› › Algebraic And Geometric Methods In Discrete Mathematics

Algebraic and Geometric Ideas in the Theory of Discrete Optimization

Author : Jesus A. De Loera

Publisher : SIAM

Page : 320 pages

File Size : 46,22 MB

Release : 2013-01-31

Category : Mathematics

ISBN : 1611972434

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Book Description

In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.



Algebraic and Geometric Methods in Discrete Mathematics

Author : Heather A. Harrington

Publisher : American Mathematical Soc.

Page : 290 pages

File Size : 21,91 MB

Release : 2017-03-16

Category : Mathematics

ISBN : 1470423219

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Book Description

This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.



Algebraic and Discrete Mathematical Methods for Modern Biology

Author : Raina Robeva

Publisher : Academic Press

Page : 383 pages

File Size : 43,62 MB

Release : 2015-05-09

Category : Mathematics

ISBN : 0128012714

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Book Description

Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. - Examines significant questions in modern biology and their mathematical treatments - Presents important mathematical concepts and tools in the context of essential biology - Features material of interest to students in both mathematics and biology - Presents chapters in modular format so coverage need not follow the Table of Contents - Introduces projects appropriate for undergraduate research - Utilizes freely accessible software for visualization, simulation, and analysis in modern biology - Requires no calculus as a prerequisite - Provides a complete Solutions Manual - Features a companion website with supplementary resources



Algebraic and Geometric Methods in Statistics

Author : Paolo Gibilisco

Publisher : Cambridge University Press

Page : 447 pages

File Size : 31,94 MB

Release : 2010

Category : Mathematics

ISBN : 0521896193

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Book Description

An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.



Polyhedral and Algebraic Methods in Computational Geometry

Author : Michael Joswig

Publisher : Springer Science & Business Media

Page : 251 pages

File Size : 38,48 MB

Release : 2013-01-04

Category : Mathematics

ISBN : 1447148177

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Book Description

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.



Analytic, Algebraic and Geometric Aspects of Differential Equations

Author : Galina Filipuk

Publisher : Birkhäuser

Page : 472 pages

File Size : 20,85 MB

Release : 2017-06-23

Category : Mathematics

ISBN : 3319528424

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Book Description

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.



Methods of Algebraic Geometry: Volume 3

Author : W. V. D. Hodge

Publisher : Cambridge University Press

Page : 350 pages

File Size : 24,94 MB

Release : 1994-05-19

Category : Mathematics

ISBN : 0521467756

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Book Description

All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.



Algebraic and Analytic Methods in Representation Theory

Author :

Publisher : Elsevier

Page : 357 pages

File Size : 16,91 MB

Release : 1996-09-27

Category : Mathematics

ISBN : 0080526950

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Book Description

This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field



Algebra & Geometry

Author : Mark V. Lawson

Publisher : CRC Press

Page : 310 pages

File Size : 31,99 MB

Release : 2016-11-25

Category : Mathematics

ISBN : 1482246503

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Book Description

Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra



Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth

Publisher : CRC Press

Page : 2354 pages

File Size : 21,5 MB

Release : 2017-11-22

Category : Computers

ISBN : 1351645919

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Book Description

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.