### Trends In Optimization: American Mathematical Society Short Course,

This volume presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). It focuses on seven exciting areas of discrete optimization. In particular, Karen Aardal describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction and H.W. Lenstra's use of this idea in the early 1980s in his polynomial-time algorithm for integer programming in fixed dimension. Aardal's article, "Lattice basis reduction in optimization: Special Topics", is one of the most lucid presentations of the material. It also contains practical developments using computational tools. Bernd Sturmfels' article, "Algebraic recipes for integer programming", discusses how methods of commutative algebra and algebraic combinatorics can be used successfully to attack integer programming problems. Specifically, Gröbner bases play a central role in algorithmic theory and practice. Moreover, it is shown that techniques based on short rational functions are bringing new insights, such as in computing the integer programming gap. Overall, these articles, together with five other contributions, make this volume an impressive compilation on the state-of-the-art of optimization. It is suitable for graduate students and...

• Brand: Brand: Amer Mathematical Society
• ASIN: 082183584X

### Different Perspectives on Wavelets: American Mathematical Society Short

The wavelet transform can be seen as a synthesis of ideas that have emerged since the 1960s in mathematics, physics, and electrical engineering. The basic idea is to use a family of "building blocks" to represent in an efficient way the object at hand, be it a function, an operator, a signal, or an image. The building blocks themselves come in different "sizes" which can describe different features with different resolutions. The papers in this book attempt to give some theoretical and technical shape to this intuitive picture of wavelets and their uses. The papers collected here were prepared for an AMS Short Course on Wavelets and Applications, held at the Joint Mathematics Meetings in San Antonio in January 1993. Here readers will find general background on wavelets as well as more detailed views of specific techniques and applications. With contributions by some of the top experts in the field, this book provides an excellent introduction to this important and growing area of research.

• ASIN: 0821855034

### Geometry Revisited (New Mathematical

Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

• Brand: Brand: The Mathematical Association of America
• ASIN: 0883856190

### Game Theory: A Playful Introduction (Student Mathematical

This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. The first four chapters develop combinatorial game theory, beginning with an introduction to game trees and mathematical induction, then investigating the games of Nim and Hackenbush. The analysis of these games concludes with the cornerstones of the Sprague-Grundy Theorem and the Simplicity Principle. The last eight chapters of the book offer a scenic journey through the mathematical highlights of classical game theory. This contains a thorough treatment of zero-sum games and the von Neumann Minimax Theorem, as well as a student-friendly development and proof of the Nash Equilibrium Theorem. The Folk Theorem, Arrow's voting paradox, evolutionary biology, cake cutting, and other engaging auxiliary topics also appear. The book is designed as a textbook for an undergraduate mathematics class. With ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the gener...

• Brand: Eurospan
• ASIN: 1470422107

### Applications of Computational Algebraic Geometry: American Mathematical Society

This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that "crunching equations" is now as easy as "crunching numbers" has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material.

• Brand: Brand: Amer Mathematical Society
• ASIN: 0821807501

### Introduction to Mathematical Finance: American Mathematical Society Short

The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Théorie de la spéculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought remarkable and important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and growth. Concurrently with these mathematical advances, markets have grown, and developments in both academia and industry continue to expand. This lively activity inspired an AMS Short Course at the Joint Mathematics Meetings in San Diego (CA). The present volume includes the written results of that course. Articles are featured by an impressive list of recognized researchers and practitioners. Their contributions present deep results, pose challenging questions, and suggest directions for future research. This collection offers compelling introductory articles on this new, exciting, and rapidly growing field.

• Brand: Brand: Amer Mathematical Society
• ASIN: 082180751X

### Different Aspects of Coding Theory: American Mathematical Society

This book connects coding theory with actual applications in consumer electronics and with other areas of mathematics. Different Aspects of Coding Theory covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science. Features: A unique combination of mathematical theory and engineering practice. Much diversity and variety among chapters, thus offering broad appeal. Topics relevant to mathematicians, statisticians, engineers, and computer scientists. Contributions by recognized scholars.

• Brand: Brand: Amer Mathematical Society
• ASIN: 0821803794

### Asymptopia (Student Mathematical

Asymptotics in one form or another are part of the landscape for every mathematician. The objective of this book is to present the ideas of how to approach asymptotic problems that arise in discrete mathematics, analysis of algorithms, and number theory. A broad range of topics is covered, including distribution of prime integers, Erd?s Magic, random graphs, Ramsey numbers, and asymptotic geometry.The author is a disciple of Paul Erd?s, who taught him about Asymptopia. Primes less than n , graphs with v vertices, random walks of t steps - Erd?s was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions nlnn , n 2 , lnn n , lnn ? ? ? ? , 1 nlnn all have distinct personalities. Erd?s knew these functions as personal friends. It is the author's hope that these insights may be passed on, that the reader may similarly feel which function has the right temperament for a given task. This book is aimed at strong undergraduates, though it is also suitable for particularly good high school students or for graduates wanting to learn some basic techniques.Asymptopia is a beautiful world. Enjoy!

• ASIN: 1470409046

### The Code Book: The Science of Secrecy from

• ASIN: B004IK8PLE

### Quantum Computation (Proceedings of Symposia in Applied

This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships with existing mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum information science. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally, exploration into dive...

• Brand: Brand: Amer Mathematical Society
• ASIN: 0821820842

### Game Theory and Its Applications (Proceedings of Symposia

Book by American Mathematical Society Short Course, Game Theory and its Applications (1979 : Biloxi, Miss.), Lucas, William F.

• Brand: Brand: Amer Mathematical Society
• ASIN: 0821800256

### Symbolic Dynamics and Its Applications: American Mathematical Society,

Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications.Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.

• ASIN: 0821831577

### When Life is Linear (Anneli Lax New Mathematical

From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This book introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. The books details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.

• ASIN: 0883856492

#### Analysis (Graduate Studies in Mathematics)

Significantly revised and expanded, this new Second Edition provides readers at all levels---from beginning students to practicing analysts---with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas. Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing. This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes: Features: a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalitie...

• Brand: Brand: American Mathematical Society
• ASIN: 0821827839

### The Interface of Knots and Physics - American

• ASIN: B01M7NQOK9

### Modeling and Simulation of Biological Networks - Proceedings

• ASIN: B00AOSD2CQ

### Cronin, Jane's Analyzing Multiscale Phenomena Using Singular Perturbation

Will be shipped from US. Used books may not include companion materials, may have some shelf wear, may contain highlighting/notes, may not include CDs or access codes. 100% money back guarantee.

• ASIN: B008ITIEMG

### Analyzing Multiscale Phenomena Using Singular Perturbation Methods: American

To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

• ASIN: 0821809296

### [(The Radon Transform, Inverse Problems, and Tomography :

• ASIN: B01J4OS2M0

### Short-Time Geometry of Random Heat Kernels: March 1998

This volume studies the behavior of the random heat kernel associated with the stochastic partial differential equation $du=\tfrac {1}{2} {\Delta}udt = (\sigma, \nabla u) \circ dW_t$, on some Riemannian manifold $M$. Here $\Delta$ is the Laplace-Beltrami operator, $\sigma$ is some vector field on $M$, and $\nabla$ is the gradient operator. Also, $W$ is a standard Wiener process and $\circ$ denotes Stratonovich integration. The author gives short-time expansion of this heat kernel. He finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.

• ASIN: 0821806491
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