This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.Applications include:Identification numbers and modular arithmetic(linear) error-correcting codes, including cyclic code...

Tough Test Questions? Missed Lectures? Not Rnough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test ...

MULTIPLY your chances of understanding DISCRETE MATHEMATICSIf you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and e...

Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent dev...

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using ...

This fundamental monograph introduces both the probabilistic and algebraic aspects of information theory and coding. It has evolved from the authors' years of experience teaching at the undergraduate level, including several Cambridge Maths Tripos courses. The book provides relevant background material, a wide range of worked examples and clear solutions to problems from real exam papers. It is a valuable teaching aid for undergraduate and graduate students, or for researchers and engineer...

Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a r...

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the a...

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gröbner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials and systems of non-linear equations. A special feature is that Gröbner bases do not appear as an isolated example. They are fully integrated as a su...

This book introduces students to the art and craft of writing proofs, beginning with the basics of writing proofs and logic, and continuing on with more in-depth issues and examples of creating proofs in different parts of mathematics, as well as introducing proofs-of-correctness for algorithms. The creation of proofs is covered for theorems in both discrete and continuous mathematics, and in difficulty ranging from elementary to beginning graduate level.Just beyond the standard introducto...

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; no...

This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provi...