and Journey Through Genius, which covered results by a variety of mathematicians, this book focuses on selected results that sprang from the remarkable mind of Leonard Euler, one of the most prolific and important mathematicians of all time. What sets Euler apart is not only the vast quantity of his output (the publication of his collected works, the Opera Omnia, spans six dozen volumes, or over 25,000 pages in all!), but also the breadth and originality of his work. Not only did Euler contribute to a wide array of mathematical fields -- from number theory to complex analysis to geometry -- but in many cases, he was the founder of those fields. For example, Euler invented the field of analytical number theory, and he was the first mathematician to recognize the importance of and to discover the important properties of complex numbers.

This book in many ways resembles Dunham's Journey Through Genius. As in that book, Dunham has selected 15 or so theorems to present in detail, and he makes an effort to keep the proofs similar in spirit to the original proofs. Although the proofs are complete and the book is full of equations, they are accessible to anyone with a high school level of mathematics education. But in addition to the proofs, Dunham also provides historical context, as well as commentary on how later mathematicians used and improved upon Euler's work. For example, we learn that Euler began to loose the sight in his right eye at the age of 32, and that despite his virtual blindness by the age of 65, he continued his prolific rate of output until his death at age 84.

The book's title is taken from a quote by Laplace, who said, ``Read Euler, read Euler. He is the master of us all.'' Indeed, if you have any interest in mathematics, you will almost certainly find yourself in complete agreement with Laplace's sentiments by the time you finish reading this wonderful book. ...

38 of 38 people found the following review helpful:

5.0 out of 5 stars A little gem., August 25, 1999

By A Customer

This review is from: Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) (Paperback)

I had never read any of William Dunham's many books before. Now I want to read them all. In a scant 173 pages he describes in great detail how Leonhard Euler, arguably the greatest mathematician ever, solved the most difficult mathematical problems of his day.

The style in this book is both unusual and clever. Each of the eight chapters covers a different branch of mathematics and each begins with a prologue, then follows with some of Euler's contributions, and finishes with an epilogue. The prologues present the history of mathematics up to Euler's time, so the reader gets a feel of what this great mathematician had to work with. And the epilogues tell where we have come since Euler.

This book is full of equations and expects some work (but not much mathematical background) from the reader. If you like mathematics or ever wondered how some of the great discoveries in this field were derived, do yourself a favor and buy, then carefully read, this wonderful book.