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Arithmetic, Geometry, Cryptography and Coding Theory
This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.
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Ranks of Elliptic Curves and Random Matrix Theory
This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Drinfeld Modules
This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics ...
Algebraic Groups: Structure and Actions
This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; sol...
Calculus
The ideal resource for promoting active learning in flipped classroom environments, Calculus: Multivariable, 8th Edition brings calculus to real life with relevant examples and a variety of problems with applications from the physical sciences, economics, health, biology, engineering, and economics. Emphasizing the Rule of Four—viewing problems graphically, numerically, symbolically, and verbally—this popular textbook provides students with numerous opportunities to master key mathematical concepts and apply critical thinking skills to reveal solutions to mathematical problems. Developed by Calculus Consortium based at Harvard University, Calculus: Multivariable uses a student-friendly approach that highlights the practical value of mathematics while reinforcing both the conceptual understanding and computational skills required to reduce complicated problems to simple procedures. The new eighth edition further reinforces the Rule of Four, offers additional problem sets and updated examples, and supports complex, multi-part questions through new visualizations and graphing questions powered by GeoGebra.
Decision Making by the Modern Supreme Court
There are three general models of Supreme Court decision making: the legal model, the attitudinal model and the strategic model. But each is somewhat incomplete. This book advances an integrated model of Supreme Court decision making that incorporates variables from each of the three models. In examining the modern Supreme Court, since Brown v. Board of Education, the book argues that decisions are a function of the sincere preferences of the justices, the nature of precedent, and the development of the particular issue, as well as separation of powers and the potential constraints posed by the president and Congress. To test this model, the authors examine all full, signed civil liberties and economic cases decisions in the 1953–2000 period. Decision Making by the Modern Supreme Court argues, and the results confirm, that judicial decision making is more nuanced than the attitudinal or legal models have argued in the past.
Hamiltonian Perturbation Theory for Ultra-Differentiable Functions
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency...
