skip to content
Fearless symmetry : exposing the hidden patterns of numbers Preview this item
ClosePreview this item
Checking...

Fearless symmetry : exposing the hidden patterns of numbers

Author: Avner Ash; Robert Gross
Publisher: Princeton : Princeton University Press, ©2006.
Edition/Format:   Print book : Document   Computer File : EnglishView all editions and formats
Summary:
Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Print version:
Ash, Avner, 1949-
Fearless symmetry.
Princeton, N.J. ; Woodstock : Princeton University Press, 2008
Material Type: Document, Internet resource
Document Type: Book, Computer File, Internet Resource
All Authors / Contributors: Avner Ash; Robert Gross
ISBN: 0691124922 9780691124926 9780691138718 0691138710
OCLC Number: 60826707
Description: xxv, 272 pages : illustrations ; 25 cm
Contents: Representations --
Groups --
Permutations --
Modular arithmetic --
Complex numbers --
Equations and varieties --
Quadratic reciprocity --
Galois theory --
Elliptic curves --
Matrices --
Groups of matrices --
Group representations --
The Galois group of a polynomial --
The restriction morphism --
The Greeks had a name for it --
Frobenius --
Reciprocity laws --
One- and two-dimensional representations --
Quadratic reciprocity revisited --
A machine for making Galois representations --
A last look at reciprocity --
Fermat's last theorem and generalized Fermat equations --
Retrospect.
Responsibility: Avner Ash and Robert Gross.
More information:

Abstract:

Focuses on how mathematicians solve equations and prove theorems. Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the symmetric patterns that lead to  Read more...

Reviews

Editorial reviews

Publisher Synopsis

The authors are to be admired for taking a very difficult topic and making it ... certainly more accessible than it was before. -- Timothy Gowers Nature The authors ... outline current research in Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(4)

User lists with this item (2)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


\n\n

Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/60826707<\/a>> # Fearless symmetry : exposing the hidden patterns of numbers<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:MediaObject<\/a>, schema:Book<\/a>, schema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"60826707<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/nju<\/a>> ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Place\/princeton<\/a>> ; # Princeton<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/512.7\/e22\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/nombres_theorie_des<\/a>> ; # Nombres, Th\u00E9orie des<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/number_theory<\/a>> ; # Number theory<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/mathematics_number_theory<\/a>> ; # MATHEMATICS--Number Theory<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/zahlentheorie<\/a>> ; # Zahlentheorie<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> bgn:PrintBook<\/a> ;\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/viaf.org\/viaf\/119226710<\/a>> ; # Robert Gross<\/span>\n\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"2006<\/span>\" ;\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/119226706<\/a>> ; # Avner Ash<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2006<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician?variste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat\'s Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Representations -- Groups -- Permutations -- Modular arithmetic -- Complex numbers -- Equations and varieties -- Quadratic reciprocity -- Galois theory -- Elliptic curves -- Matrices -- Groups of matrices -- Group representations -- The Galois group of a polynomial -- The restriction morphism -- The Greeks had a name for it -- Frobenius -- Reciprocity laws -- One- and two-dimensional representations -- Quadratic reciprocity revisited -- A machine for making Galois representations -- A last look at reciprocity -- Fermat\'s last theorem and generalized Fermat equations -- Retrospect.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/796302897<\/a>> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/worldcat.org\/entity\/work\/data\/796302897#CreativeWork\/fearless_symmetry<\/a>> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Fearless symmetry : exposing the hidden patterns of numbers<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"60826707<\/span>\" ;\u00A0\u00A0\u00A0\nschema:publication<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/60826707#PublicationEvent\/princeton_princeton_university_press_2006<\/a>> ;\u00A0\u00A0\u00A0\nschema:publisher<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Agent\/princeton_university_press<\/a>> ; # Princeton University Press<\/span>\n\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/bvbr.bib-bvb.de:8991\/F?func=service&doc_library=BVB01&doc_number=015748979&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/bvbr.bib-bvb.de:8991\/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015748979&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/catdir.loc.gov\/catdir\/enhancements\/fy0654\/2005051471-t.html<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.gbv.de\/dms\/goettingen\/501559825.pdf<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780691138718<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780691124926<\/a>> ;\u00A0\u00A0\u00A0\numbel:isLike<\/a> <http:\/\/bnb.data.bl.uk\/id\/resource\/GBA627626<\/a>> ;\u00A0\u00A0\u00A0\numbel:isLike<\/a> <http:\/\/bnb.data.bl.uk\/id\/resource\/GBA627626.<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/60826707<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Related Entities<\/h3>\n
<http:\/\/dewey.info\/class\/512.7\/e22\/<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Agent\/princeton_university_press<\/a>> # Princeton University Press<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:Agent<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Princeton University Press<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Place\/princeton<\/a>> # Princeton<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Princeton<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/mathematics_number_theory<\/a>> # MATHEMATICS--Number Theory<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"MATHEMATICS--Number Theory<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/nombres_theorie_des<\/a>> # Nombres, Th\u00E9orie des<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Nombres, Th\u00E9orie des<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/number_theory<\/a>> # Number theory<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Number theory<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Topic\/zahlentheorie<\/a>> # Zahlentheorie<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Zahlentheorie<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/nju<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"nju<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/119226706<\/a>> # Avner Ash<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1949<\/span>\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Ash<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Avner<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Avner Ash<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/119226710<\/a>> # Robert Gross<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1959<\/span>\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Gross<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Robert<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Robert Gross<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/entity\/work\/data\/796302897#CreativeWork\/fearless_symmetry<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nrdfs:label<\/a> \"Fearless symmetry.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Print version:<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/www.worldcat.org\/oclc\/60826707<\/a>> ; # Fearless symmetry : exposing the hidden patterns of numbers<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9780691124926<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0691124922<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780691124926<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9780691138718<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0691138710<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780691138718<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.gbv.de\/dms\/goettingen\/501559825.pdf<\/a>>\u00A0\u00A0\u00A0\nrdfs:comment<\/a> \"Kostenfrei<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/60826707<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/60826707<\/a>> ; # Fearless symmetry : exposing the hidden patterns of numbers<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2020-12-30<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/60826707#PublicationEvent\/princeton_princeton_university_press_2006<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:PublicationEvent<\/a> ;\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Place\/princeton<\/a>> ; # Princeton<\/span>\n\u00A0\u00A0\u00A0\nschema:organizer<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/796302897#Agent\/princeton_university_press<\/a>> ; # Princeton University Press<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n