MARC record from Internet Archive

LEADER: 06770cam a2200769 i 4500
001 ocm00162204
003 OCoLC
005 20191109071546.7
007 ta
008 710914s1971 paua b 001 0 eng
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035 $a(OCoLC)00162204$z(OCoLC)255555525$z(OCoLC)1064733816$z(OCoLC)1078808442$z(OCoLC)1081065108$z(OCoLC)1083406791$z(OCoLC)1086725223$z(OCoLC)1087115527$z(OCoLC)1087239733
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084 $aMAT 100f$2stub
088 $a74151673
049 $aMAIN
100 1 $aAndrews, George E.,$d1938-
245 10 $aNumber theory /$cGeorge E. Andrews.
264 1 $aPhiladelphia :$bW.B. Saunders Company,$c[1971]
264 4 $c©1971
300 $ax, 259 pages :$billustrations ;$c25 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
504 $aIncludes chapter notes, suggested reading, bibliographical references (pages 231-232), hints and answers to selected exercises, and indexes.
520 $aAlthough mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems. Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory. Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated.
590 $bInternet Archive - 2
590 $bInternet Archive 2
650 0 $aNumber theory
650 6 $aNombres, Théorie des
650 7 $aNumber theory.$2fast$0(OCoLC)fst01041214
650 7 $aZahlentheorie$2gnd
650 4 $aNombres, théorie des
650 07 $aZahlentheorie.$2swd
653 0 $aNumber theory
776 08 $iOnline version:$aAndrews, George E., 1938-$tNumber theory.$dPhiladelphia, Saunders, 1971$w(OCoLC)755374040
856 41 $3Table of contents$uhttp://www.gbv.de/dms/hbz/toc/ht000458279.pdf
880 00 $6505-00/(S$gPart I.$tMultiplicativity : divisibility ;$tBasis representation ;$tPrinciple of mathematical function ;$tThe basis representation theorem --$tThe fundamental theorem of arithmetic ;$tEuclid's division lemma ;$tDivisibility ;$tThe linear Diophantine equation ;$tThe fundamental theorem of arithmetic --$tCombinatorial and computational number theory ;$tPermutations and combinations ;$tFermat's little theorem ;$tWilson's theorem ;$tGenerating functions ;$tThe use of computers in number theory --$tFundamentals of congruences ;$tBasic properties of congruences ;$tResidue systems ;$tRiffling --$tSolving congruences ;$tLinear congruences ;$tThe theorems of Fermat and Wilson revisited ;$tThe Chinese remainder theorem ;$tPolynomial congruences --$tArithmetic functions ;$tCombinatorial study of ø([italic]n) ;$tFormulae for [italic]d([italic]n) and [lowercase Greek]Sigma([italic]n) ;$tMultiplicative arithmetic functions ;$tThe Möbius inversion formula --$tPrimitive roots ;$tProperties of reduced residue systems ;$tPrimitive roots modulo [italic]p --$tPrime numbers ;$tElementary properties of π([italic]x) ;$tTchebychev's theorem ;$tSome unresolved problems about primes --$gPart II.$tQuadratic congruences ;$tQuadratic residues ;$tEuler's criterion ;$tThe Legendre symbol ;$tThe quadratic reciprocity law ;$tApplications of the quadratic reciprocity law --$tDistributions of quadratic residues ;$tConsecutive residues and nonresidues ;$tConsecutive triples of quadratic residues --$gPart III.$tAdditivity ;$tSums of squares ;$tSums of two squares ;$tSums of four squares --$tElementary partition theory ;$tIntroduction ;$tGraphical representation ;$tEuler's partition theorem ;$tSearching for partition identities --$tPartition generating functions ;$tInfinite products as generating functions ;$tIdentities between infinite series and products --$gPartition identities ;$tHistory and introduction ;$tEuler's pentagonal number theorem ;$tThe Rogers-Ramanujan identities ;$tSeries and products identities ;$tSchur's theorem --$gPart IV.$tGeometric number theory ;$tLattice points ;$tGauss's circle problem ;$tDirichlet's divisor problem --$tAppendices.$gAppendix A.$tA proof that lim[over] [italic]n [right arrow][infinity symbol] [italic]p([italic]n) [superscript]1/[italic]n = 1 --$gAppendix B.$tInfinite series and products (convergence and rearrangement of series and products) ;$t(Maclaurin series expansion of infinite products) --$gAppendix C.$tDouble series --$gAppendix D.$tThe integral test.
938 $aBaker and Taylor$bBTCP$n74151673 //r92
994 $a92$bERR
976 $a31927000531563