Elliptic Tales (eBook)

Curves, Counting, and Number Theory

Avner Ash, Robert Gross (Autoren)

eBook Download: EPUB

2012
280 Seiten
Princeton University Press (Verlag)
978-1-4008-4171-4 (ISBN)

Infos

A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep-and often very mystifying-mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.

Autor

Avner Ash is professor of mathematics at Boston College. Robert Gross is associate professor of mathematics at Boston College. They are the coauthors of Fearless Symmetry: Exposing the Hidden Patterns of Numbers (Princeton).

Produkt-Details

• Erscheint lt. Verlag: 12.3.2012
• Zusatzinfo: 52 line illus. 16 tables.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Natur / Technik
• Themenwelt: Geisteswissenschaften ► Geschichte
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung
• Themenwelt: Technik
• Schlagworte: abelian group • abstract algebra • Addition • Additive group • Alfred North Whitehead • Algebraically closed field • algebraic closure • Algebraic Curve • algebraic equation • Algebraic expression • Algebraic Geometry • algebraic variety • algorithm • analytic continuation • analytic function • Birch and Swinnerton-Dyer conjecture • Calculation • Cartesian coordinate system • coefficient • Complex Analysis • complex multiplication • complex number • complex plane • Computation • Congruent number • conjecture • Convergent series • Countable set • Cubic function • Derivative • Difference quotient • Diophantine equation • Dirichlet series • Elliptic Curve • Equation • Euler product • exponential function • Factorization • Fibonacci Number • finite field • Finitely generated abelian group • functional equation • Function of a real variable • Geometric series • Hyperbola • Identity element • Infinite product • Integer • Intersection number (graph theory) • Line at infinity • Line–line intersection • logarithm • Mathematical Sciences • mathematician • Mathematics • modular form • Monomial • Multiplicative group • Natural number • Number Theory • originality • Parabola • parametric equation • parametrization • partial derivative • Plane curve • Point at infinity • polynomial • power series • Prime number • Princeton University Press • Projective line • projective plane • Pure Mathematics • Quantity • Rational number • Rational point • real number • Real projective plane • Riemann hypothesis • Riemann sphere • Riemann surface • Riemann zeta function • Right half-plane • Science • scientific notation • Series (mathematics) • Simultaneous Equations • Solution Set • Subset • subtraction • Summation • System of polynomial equations • Tangent • Taylor series • The Modern World (novel) • Theorem • Torsion subgroup • Variable (mathematics) • Zero of a function
• ISBN-10: 1-4008-4171-2 / 1400841712
• ISBN-13: 978-1-4008-4171-4 / 9781400841714