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"This book deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-acic cohomology and group representations, presented in a context that is appealing to specialists in number theory and algebraic geometry"--

Polynomials --- Number theory --- Representations of groups --- Cohomology operations

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Representations of groups. --- Categories (Mathematics) --- Représentations de groupes --- Catégories (Mathématiques) --- Group theory --- Representations of groups --- 51 <082.1> --- Group representation (Mathematics) --- Groups, Representation theory of --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Mathematics--Series

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This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.

Finite groups. --- Representations of groups. --- Finite groups --- Representations of groups --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Group representation (Mathematics) --- Groups, Representation theory of --- Groups, Finite --- Mathematics. --- Group theory. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Quantum physics. --- Group Theory and Generalizations. --- Quantum Physics. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Group theory --- Modules (Algebra) --- Quantum theory. --- Math --- Science --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematical physics. --- Physical mathematics --- Engineering --- Engineering analysis --- Mathematical analysis

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This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: • integration and differentiation on manifolds • foundations of functional analysis • Brouwer's mapping degree • generalized analytic functions • potential theory and spherical harmonics • linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.

Differential equations, Partial. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Integral representations. --- Representations, Integral --- Partial differential equations --- Mathematics. --- Partial differential equations. --- Physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Science --- Algebraic number theory --- Crystallography, Mathematical --- Representations of groups --- Differential equations, partial. --- Mathematical physics. --- Physical mathematics --- Physics

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This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric. Kristopher Tapp is currently a mathematics professor at Saint Joseph's University. He is the author of 17 research papers and one well-reviewed undergraduate textbook, Matrix Groups for Undergraduates. He has been awarded two National Science Foundation research grants and several teaching awards.

Symmetry (Mathematics). --- Symmetry groups. --- Symmetry (Mathematics) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebra --- Groups, Symmetry --- Symmetric groups --- Invariance (Mathematics) --- Mathematics. --- Geometry. --- Social sciences. --- Mathematics, general. --- Mathematics in the Humanities and Social Sciences. --- Mathematics in Art and Architecture. --- Crystallography, Mathematical --- Quantum theory --- Representations of groups --- Group theory --- Automorphisms --- Euclid's Elements --- Math --- Science --- Behavioral sciences --- Human sciences --- Sciences, Social --- Social science --- Social studies --- Civilization --- Arts. --- Architecture—Mathematics. --- Arts, Fine --- Arts, Occidental --- Arts, Primitive --- Arts, Western --- Fine arts --- Humanities