03327nam 22006615 450 991043803510332120200702025415.01-4614-7717-410.1007/978-1-4614-7717-4(CKB)3710000000019028(EBL)1466254(SSID)ssj0001010483(PQKBManifestationID)11562132(PQKBTitleCode)TC0001010483(PQKBWorkID)10999682(PQKB)11675656(DE-He213)978-1-4614-7717-4(MiAaPQ)EBC6314092(MiAaPQ)EBC1466254(Au-PeEL)EBL1466254(CaPaEBR)ebr10983366(OCoLC)859400294(PPN)172419778(EXLCZ)99371000000001902820130914d2013 u| 0engur|n|---|||||txtccrAlgebraic Theory of Quadratic Numbers /by Mak Trifković1st ed. 2013.New York, NY :Springer New York :Imprint: Springer,2013.1 online resource (206 p.)Universitext,0172-5939Description based upon print version of record.1-4614-7716-6 Includes bibliographical references (pages 193) and index.1 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.By 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.Universitext,0172-5939Number theoryAlgebraNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Number theory.Algebra.Number Theory.Algebra.512.74Trifković Makauthttp://id.loc.gov/vocabulary/relators/aut521448MiAaPQMiAaPQMiAaPQBOOK9910438035103321Algebraic theory of quadratic numbers836936UNINA