LEADER 03121nam 2200553 450 001 9910795045003321 005 20230809234402.0 010 $a3-11-051626-8 010 $a3-11-051614-4 024 7 $a10.1515/9783110516142 035 $a(CKB)4340000000203639 035 $a(MiAaPQ)EBC5049535 035 $a(DE-B1597)472902 035 $a(OCoLC)1004552174 035 $a(OCoLC)1004874654 035 $a(DE-B1597)9783110516142 035 $a(Au-PeEL)EBL5049535 035 $a(CaPaEBR)ebr11443180 035 $a(EXLCZ)994340000000203639 100 $a20171016h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 00$aAlgebra and number theory $ea selection of highlights /$fBenjamin Fine [and four others] 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (332 pages) $cillustrations 225 1 $aDe Gruyter Textbook 311 $a3-11-051584-9 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. The natural, integral and rational numbers -- $t2. Division and factorization in the integers -- $t3. Modular arithmetic -- $t4. Exceptional numbers -- $t5. Pythagorean triples and sums of squares -- $t6. Polynomials and unique factorization -- $t7. Field extensions and splitting fields -- $t8. Permutations and symmetric polynomials -- $t9. Real numbers -- $t10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations -- $t11. Quadratic number fields and Pell's equation -- $t12. Transcendental numbers and the numbers e and ? -- $t13. Compass and straightedge constructions and the classical problems -- $t14. Euclidean vector spaces -- $tBibliography -- $tIndex 330 $aThis two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. ContentsThe natural, integral and rational numbersDivision and factorization in the integersModular arithmeticExceptional numbersPythagorean triples and sums of squaresPolynomials and unique factorizationField extensions and splitting fieldsPermutations and symmetric polynomialsReal numbersThe complex numbers, the Fundamental Theorem of Algebra and polynomial equationsQuadratic number fields and Pell's equationTranscendental numbers and the numbers e and ?Compass and straightedge constructions and the classical problemsEuclidean vector spaces 410 0$aDe Gruyter textbook. 606 $aAlgebra 606 $aNumber theory 615 0$aAlgebra. 615 0$aNumber theory. 676 $a512.9 700 $aFine$b Benjamin, $056763 702 $aFine$b Benjamin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910795045003321 996 $aAlgebra and number theory$93719765 997 $aUNINA