Mathematics of Discrete Structures for Computer Science

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer

Graph theory gained initial prominence in science and engineering through its strong links with matrix algebra and computer science. Moreover, the structure of the mathematics is well suited to that o

Trees are a fundamental object in graph theory and combinatorics as well as a basic object for data structures and algorithms in computer science. During the last years research related to (random) tr

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in mul

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.

By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.

Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and linguistics. This volume is the first to attempt to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics. Topics discussed include: Thue's square free words, Van der Waerden's theorem, Ramsey's theorem; factorization of free monoids including application to free Lie algebras; equations in words, etc.

Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them t

Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies an

Szemeredi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of Szemeredi's achievemen

Porous Media are objects of research in physics, chemistry, engineering, mathematics, computer science, life and medical sciences, as well as of industrial applications. Readers might work in: Univers

Combining biology, computer science, mathematics, and statistics, the field of bioinformatics has become a hot new discipline with profound impacts on all aspects of biology and industrial application

Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory Editors Ronald L. Graham Jan Karel Lenstra Robert E. Tarjan Discrete Mathematics and Optimization involves the study of fini

Information Theory is fundamental to several areas of knowledge within engineering, computer science and mathematics, as well as many other educational disciplines. Within electrical engineering, info

Data analysis, machine learning and knowledge discovery are research areas at the intersection of computer science, artificial intelligence, mathematics and statistics. They cover general methods and

A few electrical engineers, but mostly researchers in computer science, information, mathematics, and similar soft fields explore the storage, manipulation, and retrieval of multimedia data comprised

Data Analysis, Data Handling and Business Intelligence are research areas at the intersection of computer science, artificial intelligence, mathematics, and statistics. They cover general methods and

Mathematical psychology is an interdisciplinary area of research in which methods of mathematics, operations research, and computer science in psychology are used. Now more than thirty years old, the

The theory of formal languages is widely accepted as the backbone of t- oretical computer science. It mainly originated from mathematics (com- natorics, algebra, mathematical logic) and generative lin

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily at logisticians in mathematics, philosophy, computer science and

Super-Intelligent Machines combines neuroscience and computer science to analyze future intelligent machines. It describes how they will mimic the learning structures of human brains to serve billions

One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.

Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developm

The theory of expander graphs is a rapidly developing topic in mathematics and computer science, with applications to communication networks, error-correcting codes, cryptography, complexity theory, a

During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This 2005 volume, which contains 32 papers on a broad range of topics of interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This 2005 volume, which contains 32 papers on a broad range of topics of interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

Contributors mostly from technical disciplines, but also from biology, present recent studies on the convergence of computer science and mathematics with systems biology. They focus on experimental da

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-comm

Quantum Information Processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. Its ultimate goal is to harness quantum physics to co

Phase transitions typically occur in combinatorial computational problems and have important consequences, especially with the current spread of statistical relational learning as well as sequence learning methodologies. In Phase Transitions in Machine Learning the authors begin by describing in detail this phenomenon, and the extensive experimental investigation that supports its presence. They then turn their attention to the possible implications and explore appropriate methods for tackling them. Weaving together fundamental aspects of computer science, statistical physics and machine learning, the book provides sufficient mathematics and physics background to make the subject intelligible to researchers in AI and other computer science communities. Open research issues are also discussed, suggesting promising directions for future research.

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.

Bioinformatics is a field which uses the principles and techniques of mathematics, computer science, engineering, statistics, etc. to analyse and interpret biological data. It is also used to understa

A classicist and an archaeologist are included, but the rest of the contributors are from computer science, electrical engineering, mathematics, and other fields concerned with the technology rather t

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.Proofs and Algorithms: In

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

This is an introduction to the field of efficient parallel algorithms and to the techniques for efficient parallelisation. It is self-contained and presumes no special knowledge of parallel computers or particular mathematics. The book emphasises designing algorithms within the timeless and abstracted context of a high-level programming language rather than within highly specific computer architectures. This is an approach which concentrates on the essence of algorithmic theory, determining and taking advantage of the inherently parallel nature of certain types of problem. The authors present regularly-used techniques and a range of algorithms which includes some of the more celebrated and well-known. Efficient Parallel Algorithms is targeted at non-specialists who are considering entering the field of parallel algorithms. It will be particularly useful for courses aimed at advanced undergraduate or new postgraduate students of computer science and mathematics.

For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics