| 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 |
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| 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. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aUniversitext, _x0172-5939 |
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| 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 |
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