Euler: The Master of Us All (Dolciani Mathematical Expositions) by William Dunham (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review An ideal book for enlivening undergraduate mathematics…he {Dunham} has Euler dazzling us with cleverness, page after page. — ChoiceMathematician 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 GardnerWilliam 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&TWilliam 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. About the Author William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He has won two awards for excellence in expository writing from The Mathematical Association of America: the 1993 George Plya Award, and in 1997, the Trevor Evans Award. His books Journey Through Genius: The Great Theorems of Mathematics, and The Mathematical Universe have both been selections of the Book-of-the-Month Club and the History Book Club. He has also been the recipient of several grants from the National Endowment for the Humanities to fund seminars on the great theorems of mathematics in historical context. Read more

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

⭐Bought this book as new but received in “used” condition.Smaller than I expected and too expensive.Looks like I got ripped off.

⭐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.

⭐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.

⭐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!

⭐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.

⭐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.

⭐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.

⭐” Analysis incarnate ” , no other more suitable words probably can describe the incomparable power of Euler, as his contemparies called him. Concerning the usual style of Dunham to write this stimulating book, other readers have made many comments and I think there is no need to repeat that. What I want is that Dunham to write another book, perhaps volume 2,3 etc and also write a thorough biography of Euler, one the greatest mathematicians in the history. ( To me, for mathematical ability, his should be at the same rank with Newton, Archaemedes, and Gauss, even Einstein concerning the mathematical and theroetical aspect, is below par compared with Euler )

⭐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 geniusP

⭐I enjoyed this book. The mathematics covered attempts to be representative of Euler’s colossal output, giving the reader a flavour of his contributions to Algebra, Geometry , the beginnings of Analysis and Combinatorics. For the reader entirely unaquainted with Leonhard Euler I think it would probably succeed. However my feeling is that the book is far too short and also quite expensive considering its brevity (170 pages).I am quite sure that far more material could have been included. The book is well written with a clear level of exposition.. the proofs are well set out and easy and enjoyable to follow. This book supplements the offerings from Paul Nahin (Dr Euler’s Fabulous Formula) and Julian Havil’s ‘Gamma’ ..the latter containing rather more mathematics though.

⭐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.

⭐This is a fairly slim book for the cost, but the content justifies this. Unlike some of Dunham’s other books, this is really intended for an undergraduate rather than a school or A-level student, though I would recommend it to someone at college who is expecting to do a maths degree. Euler’s works are not readily available and this book is one rare chance to see some fully worked proofs of Euler’s. Luckily for me my university has Euler’s “Opera Omnia” in its library, but even for us privaleged Euler fans, the great tomes are in all sorts of languages, (Latin, German, French &c). Take this opportunity and experience some well selected theorems with proofs belonging to Euler presented by Dunham in English and with informal commentary. I have worked through one or two of the proofs in “Euler, The Master Of Us All” in detail, ensuring that I followed every step, and the rewards are massive. I was so enthusiastic about one of the proofs that I tried to learn it off by heart, (and I think I succeeded short term, but I suspect I would need to revise it now). I am a pure mathematics enthusiast, (though I won’t go into my philosophical uncertainties about today’s frontiers), and this is what might be called elegant pure maths before all the big fish were caught, (Euler was himself a master fisherman, and could probably fish with a rod in both hands and undoubtedly knew every kind of knot).

⭐With Euler it is always easist to write a long book. He did so much that the temptation is to give usa long text one some concept. The author here manages to give us a shorter book on Euler that exposes how he worked. Euler seemed to drain every last drop of valuable mathematics from each of his marvellous insights. I found this book gave me a view of this in action over a group of topics. An enjoyable read.

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