Nice book for readers with a background in math

books:

	• Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) (Dolciani Mathematical Expositions) William Dunham The Mathematical Association of America, 1999 - 192 pages average customer review:based on 12 reviews view larger image
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highly recommended

Nice book for readers with a background in math

I really enjoyed reading this book that describes some background on Euler and his work. It is written in an informal style, so for people with a math background it reads like a novel.

The book is not suitable for people who want to learn more about the person Euler, but do not have a math background, because 75% of the book is about real math (equations). So if you don't enjoy reading equations, do not buy the book.

Summary: as enjoyable as the other Dunham books, although a bit more expensive (but still worth the money).

A great book

Don't be fooled by the brevity or put off by the high price of this book - it's worth its weight in gold. If you have a university level math degree and you want to do proofs again, this book is for you. I have been able to understand everything in the book as a result of Prof. Dunham's amazing ability to explain things. I did have to resort to the Internet on occasion to brush up on some trigonometry and calculus. I have been reading it slowly for 2 years now and I'm only half way through - sometimes I pull it out when I need some brain exercise. If you like math, you will like this book.

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William Dunham has done it again!

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. ...

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Charming but historically inaccurate.

Once again, the Ivy League establishment has got it all wrong. They continue to perpetrate error in the historical record just as they do in the scientific record with that preposterous theory of evolution.

First of all, Euler should not be credited with topology. Descartes had formulated, before Euler was born, the key topological equation F + V - E = 2.

The Greeks attached mystical significance to the five platonic solids. So much so, Euclid included the five regular solids in book 13 of his Elements as if it were the culimination of his work, as if the three-dimensionality were a culimination of the two-dimensionality of the earlier books.

These "regular" solids are three-dimensional objects: namely, the Tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. They are "regular" because, on each, the faces are congruent. Furthermore, the face angles are equal. For example, a cube's faces are all the same size.

If we count the faces on the tetrahedron, cube, octahedron, dodecahedron and icosahedron respectively, we get 4, 6, 8, 12, 20 respectively.

If we count the vertices of each respectively, we get 4, 8, 6, 20, 12.

If we count the edges respectivley, we get 6, 12, 12, 30, 30.

Now, create an array of the faces, vertices and edges:

F:4 6 8 12 20
V:4 8 6 20 12
E:6 12 12 30 30

Descartes noticed that F + V - E = 2. For example, 4 + 4 - 6 = 2. Or take the second column: 6 + 8 - 12 = 2. Descartes conjectured (as we all would) that this formula represents an invariant amongst all polyhedra.

Descartes died in 1650 A.D. when he was poisoned by some jealous Swede. Euler was born in 1707 A.D., some time after Descartes's death. Liebnitz had translated this work of Descartes which shows F + V - E = 2. And Euler is known to have read all of these Liebnitz manuscripts at the Hanover archives.

Why scholars persist in giving Euler credit for this equation boggles my imaginatino unless their reading is limited. If it is limited, then appellation of scholar for such men is unwarranted.

Pictures of the five platonic regular solids can be seen in Daud Sutton's little book "Platonic and Archimedian Solids."

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" Euler, the anlysis incarnate "!!!!

" 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 )

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reviews: page 1, 2, 3

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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