LEADER 03828nam 22006135 450 001 9910483580303321 005 20250707124344.0 010 $a3-030-55233-0 024 7 $a10.1007/978-3-030-55233-6 035 $a(CKB)4100000011491439 035 $a(DE-He213)978-3-030-55233-6 035 $a(MiAaPQ)EBC6363220 035 $a(MiAaPQ)EBC6647479 035 $a(Au-PeEL)EBL6363220 035 $a(OCoLC)1199056038 035 $a(Au-PeEL)EBL6647479 035 $a(PPN)258851163 035 $a(EXLCZ)994100000011491439 100 $a20201003d2020 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Journey Through The Realm of Numbers $eFrom Quadratic Equations to Quadratic Reciprocity /$fby Menny Aka, Manfred Einsiedler, Thomas Ward 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIX, 344 p.) 225 1 $aSUMS Readings,$x2730-5821 311 08$a3-030-55232-2 320 $aIncludes bibliographical references and index. 327 $a1 Introduction: Polynomial Equations -- 2 Cantor's Paradise -- 3 Sums of Squares -- 4 Sums of Two Squares -- 5 Abstract Algebra: Ring Theory -- 6 Cubic and Quartic Diophantine Equations -- 7 The Structure of the Group Fp? -- 8 Studying Squares Again -- Hints to Selected Exercises -- References and further reading -- Index. 330 $aThis book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations. 410 0$aSUMS Readings,$x2730-5821 606 $aNumber theory 606 $aAlgebra 606 $aNumber Theory 606 $aAlgebra 615 0$aNumber theory. 615 0$aAlgebra. 615 14$aNumber Theory. 615 24$aAlgebra. 676 $a512.7 676 $a510 700 $aAka$b Menny$0845356 702 $aEinsiedler$b Manfred Leopold$f1973- 702 $aWard$b Thomas$f1963- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483580303321 996 $aA Journey Through The Realm of Numbers$91886622 997 $aUNINA