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024 7 $a10.1007/978-1-4614-7717-4
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035   $a(DE-He213)978-1-4614-7717-4
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100   $a20130914d2013      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aAlgebraic Theory of Quadratic Numbers /$fby Mak Trifkovi?
205   $a1st ed. 2013.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013.
215   $a1 online resource (206 p.)
225 1 $aUniversitext,$x0172-5939
300   $aDescription based upon print version of record.
311   $a1-4614-7716-6 
320   $aIncludes bibliographical references (pages 193) and index.
327   $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.
330   $aBy focusing on quadratic numbers, this advanced undergraduate or master?s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group.  The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms.  The treatment of quadratic forms is somewhat more advanced  than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields.  The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders.  Prerequisites include elementary number theory and a basic familiarity with ring theory.
410  0$aUniversitext,$x0172-5939
606   $aNumber theory
606   $aAlgebra
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
615  0$aNumber theory.
615  0$aAlgebra.
615 14$aNumber Theory.
615 24$aAlgebra.
676   $a512.74
700   $aTrifkovi?$b Mak$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521448
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910438035103321
996   $aAlgebraic theory of quadratic numbers$9836936
997   $aUNINA