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This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.
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Elliptic 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.
Counting. --- Curves, Elliptic. --- Elliptic functions. --- Number theory. --- Elliptic functions --- Curves, Elliptic --- Number theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Fonctions elliptiques --- Courbes elliptiques --- Théorie des nombres --- Number study --- Numbers, Theory of --- Elliptic curves --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Algebra --- Curves, Algebraic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic
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