This useful book, which is based around the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.
Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook or as a valuable resource for researchers.
This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.
Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.
This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9 shows how to mix known algorithms and create new ones, while Chapter 10 presents the "Chop-Sticks" algorithm, used to obtain all minimum cuts in an undirected network without applying traditional maximum flow techniques. This algorithm has led to the new mathematical specialty of network algebra. The text assumes no background in linear programming or advanced data structure, and most of the material is suitable for undergraduates. 153 black-and-white illus. 23 tables. Exercises, with answers at the ends of chapters.
Written by well-known scholars in the field, CombinatorialReasoning: An Introduction to the Art ofCounting introduces combinatorics alongside moderntechniques, showcases the interdisciplinary aspects of the topic,and illustrates how to problem solve with a multitude of exercisesthroughout. The authors' approach is very reader-friendly andavoids the "scholarly tone" found in many books on this topic.
The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography, including an extensive treatment of private-key encryption, message authentication codes, and hash functions. The authors also present design principles for widely used stream ciphers and block ciphers including RC4, DES, and AES, plus provide provable constructions of stream ciphers and block ciphers from lower-level primitives. The second half of the book covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), followed by a thorough treatment of several standardized public-key encryption and digital signature schemes.
Integrating a more practical perspective without sacrificing rigor, this widely anticipated Second Edition offers improved treatment of:Stream ciphers and block ciphers, including modes of operation and design principles Authenticated encryption and secure communication sessions Hash functions, including hash-function applications and design principles Attacks on poorly implemented cryptography, including attacks on chained-CBC encryption, padding-oracle attacks, and timing attacks The random-oracle model and its application to several standardized, widely used public-key encryption and signature schemes Elliptic-curve cryptography and associated standards such as DSA/ECDSA and DHIES/ECIES
Containing updated exercises and worked examples, Introduction to Modern Cryptography, Second Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a valuable reference for researchers and practitioners, or a general introduction suitable for self-study.
This book will be useful to everyone who has struggled with displaying data in an informative and attractive way. Some basic knowledge of R is necessary (e.g., importing data into R). ggplot2 is a mini-language specifically tailored for producing graphics, and you'll learn everything you need in the book. After reading this book you'll be able to produce graphics customized precisely for your problems, and you'll find it easy to get graphics out of your head and on to the screen or page.
Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why.
Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.
Balancing abstract ideas with specific topical coverage, thebook utilizes real world examples with problems ranging from basiccalculations that are designed to develop fundamental concepts tomore challenging exercises that allow for a deeper exploration ofcomplex combinatorial situations. Simple cases are treated firstbefore moving on to general and more advanced cases. Additionalfeatures of the book include:
• Approximately 700 carefully structured problems designedfor readers at multiple levels, many with hints and/or shortanswers
• Numerous examples that illustrate problem solving usingboth combinatorial reasoning and sophisticated algorithmicmethods
• A novel approach to the study of recurrence sequences,which simplifies many proofs and calculations
• Concrete examples and diagrams interspersed throughout tofurther aid comprehension of abstract concepts
• A chapter-by-chapter review to clarify the most crucialconcepts covered
Combinatorial Reasoning: An Introduction to the Art ofCounting is an excellent textbook for upper-undergraduate andbeginning graduate-level courses on introductory combinatorics anddiscrete mathematics.
Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems.
Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter
Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.
Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.
The first part of the book presents the syntax and semantics of access control logic, basic access control concepts, and an introduction to confidentiality and integrity policies. The second section covers access control in networks, delegation, protocols, and the use of cryptography. In the third section, the authors focus on hardware and virtual machines. The final part discusses confidentiality, integrity, and role-based access control.
Taking a logical, rigorous approach to access control, this book shows how logic is a useful tool for analyzing security designs and spelling out the conditions upon which access control decisions depend. It is designed for computer engineers and computer scientists who are responsible for designing, implementing, and verifying secure computer and information systems.
The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.
Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.
New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.
The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.
The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.
The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to firstname.lastname@example.org.
The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
New to the Fifth Edition
New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate
Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, Germany
Royal Institute of Technology, Sweden
Johannes Kepler University, Austria
Georgia Tech, USA
University of Washington, USA
Ohio University, USA
A manual of selected solutions is available for sale to students; see sidebar. A complete solution manual is available free to instructors who have adopted the book as a required text.
Chapter 3 contains an extended treatment of the principle of inclusion and exclusion which is indispensable to the enumeration of permutations with restricted position given in Chapters 7 and 8. Chapter 4 examines the enumeration of permutations in cyclic representation and Chapter 5 surveys the theory of distributions. Chapter 6 considers partitions, compositions, and the enumeration of trees and linear graphs.
Each chapter includes a lengthy problem section, intended to develop the text and to aid the reader. These problems assume a certain amount of mathematical maturity. Equations, theorems, sections, examples, and problems are numbered consecutively in each chapter and are referred to by these numbers in other chapters.
Key features of Number Theory: Structures, Examples, and Problems:
* A rigorous exposition starts with the natural numbers and the basics.
* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.
* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.
* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.
* Glossary, bibliography, and comprehensive index round out the text.
Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.
The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.
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.
The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.
This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.
The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory, the authors then apply the theory to memoryless, discrete channels with zeroth-order, one-state sources.
The chapters on data compression acquaint students with a myriad of lossless compression methods and then introduce two lossy compression methods. Students emerge from this study competent in a wide range of techniques. The authors' presentation is highly practical but includes some important proofs, either in the text or in the exercises, so instructors can, if they choose, place more emphasis on the mathematics.
Introduction to Information Theory and Data Compression, Second Edition is ideally suited for an upper-level or graduate course for students in mathematics, engineering, and computer science.
Expanded discussion of the historical and theoretical basis of information theory that builds a firm, intuitive grasp of the subject
Reorganization of theoretical results along with new exercises, ranging from the routine to the more difficult, that reinforce students' ability to apply the definitions and results in specific situations.
Simplified treatment of the algorithm(s) of Gallager and Knuth
Discussion of the information rate of a code and the trade-off between error correction and information rate
Treatment of probabilistic finite state source automata, including basic results, examples, references, and exercises
Octave and MATLAB image compression codes included in an appendix for use with the exercises and projects involving transform methods
Supplementary materials, including software, available for download from the authors' Web site at www.dms.auburn.edu/compression