000 02679nam a22004575i 4500
001 978-1-4614-7717-4
003 DE-He213
005 20140220082830.0
007 cr nn 008mamaa
008 130914s2013 xxu| s |||| 0|eng d
020 _a9781461477174
_9978-1-4614-7717-4
024 7 _a10.1007/978-1-4614-7717-4
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aTrifković, Mak.
_eauthor.
245 1 0 _aAlgebraic Theory of Quadratic Numbers
_h[electronic resource] /
_cby Mak Trifković.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXI, 197 p. 29 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 _a1 Examples -- 2 A Crash Course in Ring Theory -- 3 Lattices -- 4 Arithmetic in Q[√D] -- 5 The Ideal Class Group and Geometry of Numbers -- 6 Continued Fractions -- 7 Quadratic Forms -- Appendix -- Hints to Selected Exercises -- Index.
520 _aBy focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group.  The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms.  The treatment of quadratic forms is somewhat more advanced  than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields.  The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders.  Prerequisites include elementary number theory and a basic familiarity with ring theory.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aAlgebra.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461477167
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-7717-4
912 _aZDB-2-SMA
999 _c95970
_d95970