000 03740nam a22005295i 4500
001 978-1-4471-2131-2
003 DE-He213
005 20140220083731.0
007 cr nn 008mamaa
008 110808s2011 xxk| s |||| 0|eng d
020 _a9781447121312
_9978-1-4471-2131-2
024 7 _a10.1007/978-1-4471-2131-2
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aHindry, Marc.
_eauthor.
245 1 0 _aArithmetics
_h[electronic resource] /
_cby Marc Hindry.
264 1 _aLondon :
_bSpringer London,
_c2011.
300 _aXVIII, 322p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aFinite Structures -- Applications: Algorithms, Primality and Factorization, Codes -- Algebra and Diophantine Equations -- Analytic Number Theory -- Elliptic Curves -- Developments and Open Problems -- Factorization -- Elementary Projective Geometry -- Galois Theory.
520 _aNumber theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing an elementary introduction to the central topics in number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of course accompanied by their proofs, with perhaps the exception of some results appearing at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and is relevant for the first year of graduate school. It contains an introduction to elliptic curves and a chapter entitled “Developments and Open Problems”, which introduces and brings together various themes oriented toward ongoing mathematical research. Given the multifaceted nature of number theory, the primary aims of this book are to: - provide an overview of the various forms of mathematics useful for studying numbers - demonstrate the necessity of deep and classical themes such as Gauss sums - highlight the role that arithmetic plays in modern applied mathematics - include recent proofs such as the polynomial primality algorithm - approach subjects of contemporary research such as elliptic curves - illustrate the beauty of arithmetic The prerequisites for this text are undergraduate level algebra and a little topology of Rn. It will be of use to undergraduates, graduates and phd students, and may also appeal to professional mathematicians as a reference text.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGeometry, algebraic.
650 0 _aField theory (Physics).
650 0 _aAlgorithms.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aAlgebra.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aField Theory and Polynomials.
650 2 4 _aAlgorithms.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447121305
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-2131-2
912 _aZDB-2-SMA
999 _c106168
_d106168