LEADER 04999nam 22007815 450 001 9910457972603321 005 20210114162008.0 010 $a1-282-96489-5 010 $a9786612964893 010 $a1-4008-3777-4 024 7 $a10.1515/9781400837779 035 $a(CKB)2560000000049182 035 $a(EBL)664559 035 $a(OCoLC)705944534 035 $a(SSID)ssj0000469101 035 $a(PQKBManifestationID)12194618 035 $a(PQKBTitleCode)TC0000469101 035 $a(PQKBWorkID)10510513 035 $a(PQKB)10137301 035 $a(SSID)ssj0000543676 035 $a(PQKBManifestationID)11354860 035 $a(PQKBTitleCode)TC0000543676 035 $a(PQKBWorkID)10530723 035 $a(PQKB)10260622 035 $a(DE-B1597)446841 035 $a(OCoLC)1013946211 035 $a(OCoLC)1029818777 035 $a(OCoLC)1032685261 035 $a(OCoLC)1037925500 035 $a(OCoLC)1041989782 035 $a(OCoLC)1046608148 035 $a(OCoLC)1047020686 035 $a(OCoLC)1049620159 035 $a(OCoLC)1054880021 035 $a(OCoLC)979749693 035 $a(DE-B1597)9781400837779 035 $a(MiAaPQ)EBC664559 035 $a(EXLCZ)992560000000049182 100 $a20190708d2008 fg 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFearless Symmetry $eExposing the Hidden Patterns of Numbers - New Edition /$fRobert Gross, Avner Ash 205 $aNew edition with a New preface by the authors 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2008] 210 4$d©2008 215 $a1 online resource (307 p.) 300 $aDescription based upon print version of record. 311 $a0-691-13871-0 327 $t Frontmatter -- $tContents -- $tForeword -- $tPreface To The Paperback Edition -- $tPreface -- $tAcknowledgments -- $tGreek Alphabet -- $tPart One. Algebraic Preliminaries -- $tChapter 1. Representations -- $tChapter 2. Groups -- $tChapter 3. Permutations -- $tChapter 4. Modular Arithmetic -- $tChapter 5. Complex Numbers -- $tChapter 6. Equations and Varieties -- $tChapter 7. Quadratic Reciprocity -- $tPart Two. Galois Theory and Representations -- $tChapter 8. Galois Theory -- $tChapter 9. Elliptic Curves -- $tChapter 10. Matrices -- $tChapter 11. Groups of Matrices -- $tChapter 12. Group Representations -- $tChapter 13. The Galois Group Of A Polynomial -- $tChapter 14. The Restriction Morphism -- $tChapter 15. The Greeks Had a Name for it -- $tChapter 16. Frobenius -- $tPart Three. Reciprocity Laws -- $tChapter 17. Reciprocity Laws -- $tChapter 18. One- And Two-Dimensional Representations -- $tChapter 19. Quadratic Reciprocity Revisited -- $tChapter 20. A Machine for Making Galois Representations -- $tChapter 21. A Last Look at Reciprocity -- $tChapter 22. Fermat's Last Theorem and Generalized Fermat Equations -- $tChapter 23. Retrospect -- $tBibliography -- $tIndex 330 $aMathematicians 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 évariste 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. 606 $aNumber theory 606 $aNumber theory 608 $aElectronic books. 615 4$aNumber theory. 615 0$aNumber theory 676 $a512.7 686 $aSK 180$2rvk 700 $aAsh$b Avner, $01034316 702 $aGross$b Robert, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910457972603321 996 $aFearless Symmetry$92453358 997 $aUNINA