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Linear Optimization: The Simplex Workbook
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Linear Optimization: The Simplex WorkbookLinear Optimization: The Simplex Workbook

This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment follows the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own experiments and arguments while they are reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. 
 
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Learning and Teaching Mathematics: An International Perspective
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Learning and Teaching Mathematics: An International PerspectiveLearning and Teaching Mathematics: An International Perspective

The authors of this volume, which is newly available in paperback, all hold the view that mathematics is a form of intelligent problem solving which plays an important part in children's lives outside the classroom as well as in it. Learning and Teaching Mathematics provides an exciting account of recent and radically different research on teaching and learning mathematics which will have a far reaching effect on views about mathematical education.
 
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Linear Algebra and Geometry
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Linear Algebra and GeometryLinear Algebra and Geometry

The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metric, the theory of Hilbert polynomials, and projective and affine geometries. This comprehensive volume is unusual in its extensive use of applications in physics to clarify each topic.
This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics.

 
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The Arithmetic of Dynamical Systems
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The Arithmetic of Dynamical SystemsThe Arithmetic of Dynamical Systems

This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function.
A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. 
 
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Theta Constants, Riemann Surfaces and the Modular Group
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Theta Constants, Riemann Surfaces and the Modular Group There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for number-theoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. 
 
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