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William W. Dunham
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Euler: The Master of Us All (Dolciani Mathematical Expositions)

by William Dunham (Author)
4.5 4.5 out of 5 stars 69 ratings
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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.
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  1. ISBN-10
    0883853280
  2. ISBN-13
    978-0883853283
  3. Publisher
    American Mathematical Society
  4. Publication date
    March 4, 1999
  5. Language
    English
  6. Dimensions
    6.25 x 0.5 x 9.25 inches
  7. Print length
    208 pages
  8. See all details
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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

This book examines the huge scope of mathematical areas explored and developed by Leonhard Euler.

Product details

  • Publisher ‏ : ‎ American Mathematical Society (March 4, 1999)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 208 pages
  • ISBN-10 ‏ : ‎ 0883853280
  • ISBN-13 ‏ : ‎ 978-0883853283
  • Item Weight ‏ : ‎ 10.4 ounces
  • Dimensions ‏ : ‎ 6.25 x 0.5 x 9.25 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 69 ratings

About the author

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William W. Dunham

William W. Dunham

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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

4.5 out of 5 stars
4.5 out of 5
69 global ratings

Top reviews from the United States

Carlos A. Morales
5.0 out of 5 stars So much fun it makes you chuckle
Reviewed in the United States on November 18, 2000
Verified Purchase
I don't have much to add to the excellent reviews above, except to say that if you like clear exposition of sometimes obscure mathematical themes, like logarithms of imaginary numbers, or the almost magical Euler line, you can't do better than read Professor Dunham's books. And when you mix this talent with a subject such as the incredibly clever and curious Leonhard Euler, you can't help but be carried away. I literally found myself chuckling with awe at some of the amazing leaps of intuition this 18th-century mathematician was able to make, even as he was losing his sight and fathering 13 children! I've always been an admirer of Euler's, and Prof. Dunham's wonderful little book only increased my admiration -for both.

I hope Prof. Dunham will decide to write a sequel, and/or tackle the work of other prolific mathematicians, like the Indian Srinivasa Ramanujan, another one of my heroes.

This is the third book by Prof. Dunham I've read. I have enjoyed them all and keep them handy to lift my spirits when I'm down -they're that much fun. I wish I'd had him as a teacher in college, and I envy his students at Muhlenberg College. I just hope they appreciate how lucky they are!
51 people found this helpful
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Marc
5.0 out of 5 stars Dunham at his best, this is book is a must have
Reviewed in the United States on February 1, 2012
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Dunham is the master of writing historical math texts. His passion clearly comes through in the writing.

I am a perpetual student, and I find the historical texts helpful in many ways. Probably the biggest contribution is that they put math in a historical context, and it really does help understand the theorems. Textbooks do provide some context, but never really link how various problems and solutions led to other major discoveries.

The format of the book is perfect. Dunham chose theorems which were his personal favorite. ( consider the challenge of choosing from Euler's body of work ).

Part of it is biographical, well a small part. But it is all biographical, since the theorems themselves define Euler and his remarkable contribution to math. Duhnam does a great job of telling Euler's story with his theorems. Each chapter is structed where it explains the context of Eulers work by first providing a historical record of the problem. And the solutions at the time, or lack of. Then Eulers efforts and theorem are documented, and of course a discussion of future devleopments by others.

This is not exactly a popular math book, because to enjoy the text you should really be a math person since Dunham's treatment does work through the math.
17 people found this helpful
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ddelaney2011
4.0 out of 5 stars Bought new but got used.
Reviewed in the United States on October 6, 2022
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Bought this book as new but received in “used” condition.

Smaller than I expected and too expensive.

Looks like I got ripped off.
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Carles V
5.0 out of 5 stars Another example of Dunham's brilliant work
Reviewed in the United States on January 28, 2013
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William Dunham has become one of my favourites "mathematics expository" writers.

In his book "The Calculus Gallery" he explained the history of Calculus, sampling from the masterworks of the best mathematicians that have contributed to this subject.

In "Euler, The Master of Us All", he dedicates his masterful writing to one of the most prolific, exciting and greatest mathematician of all times: Leonhard Euler.

With Dunham's beautiful clarity and engaging prose, you can follow with amazement Euler's strokes of genius in several fields of Mathematics: Number Theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry/topology and combinatorics.

I can't hightlight one section more than the others. All of them are simply superb.

This book is one of the best books on mathematics I've ever read.
(By the way, another one of my very favourites, is John Derbyshire's "Prime Obsession")

As Laplace said, "Read Euler, read Euler. He is the master of us all".
He was right, and Dunham's book proves it.

And just a last word: The Dolciani Mathematical Editions are one of the most fine editions I've found.
The quality of printing and the presentation of the book are superb.
6 people found this helpful
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Jordan Bell
5.0 out of 5 stars Easy to follow introduction to Euler's writings
Reviewed in the United States on November 11, 2017
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This is an excellent introduction to some of the mathematics of Euler. Chapter 1 is on multiplicative functions, particularly the sum of divisors function. Chapter 2 is on Euler's constant (for harmonic sums). Chapter 3 applies Newton's identities to infinite product and infinite series for sin x to get evaluations for zeta(2), zeta(4), etc. Chapter 4 is on the Euler product for the Riemann zeta function, from which it follows that the sum of the reciprocals of the primes is infinite. Chapter 5 is about Euler's identity for the imaginary exponential. Chapter 6 is about the theory of equations. Chapter 7 proves that the orthocenter, the circumcenter, and the centroid of triangles are collinear; the common line is the "Euler line". Chapter 8 is on combinatorics, and proves a recurrence formula for derangements and an explicit formula.
6 people found this helpful
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A. B. Whiting
5.0 out of 5 stars Excellent presentation of a genius
Reviewed in the United States on May 1, 2019
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This book presents a sample of the mathematical work of Euler, one of the greatest mathematicians of all time. It is more than just a recitation of proofs: the author comments on Euler's technique, and places his work in context with both earlier and later accomplishments. It gives a wonderful flavor of what it is to do mathematics.
One person found this helpful
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Lee De Cola
5.0 out of 5 stars an apparently ordinary fellow who had a devine brain.
Reviewed in the United States on January 1, 2018
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a book for the mathematically sophisticated that reaches across the centuries to illuminate one of the giants of mathematics. like all good scientific writing, there's a minimum of verbiage and frequently really elegant prose. read it with a pencil and paper at your side; you can even program some of the theorems.
One person found this helpful
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Reviewer
5.0 out of 5 stars tour de force
Reviewed in the United States on April 2, 2015
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This is quite a wonderful book about a remarkable person and stunningly insightful mathematician. It emphasizes his contributions to mathematics but also interweaves his life story in what for me was the right proportion. I'm inspired to return to and delve more deeply into areas of mathematics I had long ago forgotten.
9 people found this helpful
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Top reviews from other countries

David Cooper
5.0 out of 5 stars How a genius invented maths
Reviewed in the United Kingdom on January 8, 2021
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As a recent reader I feel the need to confirm what many others have said. This is an exhilarating, path - breaking introduction to mathematics as a craft. Euler's genius is vividly demonstrated with a variety of examples showing his astonishing ability to think inductively, see patterns and relationships in simple numerical examples and then draw on his tool box to convince himself that his guesses were right. His use of power series is spectacular and in a different plane from the mechanistic way I was taught maths - admittedly 60 years ago! I could not put this book down and spent two happy days refreshing my mathematical skills. A perfect lock down treat for an A level student with a good grounding in algebra, logarithms, trigonometry, power series and geometry, who wants a real insight into how mathematics was invented by a genius

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Adarsh Kumar
5.0 out of 5 stars Good
Reviewed in India on November 9, 2018
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Awesome for beginners only. Paper quality is too good and have very nice print.
One person found this helpful
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David Richard Fattori
5.0 out of 5 stars Math people will love this book
Reviewed in Canada on September 11, 2013
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You will need a very strong background in mathematics in order to appreciate
the book fully. The math is often sophisticated and the author does not always
completly explain the outcomes. Despite this, the book is very well written and the sidebars
about the various mathematicians, principally Euler, are fascinating. One really is
left with an awe and amazement and an appreciation of Euler's genius.
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Amazon Customer
5.0 out of 5 stars This is a masterpiece for any person who enjoys math ...
Reviewed in Canada on September 9, 2016
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This is a masterpiece for any person who enjoys math and has a college level in calculus and integrals.
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Biro
5.0 out of 5 stars Excellent read.
Reviewed in the United Kingdom on March 13, 2013
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This would be a very good book for students who have done the further maths A level. The book is funny in places and very entertaining, although there were a number of places where I needed to get out the paper and pencil. It would be very helpful if equations were kept on the same page as the text that describes them as I found myself having to flick between pages quite a bit. I found myself asking `how on earth did Euler think of that' quite a bit, but then I suppose he was a genius... One of the best maths books I have read, both entertaining and instructional.
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