open problems in mathematics and computational science

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Open Problems In Mathematics And Computational Science

Author : Çetin Kaya Koç
ISBN : 9783319106830
Genre : Computers
File Size : 29. 8 MB
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This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.

Cryptography And Coding

Author : Jens Groth
ISBN : 9783319272399
Genre : Computers
File Size : 67. 71 MB
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This book constitutes the proceedings of the 15th IMA International Conference on Cryptography and Coding, IMACC 2015, held at Oxford, UK, in December 2015. The 18 papers presented together with 1 invited talk were carefully reviewed and selected from 36 submissions. The scope of the conference was on following topics: authentication, symmetric cryptography, 2-party computation, codes, Boolean functions, information theory, and leakage resilience.

Unsolved Problems In Mathematical Systems And Control Theory

Author : Vincent D. Blondel
ISBN : 9781400826155
Genre : Mathematics
File Size : 49. 10 MB
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This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

Principles Of Quantum Computation And Information

Author : Giuliano Benenti
ISBN : 9812388583
Genre : Science
File Size : 60. 20 MB
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Quantum computation and information is a new, rapidly developing interdisciplinary field. This book provides the reader a useful and not-too-heavy guide. It offers a simple and self-contained introduction; no previous knowledge of quantum mechanics or classical computation is required. Volume 1 may be used as a textbook for a one-semester introductory course in quantum information and computation, both for upper-level undergraduate students and for graduate students. It contains a large number of solved exercises, which are an essential complement to the text, as they will help the student to become familiar with the subject.

Computing The Continuous Discretely

Author : Matthias Beck
ISBN : 9780387291390
Genre : Mathematics
File Size : 58. 30 MB
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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

The Golden Ticket

Author : Lance Fortnow
ISBN : 9781400846610
Genre : Computers
File Size : 58. 95 MB
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The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

Advances In Applied Mathematics Modeling And Computational Science

Author : Roderick Melnik
ISBN : 9781461453888
Genre : Mathematics
File Size : 42. 78 MB
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The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science. This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.

Current Trends In Theoretical Computer Science

Author : Gheorghe P?un
ISBN : 9812389660
Genre : Computers
File Size : 63. 24 MB
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contents: vol 1 : Algorithms; Computational Complexity; Distributed Computing; Natural Computing.

Mathematical Foundations Of Computer Science 2013

Author : Krishnendu Chatterjee
ISBN : 9783642403132
Genre : Computers
File Size : 47. 65 MB
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This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.

Introduction To Computational Modeling Using C And Open Source Tools

Author : Jose M. Garrido
ISBN : 9781482216790
Genre : Computers
File Size : 30. 46 MB
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Introduction to Computational Modeling Using C and Open-Source Tools presents the fundamental principles of computational models from a computer science perspective. It explains how to implement these models using the C programming language. The software tools used in the book include the Gnu Scientific Library (GSL), which is a free software library of C functions, and the versatile, open-source GnuPlot for visualizing the data. All source files, shell scripts, and additional notes are located at ksuweb.kennesaw.edu/~jgarrido/comp_models. The book first presents an overview of problem solving and the introductory concepts, principles, and development of computational models before covering the programming principles of the C programming language. The author then applies programming principles and basic numerical techniques, such as polynomial evaluation, regression, and other numerical methods, to implement computational models. He also discusses more advanced concepts needed for modeling dynamical systems and explains how to generate numerical solutions. The book concludes with the modeling of linear optimization problems. Emphasizing analytical skill development and problem solving, this book helps you understand how to reason about and conceptualize the problems, generate mathematical formulations, and computationally visualize and solve the problems. It provides you with the foundation to understand more advanced scientific computing, including parallel computing using MPI, grid computing, and other techniques in high-performance computing.

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