Product 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. ... Read more

Customer Reviews (14)

Too good
Anything by Dunham is worth reading multiple times. If you like math and you have kids and you want to teach them - read this over and over and share the joy that is math. Euler in particular comes through as a pragmatist - and his immense output inspires one.

My Favorite Non-Fiction Book.
I found this book in the university library when I was a Freshman in college and started reading it for fun. In High School I enjoyed mathematical Olympiad type problems very much and I had heard of Euler often, because he has many basic theorems. I was excited to read a book that would give a bit of biographical information on Euler, write a theorem of Euler with proof and then write how the subject changed afterwards.

The book has many cool proofs. I mainly remember the chapter on the Basil problem, the problem of summing 1/1 + 1/4 + 1/9 + 1/16 + .... Euler magically found the answer to be pi squared over 6. This book was the first place I saw this result (one of my favorite results) and it showed a sketch of a proof.

The book also has the proof that every even perfect number is of the form 2^(p-1) * (2^p - 1). This is in fact the first chapter I read of the book because it was a subject that had interested me for a long time (and it still interests me, now that I am doing research in number theory).

This book reinforced my love for mathematics. It is one of my favorite books. I highly recommend it.

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.

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:4681220
V:4862012
E:612 12 3030

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."

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). ... Read more

Product Description
The Early Mathematics of Leonhard Euler gives an article-by-article description of Leonhard Euler s early mathematical works, the 50 or so mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin.These early pieces contain some of Euler s greatest work, the Königsberg bridge problem, his solution to the Basel problem, and his first proof of the Euler-Fermat theorem.It also presents important results that we seldom realize are due to Euler; that mixed partial derivatives are (usually) equal, our f(x) notation, and the integrating factor in differential equations.The books shows how contributions in diverse fields are related, how number theory relates to series, which, in turn, relate to elliptic integrals and then to differential equations. There are dozens of such strands in this beautiful web of mathematics. At the same time, we see Euler grow in power and sophistication, from a young student when at 18 he published his first work on differential equations (a paper with a serious flaw) to the most celebrated mathematician and scientist of his time. It is a portrait of the world s most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler s work and with the work of other mathematicians in other times and places, laced with historical context. ... Read more

Customer Reviews (1)

The vol 1. and 2. a must for all mathematicians.
Happy Birthdays to our hero, Leonhard Euler, 1707 -1783, one the greatest mathematicians of all time nd undoubtedly the most popular among mathematicians ( profeesional and amateur ). Total 4 volumesto commemorate the 300 birthdays of Euler. Edited by enthusiastic current matematicians who are fervent fans of Euler. Need I to say anymore?? ... Read more

Product Description
This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler's works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler's personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author's historically motivated method of teaching, special attention is given to demonstrate that Euler's work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler's extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Customer Reviews (2)

Another Magnum Opus by Leonhard Euler
Elements of Algebra by Leonhard Euler is in a class all its own.His masterful exposition of rudimentary and not-so-rudimentary algebra is extraordinarily clear and notably readable.The problems that Euler designed are both profoundly elegant and in-depth.A percentage of each of his problem sets is relatively straightforward while other problems require some attentive thought.If one is interested in becoming a proficient algebraist in the classical sense, then Euler's work will greatly facilitate this objective.If one simply desires to 'read' mathematics for the sheer pleasure of it, this book will fulfill that aim.

By the way, the other reviewer's one-star rating has to do with a softcover and edited edition of this work.

Extreme Abridgment of Euler's Work
This book is NOT a reprint of Euler's book as the publisher claims. Point one..is has significantly fewer than 300 pages and the Hewlett reprint requires close to 600 pages. Furthermore, Euler, a genius in mathematics, is corrupted by a new organizing of its contents as if this new editor had the genius to select and reorder the contents. Important footnotes have been removed under the pretense that they just took up space..etc. These include the famous Lagrange notes. Part II of the Algebra is completely left out. The title of this so-called reprint of Euler's brilliant book translated so well by Hewlett would better be entitled..Euler's Elements of Algebra Highly Abridged and Re-organized (by a scholar who has yet to prove he is up to such discernment)... ... Read more

Product Description
In the 17th century, the small but culturally and intellectually eminent city of Basel was the home of one of the most prominent mathematical families of all time, the Bernoullis, and their friend, protege, and master Leonhard Euler. The author chronicles their lives and achievements at a time when modern analysis and its applications to physics burst on the scene and created a methodological framework for modern science. Written for young adults, this book conveys the excitement of a scientific culture that impacts our life to this day and will serve as an inspiration to gifted young people to devote their lives to scientific pursuits. ... Read more

Product Description

Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein.

Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin.

Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition.

This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.

Customer Reviews (2)

English translation of German Euler biography
The translators for this biography of Leonhard Euler (originally published in German) are clearly not 100% fluent in English - but that did not stop me from learning a great deal more about Euler's life than I had known previously.This book includes numerous illustrations of Euler book covers, diagrams from his works, portraits of important persons who lived during Euler's lifetime, etc.There is very little actual math in this book, if that's what you're looking for.However, it does give a good account of all of Euler's major mathematical and scientific contributions.This biography was a very enjoyable and quick read.

A good biography of an important mathematician
This book is an excellent presentation of the story of Euler's life.It includes some bits of humor (like seeing the streets in Basel named respectively Leonhardstrasseand Eulerstrasse as jointly honoring the man although neither street is actually named for the great mathematician).Unlike "Euler the Master of us All," the book is organized around the chronology of his life rather than the concepts he studied, and it includes new details of his life.It also has some wonderful illustrations. ... Read more

Product Description
This book celebrates the 300th birthday of Leonhard Euler (1707 1783), one of the brightest stars in the mathematical firmament. The book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuityone who has been rightly calledthe master of us all.The collected articles, aimed at a mathematically literate audience, address aspects of Euler s life and work, from the biographical to the historical to the mathematical.The oldest of these was written in 1872, and the most recent dates to 2006. Some of the papers focus on Euler and his world, others describe a specific Eulerian achievement, and still others survey a branch of mathematics to which Euler contributed significantly.Along the way, the reader will encounter the Königsberg bridges, the 36-officers, Euler s constant, and the zeta function.There are papers on Euler s number theory, his calculus of variations, and his polyhedral formula. Of special note are the number and quality of authors represented here.Among the 34 contributors are some of the most illustrious mathematicians and mathematics historians of the past century e.g., Florian Cajori, Carl Boyer, George Pólya, Andre Weil, and Paul Erdös. And there are a few poems and a mnemonic just for fun. ... Read more

Customer Reviews (1)

Dunham and Euler together again!
Dunham's 1999 book _Euler: The Master of Us All_ is probably the best general introduction to the mathematical work of Euler available.Therefore, it's no surprise that he has edited such a great collection of articles, put together to celebrate Euler's 300th birthday in 2007.

The chapters are collected from various journals and feature the work of more than thirty authors.They were originally published as long ago as 1872 and as recently as 2006.They were written for a general mathematical audience and are accessible to faculty and students alike.They don't assume any particular background in the history of mathematics.Among the authors are many well-known mathematicians and historians of mathematics, including Boyer, Cajori, Erdös, Morris Kline, Pólya, W. W. Rouse Ball and André Weil.

Read this book for the sheer fun of it!It's very entertaining and well-written. ... Read more

Product Description
"How Euler Did It" is a collection of the monthly columns that appeared on MAA Online between November 2003 and February 2007 about the life and mathematical and scientific work of the great 18th century mathematician Leonhard Euler. Almost every column is self-contained, and gives the context, significance and some of the details of a particular facet of Euler's work. Interesting anecdotes about Euler's work in geometry are described In a discussion of Euler's polyhedral formula the author speculates as to whether Descartes had a role in Euler's discovery and analyzes the flaw in Euler's proof. Euler's solution to Cramer s paradox and its role in the early days of linear algebra is also discussed. Some of Euler's work in number theory is described. Euler's first proof using mathematical induction to prove Fermat s little theorem is explored, as well as his discovery of over a hundred pairs of amicable numbers, and his proof for odd perfect numbers. Elsewhere in the book we learn of the development of what we now call Venn diagrams, what Euler knew about orthogonal matrices, Euler s ideas on the foundations of calculus, before the days of limits, epsilons and deltas, and his proof that mixed partial derivatives are equal. Professor Sandifer based his MAA Online columns on Euler's own words in the original language in which they were written. In this way, the author was able to uncover many details that are not found in other sources. For example, we see how Euler used differential equations and continued fractions to prove that the constant e is irrational, several years before Lambert, who is usually credited with this discovery. He also made an observation equivalent to saying that the number of prime number less than a number x is approximately x/ln(x), an observation usually attributed to Gauss some 15 years after Euler died. The collection ends with a somewhat playful, but factual, account of Euler's role in the discovery of America. ... Read more

Product Description
The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work.

Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.

- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich
- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova
- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century ... Read more

Product Description
This book is an English translation of a collection of papers in Russian from a conference held in Moscow and St. Petersburg in 1983, 200 years after Euler's death. Two of the Russian papers in the collection are themselves translations from the German. The present English translation appears in 2007, 300 years after his birth. We speak of the "Age of Euler". A justification of this term is provided by a list of scientific terms connected with Euler s name and his many contributions to pure mathematics, well-known in the mathematical community and, in part, covered in this volume. What makes this collection remarkable, though, is the extensive treatment of Euler's contributions outside pure mathematics--to astronomy, celestial mechanics, ballistics, history of science, instruments and technology, physics, mechanics, hydromechanics, mechanics of elastic systems, variational principles of mechanics, and a mathematical theory of music. In addition to this survey of his contributions to science, we find here material otherwise very difficult to find detailed accounts of Euler's family life and the careers pursued by his children and grandchildren. Readers otherwise well-informed about Euler and his work will find here much to enhance their appreciation of this extraordinary scientist and human being. For significant and factual knowledge of Euler's contributions to science past and present, this book is easily the best available choice. ... Read more

Product Description
When an important mathematician celebrates a landmark birthday, other mathematicians sometimes gather together to give papers in appreciation of the life and work of the great person. When a mathematician as influential and productive as Euler celebrates an anniversary as important as the 300th, a single meeting isn t sufficient to present all of the contributions. Leonhard Euler (1707-1783) was the most important mathematician of the 18th century. His collected works, with 800 books and articles, fill over 70 large volumes. He revolutionized real analysis and mathematical physics, single-handedly established the field of analytic number theory, and made important contributions to almost every other branch of mathematics. A great pedagogue as well as a great researcher, his textbooks educated the next generation of mathematicians. During the years leading up to Leonhard Euler's tercentenary, at more than a dozen academic meetings across the USA and Canada, mathematicians and historians of mathematics honored Euler in papers detailing his life and work. This book collects more than 20 papers based on some of the most memorable of these contributions. These papers are accessible to a broad mathematical audience. They will appeal to those who already have an interest in the history of mathematics. For those who don t, they will serve as a compelling introduction to the subject, focused on the accomplishments of one of the great mathematical minds of all times, topics include analysis especially Euler s fearless and masterful manipulation of power series, geometry, algebra, probability, astronomy and mechanics. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description

His ideas turned the mathematical world on its head. As a scientist he should be placed on the same level as Newton and Einstein. This account of Euler's life and livings is embedded in the great political developments of his time, particularly in Austria, Prussia and Russia. The comic by Elena Pini (illustrations) and Alice and Andreas K. Heyne (text) follows the life of the genius from Basel, who, born 300 years ago, would set out to change the scientific world. The book is completed by a short biography of Euler and relevant data of the most important politicians and contemporaries.

Customer Reviews (1)

hannibal2rome
Euler was a probably the greatest mathematician in history. Many english would disagree and say it was Isaac Newton. Newton would have been the greatest if he wasnt wasting his time trying to turn lead into gold. ... Read more

Product Description
Publisher: Leipzig Und BerlinPublication date: 1922Notes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more