Euler: The Master of Us All (Dolciani Mathematical Expositions)

How can one tell the story of a giant like Leonard Euler?''The greatest resource of him is his collected works, the 'Opera Omnia'. Their publication begun in 1911, has consumed the remainder of the twentieth century. Only six dozen volumes have appeared until 1999, but his output has not yet run dry.''''Euler contributed to long-established branches of mathematics like number theory, analysis, algebra and geometry. He also ventured into the largely unexplored territory of analytic number theory, graph theory, and differential geometry. In addition, he was his century's foremost applied mathematician, as his work in mechanics, optics, and acoustics amply demonstrates.''Let's ask the question again: How can one write a book about Euler, which will attract the interest of even non-mathematicians and at the same time will clearly show the greatness of him and rise the readers' utmost admiration, which he definitely deserves?Well, Mr. Dunham has achieved this in a masterful way. He has searched among Euler's works and selected only three dozen of Euler's original proofs drawn from thirteen different volumes of the 'Opera Omnia' to discuss them with the reader, scattered in eight chapters of his book: Euler and-Number Theory, Logarithms, Infinite Series, Analytical Number Theory, Complex Variables, Algebra, Geometry, Combinatorics. The book starts with a small but very informative biography of Euler and ends with an Appendix about volume names and subjects of 'Opera Omnia'.Mr. Dunham proves again that he is a master in expository writing of mathematics in historical context. His style is very casual, friendly, clear, with awareness of what the reader will need more and when in order to grasp the subject better. As can be seen from the selected chapters, he has chosen subjects which will appeal most to the interest of a wide group of potential readers. At the beginning of each chapter, he gives a brief history of that subject and then he allows Euler to enter the scene and tells his contribution, and he ends the chapter with an epilogue where he discusses and concludes all that chapter. This makes the reader to clearly understand the place of each mathematical development in time and who have contributed to it.I could not leave the book once I started and it took a few days only to finish it. I am a retired electronics engineer spending my time in studying the development of scientific thoughts in historical context and preparing seminar lectures for some distinguished high school students in physics and mathematics. The content of this book fit so well into my study. The information I met here is not available in any curriculum, which are mostly so dull. The way Mr. Dunham explains it is so inspirational in all ways.On top of everything he has a special sense of humor, which makes you smile from time to time. I loved the paragraph where he makes an analogy for 'inspiration' while he discusses the proof of 'Euler Line' . He asks 'How did Euler know to construct that special triangle in his proof of Heron's formula?' He continues, 'Ultimately, the answer to this question lies in the mysterious realm of the human imagination. One might just as well ask of Shakespeare why he put the balcony scene in 'Romeo Juliet'. This is so wonderful. I wish I could be one of his students but in my age now:)I highly recommend this superb book to everyone who has a moderate college level of mathematics and is interested in the development of science and math in historical context. Especially the parents in this category might find it very useful to help and inspire their children in loving math, if they need it.

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.

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.

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.