combinatorics a very short introduction very short introductions

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Combinatorics

Author : Robin Wilson
ISBN : 9780198723493
Genre : Mathematics
File Size : 52. 79 MB
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How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

An Introduction To Mathematical Cryptography

Author : Jeffrey Hoffstein
ISBN : 9781493917112
Genre : Mathematics
File Size : 83. 73 MB
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This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

Recent Trends In Algebraic Combinatorics

Author : Hélène Barcelo
ISBN : 9783030051419
Genre : Mathematics
File Size : 34. 71 MB
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This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.

Artificial Intelligent Approaches In Petroleum Geosciences

Author : Constantin Cranganu
ISBN : 9783319165318
Genre : Science
File Size : 85. 88 MB
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This book presents several intelligent approaches for tackling and solving challenging practical problems facing those in the petroleum geosciences and petroleum industry. Written by experienced academics, this book offers state-of-the-art working examples and provides the reader with exposure to the latest developments in the field of intelligent methods applied to oil and gas research, exploration and production. It also analyzes the strengths and weaknesses of each method presented using benchmarking, whilst also emphasizing essential parameters such as robustness, accuracy, speed of convergence, computer time, overlearning and the role of normalization. The intelligent approaches presented include artificial neural networks, fuzzy logic, active learning method, genetic algorithms and support vector machines, amongst others. Integration, handling data of immense size and uncertainty, and dealing with risk management are among crucial issues in petroleum geosciences. The problems we have to solve in this domain are becoming too complex to rely on a single discipline for effective solutions and the costs associated with poor predictions (e.g. dry holes) increase. Therefore, there is a need to establish a new approach aimed at proper integration of disciplines (such as petroleum engineering, geology, geophysics and geochemistry), data fusion, risk reduction and uncertainty management. These intelligent techniques can be used for uncertainty analysis, risk assessment, data fusion and mining, data analysis and interpretation, and knowledge discovery, from diverse data such as 3-D seismic, geological data, well logging, and production data. This book is intended for petroleum scientists, data miners, data scientists and professionals and post-graduate students involved in petroleum industry.

Combinatorial Number Theory

Author : Bruce Landman
ISBN : 9783110280616
Genre : Mathematics
File Size : 80. 47 MB
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This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.

Forthcoming Books

Author : Rose Arny
ISBN : UOM:39015058394100
Genre : American literature
File Size : 20. 23 MB
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An Introduction To Combinatorics

Author : A. B. Slomson
ISBN : UOM:39015019838922
Genre : Science
File Size : 78. 11 MB
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By concentrating on counting problems, Introduction to Combinatorics conveys basic ideas of its subject. Topics include combinations, permutations, the inclusion-exclusion principles, partitions, Stirling's Formula, generating functions, recurrence relations, groups, group actions, and graphs. The final two chapters discuss the application of group theory to counting patterns, via Burnside's Theorem and Polya's Theorem. Slomson's approach is to begin with concrete problems, and to use them as a lead-in to general theory. Numerous exercises-most of which are provided with detailed answers-are included for the advanced student. Among the applications considered are approaches to probability problems, especially in card games.

Phase Transitions In Combinatorial Optimization Problems

Author : Alexander K. Hartmann
ISBN : 9783527606863
Genre : Science
File Size : 74. 54 MB
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A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.

Computing And Combinatorics

Author : Ding-Zhu Du
ISBN : 354060216X
Genre : Computers
File Size : 52. 29 MB
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This book constitutes the proceedings of the First Annual International Conference on Computing and Combinatorics, COCOON '95, held in Xi'an, China in August 1995. The 52 thoroughly refereed full papers and the 22 short presentations included in this volume were selected from a total of 120 submissions. All current aspects of theoretical computer science and combinatorial mathematics related to computing are addressed; in particular, there are sections on complexity theory, graph drawing, computational geometry, databases, graph algorithms, distributed programming and logic, combinatorics, machine models, combinatorial designs, algorithmic learning, algorithms, distributed computing, and scheduling.

Introduction To Combinatorial Theory

Author : R. C. Bose
ISBN : MINN:31951000333687X
Genre : Mathematics
File Size : 70. 88 MB
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A ``hands-on'' constructive and computational approach to combinatorial topics with real-life modern applications. Provides a simple treatment of the subject. Introduces topics such as counting, designs and graphs. The notation is standard and kept to a minimum. Chapters end with historical remarks and suggestions for further reading.

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