MARC Record from marc_columbia

LEADER: 02920fam a22003734a 4500
001 2690938
005 20221012222940.0
008 000501t20002000riua b 001 0 eng
010 $a 00033180
020 $a0821826409 (alk. paper)
035 $a(OCoLC)44084037
035 $a(OCoLC)ocm44084037
035 $9ARE1047CU
035 $a(NNC)2690938
035 $a2690938
040 $aDLC$cDLC$dOrLoB-B
042 $apcc
050 00 $aQA242$b.B96 2000
082 00 $a512/.74$221
100 1 $aBurger, Edward B.,$d1963-$0http://id.loc.gov/authorities/names/n00011204
245 10 $aExploring the number jungle :$ba journey into diophantine analysis /$cEdward B. Burger.
260 $aProvidence, RI :$bAmerican Mathematical Society,$c[2000], ©2000.
300 $avi, 151 pages :$billustrations ;$c22 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aStudent mathematical library,$x1520-9121 ;$vv. 8
504 $aIncludes bibliographical references (p. 145-146) and index.
505 00 $tOpening thoughts: Welcome to the jungle --$g1.$tA bit of foreshadowing and some rational rationale --$g2.$tBuilding the rationals via Farey Sequences --$g3.$tDiscoveries of Dirichlet and Hurwitz --$g4.$tThe theory of continued fractions --$g5.$tEnforcing the law of best approximates --$g6.$tMarkoff's spectrum and numbers --$g7.$tBadly approximable numbers and quadratics --$g8.$tSolving the alleged "Pell" equation --$g9.$tLiouville's work on numbers algebraic and not --$g10.$tRoth's stunning result and its consequences --$g11.$tPythagorean triples through diophantine geometry --$g12.$tA quick tour through elliptic curves --$g13.$tThe geometry of numbers --$g14.$tSimultaneous diophantine approximation --$g15.$tUsing geometry to sum some squares --$g16.$tSpinning around irrationally and uniformly --$g17.$tA whole new world of p-adic numbers --$g18.$tA glimpse into p-adic analysis --$g19.$tA new twist on Newton's method --$g20.$tThe power of acting locally while thinking globally --
505 80 $gApp. 1.$tSelected Big Picture Question commentaries.
520 1 $a"This book brings to life the fundamental ideas and theorems from diophantine approximation and equations, geometry of numbers, diophantine geometry, and p-adic analysis. Through his engaging style, the author creates an inviting atmosphere where readers actively build intuition, develop ideas, and prove results as they journey through some beautiful areas of number theory.
520 8 $aThe minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--BOOK JACKET.
650 0 $aDiophantine analysis.$0http://id.loc.gov/authorities/subjects/sh85038122
830 0 $aStudent mathematical library ;$vv. 8.$0http://id.loc.gov/authorities/names/n99017061
852 00 $bmat$hQA242$i.B96 2000