Buy new:
$20.99
FREE delivery Wednesday, May 15 on orders shipped by Amazon over $35
Ships from: Amazon.com
Sold by: Amazon.com
$20.99
Get Fast, Free Shipping with Amazon Prime FREE Returns
FREE delivery Wednesday, May 15 on orders shipped by Amazon over $35
Or fastest delivery Friday, May 10. Order within 20 hrs 20 mins
Only 2 left in stock (more on the way).
$$20.99 () Includes selected options. Includes initial monthly payment and selected options. Details
Price
Subtotal
$$20.99
Subtotal
Initial payment breakdown
Shipping cost, delivery date, and order total (including tax) shown at checkout.
Ships from
Amazon.com
Ships from
Amazon.com
Sold by
Amazon.com
Sold by
Amazon.com
Returns
Eligible for Return, Refund or Replacement within 30 days of receipt
Eligible for Return, Refund or Replacement within 30 days of receipt
This item can be returned in its original condition for a full refund or replacement within 30 days of receipt.
Read full return policy
Returns
Eligible for Return, Refund or Replacement within 30 days of receipt
This item can be returned in its original condition for a full refund or replacement within 30 days of receipt.
Read full return policy
Payment
Secure transaction
Your transaction is secure
We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more
Payment
Secure transaction
We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more
$8.97
Preowned copy in good condition. May have general signs of wear and tear, markings, highlighting, etc. Preowned copy in good condition. May have general signs of wear and tear, markings, highlighting, etc. See less
FREE delivery Friday, May 17. Details
Or fastest delivery Friday, May 10. Order within 8 hrs 20 mins. Details
Only 1 left in stock - order soon.
$$20.99 () Includes selected options. Includes initial monthly payment and selected options. Details
Price
Subtotal
$$20.99
Subtotal
Initial payment breakdown
Shipping cost, delivery date, and order total (including tax) shown at checkout.
Access codes and supplements are not guaranteed with used items.
Ships from and sold by -Bookworm-.
Amazon book clubs early access
Loading your book clubs
There was a problem loading your book clubs. Please try again.
Not in a club? Learn more
Amazon book clubs early access

Join or create book clubs

Choose books together

Track your books
Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club that’s right for you for free.
Explore Amazon Book Clubs
Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Follow the author

Mark Ronan
+ Follow
More books from this author
Something went wrong. Please try your request again later.

Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics Revised ed. Edition

by Mark Ronan (Author)
4.2 4.2 out of 5 stars 66 ratings
See all formats and editions
{"desktop_buybox_group_1":[{"displayPrice":"$20.99","priceAmount":20.99,"currencySymbol":"$","integerValue":"20","decimalSeparator":".","fractionalValue":"99","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"oMOfhpWkT8Gb5ja%2BIt0KJifXkBB3SeJvIeVfwOC%2BxFmXuIsW5pCwcA53TJIIdSkHJk%2FsxtUiGl4Q%2BrhX%2FCvuZTvqFQz5bHiI4TmN%2FhqlXsrVb2owNddiURacUwOt8zcw6z%2BLo8Fe3nI%3D","locale":"en-US","buyingOptionType":"NEW","aapiBuyingOptionIndex":0}, {"displayPrice":"$8.97","priceAmount":8.97,"currencySymbol":"$","integerValue":"8","decimalSeparator":".","fractionalValue":"97","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"oMOfhpWkT8Gb5ja%2BIt0KJifXkBB3SeJvLjUSrO%2B59q3LrhQE92%2F%2FvoJXhFLXA3lmurpjwKvOfCqNcV6kNVRkxXaHp6LcEeZzZOkPwoI8NgCo6NaiXXIwtGyeTiz4ljwF%2FeaKwSlzO4ZoyqGjG5nKAXrWsyHvKGwoqaV3Ks%2F8HYREVFXpmENGsx1mw7pkz0rr","locale":"en-US","buyingOptionType":"USED","aapiBuyingOptionIndex":1}]}

Purchase options and add-ons

Mathematics is driven forward by the quest to solve a small number of major problems--the four most famous challenges being Fermat's Last Theorem, the Riemann Hypothesis, Poincaré's Conjecture, and the quest for the "Monster" of Symmetry. Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest.

Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry." Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed "the Monster"--a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe.
This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science--and especially readers of such books as Fermat's Last Theorem.
Read more Read less
Previous page
  1. ISBN-10
    0192807234
  2. ISBN-13
    978-0192807236
  3. Edition
    Revised ed.
  4. Publisher
    Oxford University Press
  5. Publication date
    September 4, 2007
  6. Language
    English
  7. Dimensions
    7.8 x 5.08 x 0.24 inches
  8. Print length
    264 pages
  9. See all details
Next page
Amazon First Reads | Editors' picks at exclusive prices

Frequently bought together

Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics
$20.99
Get it as soon as Wednesday, May 15
Only 2 left in stock (more on the way).
Ships from and sold by Amazon.com.
+
Gödel, Escher, Bach: An Eternal Golden Braid
$14.99
Get it as soon as Tuesday, May 14
In Stock
Ships from and sold by Amazon.com.
Total price:
To see our price, add these items to your cart.
Details
Added to Cart
One of these items ships sooner than the other.
Show details Hide details
Choose items to buy together.

Customers who viewed this item also viewed

Page 1 of 1 Start overPage 1 of 1
Previous page
  1. Surreal Numbers
Next page

Editorial Reviews

Review

"Succeeds in bringing to the fore an aspect of mathematics that some popularizers miss--that math is not a science of monuments, but a living tradition as vibrant as physics or ethics or law, one in which new monuments pop up weekly and old ones are retrofitted for purposes inconceivable to their creators."--Seed Magazine

About the Author

Mark Ronan is a Professor at the University of Illinois at Chicago, and a Visiting Professor of Mathematics at University College London.

Product details

  • Publisher ‏ : ‎ Oxford University Press; Revised ed. edition (September 4, 2007)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 264 pages
  • ISBN-10 ‏ : ‎ 0192807234
  • ISBN-13 ‏ : ‎ 978-0192807236
  • Item Weight ‏ : ‎ 4.2 ounces
  • Dimensions ‏ : ‎ 7.8 x 5.08 x 0.24 inches
  • Customer Reviews:
    4.2 4.2 out of 5 stars 66 ratings

About the author

Follow authors to get new release updates, plus improved recommendations.
Mark Ronan

Mark Ronan

Brief content visible, double tap to read full content.
Full content visible, double tap to read brief content.

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

4.2 out of 5 stars
4.2 out of 5
66 global ratings

Top reviews from the United States

Keith
5.0 out of 5 stars This book is deeply flawed and I enjoyed it immensely
Reviewed in the United States on November 18, 2017
Verified Purchase
This book is deeply flawed and I enjoyed it immensely. Mark Ronan tries to avoid using mathematics in the text to increase the accessibility. The result is that for aspects of the mathematical story I am a small bit familiar with I can follow along. For aspects that I am completely unfamiliar with the descriptions are too metaphorical and vague: I am completely lost. It would have been so much better to stick to the painstakingly crafted technical language that already exists instead of inventing new language. Still, I found the technical part of the story fascinating and energizing. For me it rekindled an interest in group theory that I left behind many years ago and I am grateful. And of course informal material like this from an expert is very helpful to anyone attempting to learn more themselves, no matter how vague or even correct the description is.

The human story in this book is pure gold for anyone who cares deeply about the potential and achievements of individuals and collectives, and particularly for anyone interested in this field. The human story is the real focus of the book and it is well done.

Mark Ronan: Thank you for this wonderful book. Please try again, and bring out more of the real mathematics and problem solving next time, because you have made an important contribution to the public. Non-mathematicians like myself may read this book for a few different reasons. We care about how the contributors to this story were able to self-actualize and do what they did. We are interested in learning more about the mathematics. We are curious about what the day-to-day effort of practitioners in this field really look like. We'd like to understand in more detail what problem solving approaches practitioners are using--the things that are not otherwise easy to find in publications. And if you happen to have some insight into what the results in this area mean to our entire intellectual understanding as humans we are interested in that too. At least for me that philisophical content is a bit less important, and the taxonomy of practical applications and methods is of the greatest importance. The book you wrote is sufficient for people to extract some of these things, so thank you.
8 people found this helpful
Helpful
 Report
A. Menon
4.0 out of 5 stars very approachable introduction to a very opaque problem
Reviewed in the United States on April 9, 2010
Verified Purchase
I remember being described the monster by a cousin of mine who had done his PhD in number theory via some similarities to the j-function, i followed little of what he said... I saw this book only recently and decided to see what it had to say, I was very pleased with the book, though admittedly I understand the monster only a little bit better.

Several ideas are presented very well, the ideas of groups and examples of symmetries are very well written and give excellent intuition. Even descriptions of the correspondence in geometry between faces and verteces in symmetry opperations was illuminating (which was right at the beginning). The histories of many mathematicians is great and gives excellent introductions to some of those most famous in mathematics' history. The book is worth reading alone for these materials.

Things move on to the more abstract as we get into the representation theory behind some groups and how lie groups work... I dont think these are easy to follow, when the author starts listing out the "Atoms of symmetry" of increasing complexity, like Conway(x) one starts to get lost. The list of achievements with respect to the monster and baby monster are listed, but they arent particularly comprehensible to the reader with this book as sole background. I am not surprised by this given the subjects difficulty.

The books attempt is admirable, and I think most of the goals of the book are achieved. The best aspects are the books are the introduction to group theory, various symmetries and how they operate, some of the issues arising in things like even and odd permutations and in particular the historical commentary. The meat of the problems related to the monster are not easily understood though its not a function of the writing rather its the subject matter that im not sure is approachable through any hand wavy introductions. I recommend reading it as a broad introduction to some of the problems that mathematicians attach and a view into what sorts of things they find beauty and elegance in.
Helpful
 Report

Top reviews from other countries

Translate all reviews to English
Dr. T.
5.0 out of 5 stars Symmetrien, Gruppen, Monster und Moonshine
Reviewed in Germany on October 8, 2015
Verified Purchase
Mark Ronan ist emeritierter Professor für Mathematik der Universität von Chicago, mit seinem Buch 'Symmetry and the Monster' versucht er das überaus spannende, wie auch komplexe Gebiet der endlichen einfachen Gruppen einem breiten Publikum nahe zu bringen.

Symmetrien faszinieren Menschen schon seit dem Altertum, das richtige mathematische Mittel zu ihrer Beschreibung ist hingen noch relativ jung: Gruppen, diese Objekte wurden zunächst unter anderem von N. Abel und E. Galois in Zusammenhang mit der Auflösbarkeit algebraischer Gleichungen untersucht. Gruppen erwiesen sich bald als eines der fruchtbarsten mathematischen Konzepte: Felix Klein deckte ihre Beziehungen zur Geometrie auf, und nachdem Sophus Lie speziell stetige Gruppen untersucht hatte, konnte Emmy Noether einen tiefen Zusammenhang zwischen physikalischen Erhaltungsgrößen und Symmetrien beweisen, der heute einen der Grundsteine der quantenmechanischen Elementarteilchen Theorien darstellt.

Wenn Mathematiker bedeutende Strukturen entdecken, sind sie sehr daran interessiert, diese vollständig zu verstehen und möglichst zu klassifizieren, das kann oft bedeuten, eine Liste aller möglichen 'kleinsten Bausteine' solcher Strukturen zu finden. Für den Fall stetiger Gruppen, sogenannter Lie Gruppen, brachten die Arbeiten von Wilhelm Killing und Elie Cartan recht schnell Erfolg.

Es wird vielleicht verwundern, dass sich eine entsprechende Klassifizierung von endlichen Gruppen, als wesentlich komplizierter herausstellen sollte. Einer der Gründe dafür ist, dass die Mittel der Differential Geometrie, die für das Verständnis der Lie Gruppen, so entscheidend waren, auf endliche Gruppen nicht anwendbar sind; die Mathematiker mussten sich also vollkommen neue Werkzeuge schaffen; dazu legten L.E. Dickson und William Burnside wichtige Grundlagen ' u.a. mit der Theorie der Gruppen Charaktere.

Nach dem Krieg brachten die Beiträge von Claude Chevalley und Jaques Tits einen neuen Aufschwung zur Arbeit an der Klassifikation endlicher Gruppen; das 'Odd Oder Theorem' von Walter Feit und John Thompson eröffnete zu dem eine Möglichkeit zu einer Liste der einfachen endlichen Gruppen zu gelangen.

Neben den Serien, wie sie schon von den Lie Gruppen bekannt waren, waren um 1900 fünf sogenannte sporadische Gruppen bekannt, die von E.L. Mathieu gefunden worden. Der Autor schildert die Geschichte der Vervollständigung der Liste dieser sporadischen Gruppen, die mit Zvonimir Janko wieder einsetzt. Als einer der wesentlichen Katalysatoren erwies sich ein von John Leech im Zusammenhang mit error correcting codes untersuchtes hoch symmetrisches Gitter in 24 Dimensionen, auf das John Conway von J. McKay gestoßen wurde; mit Unterstützung von Thompson untersuchte Conway die Eigenschaften dieses Gitters und identifizierte Verbindungen zu 12 solchen Gruppen, darunter drei neuen, die später nach Conway benannt wurden. Bernd Fischer kam schließlich das Privileg zu, die größte dieser sporadischen Gruppen zu entdecken ' dem Monster (einer von Conways typischen Namenskreationen).

Diese gerade neue entdeckten, unvorstellbar großen, Gruppen sollten aber noch weitere Überraschung bereithalten. Bei der Durchsicht einer zahlentheoretischen Arbeit, stieß John McKay auf die Entwicklung einer modularen Funktion, in der als Koeffizient 196884 auftauchte, das ist gerade die Dimension der ersten Darstellung des Monsters + 1; das hätte ein Zufall sein können, gemeinsam mit Conway untersuchten sie die Angelegenheit näher, und fanden noch eine ganze Reihe weiterer solcher 'numerologischen' Beziehungen, die sie unter der Bezeichnung 'monstrous moonshine' veröffentlichten (einer weiteren von Conways Kreationen als 'moonshine' bezeichnet man illegal gebraute Spirituosen).

Richard Borcherds, ein Schüler Conways, gelang es schließlich, unter Verwendung von Resultaten von Frenkel, Lepowsky und Meurman, die auch Bezug zur String- Theorie haben, die Moonshine Vermutung zu beweisen; er wurde dafür 1998 mit der Fields Medaille geehrt.

Der Autor geht auf all diese faszinierende Entwicklungen ein, versucht beim Leser zumindest eine Vorstellung von den dabei zu bewältigenden Problemen zu schaffen; auf dem Weg dahin streift er das Leben und Schaffen, einer Reihe daran beteiligter Mathematiker. Schlaglichtartig werden gut 200 Jahre Mathematikgeschichte eines der bedeutendsten Probleme der neuen Zeit beleuchtet.

Entsprechend dem Anliegen der Allgemeinverständlichkeit, verzichtet der Autor auf dem Gebrauch zu technischer Begriffe, er spricht zum Beispiel lieber von Symmetrie Atomen statt von einfacher Gruppen, das wird durch eine Reihe Anmerkungen zum Text und vier Anhängen mit mathematischen Details, ein wenig ausgeglichen; man wird allerdings eine Bibliographie mit weiterführender Literatur vermissen.
Report
Sundaebb
5.0 out of 5 stars The best book telling the history of the study of finite groups
Reviewed in Japan on November 10, 2013
Verified Purchase
It is a story that introduces the history to reach the vast finite group called the Monster of finite order:8.10^53. It is also known that lying behind monstrous moonshine is a certain conformal field theory having the Monster group as symmetries. The study of finite groups, starting from Galois of 200 years ago. and then research the discovery of simple groups has ended abruptly. However, Moonshine phenomenon is also found in Matthew series, subtle relationship between number theory is revealed. Relationship between string theory in physics has also become a topic further. Never run out of interests in research in this area. So this books the best way to start with the finite group theory for student, math-lovers and practitioners in general.
Report
doktorstrangelove
2.0 out of 5 stars Lobenswerte Absicht...
Reviewed in Germany on May 20, 2009
Verified Purchase
Die Absicht die mathematische Abhandlung der endlichen Gruppen allgemeinverständlich zu erläutern, eine mathematische Unternehmung die schließlich mehrere Jahrhunderte und Abertausende Zeitschriftenseiten benötigt hat, um zu ihrem Abschluß zu kommen, ist lobenswert. In der Umsetzung mangelt es aber am wichtigsten...der Mathematik! Somit ist vielleicht ein leicht lesbares Werk enstanden, aber leider erfährt man nur sehr wenig, über das eigentliche Untersuchungsobjekt. Alles bleibt qualitativ und bildlich. Wenn man etwas essentielles dazulernen wollte, wird man so enttäuscht. Die eingstreuten mathematischen Anekdoten und Historien sind unterhaltsam, aber auch sie dienen nur selten der Erhellung des mathematischen Kerns, der Anlaß für die genannten Mathematiker war, sich mit dem Thema auseinanderzusetzen. Dem unbedarften Leser muß es am Ende komisch vorkommen, daß die Erforschung eines scheinbar so seichten Forschungsgegenstandes so viel Anstrengung gekostet hat. Alles in allem...Chance vertan...
5 people found this helpful
 Report
A. Wasenczuk
4.0 out of 5 stars Fascinating but frustrating
Reviewed in the United Kingdom on April 10, 2008
Verified Purchase
Four stars because as a scientist but non-mathematician I would have liked a little more time spent getting a toe-hold on the basics of this fascinating field. Like: why are five objects different from four? Presumably with pencil and paper I can sit and work this out - but I'd have liked a paragraph to point me in the right direction. And the throwaway comment right in the middle about the sizes of successive atomic orbitals (2, 6, 10, 14...) being determined entirely by their symmetry: I'd love to know where that came from. Held my interest but left me feeling empty.
2 people found this helpful
 Report
Kindle Customer
3.0 out of 5 stars Clear and understable topic on symmetry,monster-group and related matters
Reviewed in the United Kingdom on February 18, 2015
Verified Purchase
A very well written book with clear language use and understanding of a fascinating but small part of modern mathematics. A history of mathematicians involved with the evolution of "the monster-group' is a must for some film producer. Written for novice or otherwise i would suggest anyone serious about math study should have it as part of their library. One minor point some of the analogies used may confuse but that probably tells you more about my reading of it.
One person found this helpful
 Report