Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo

Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.

Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists that has a particular set of properties. To give students a better idea of what the subject covers, the authors first discuss several examples of typical combinatorial problems. They also provide basic information on sets, proof techniques, enumeration, and graph theory—topics that appear frequently throughout the book. The next few chapters explore enumerative ideas, including the pigeonhole principle and inclusion/exclusion. The text then covers enumerative functions and the relations between them. It describes generating functions and recurrences, important families of functions, and the theorems of Pólya and Redfield. The authors also present introductions to computer algebra and group theory, before considering structures of particular interest in combinatorics: graphs, codes, Latin squares, and experimental designs. The last chapter further illustrates the interaction between linear algebra and combinatorics. Exercises and problems of varying levels of difficulty are included at the end of each chapter. Ideal for undergraduate students in mathematics taking an introductory course in combinatorics, this text explores the different ways of arranging objects and selecting objects from a set. It clearly explains how to solve the various problems that arise in this branch of mathematics.

Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.

Discover the Connections between Different Structures and FieldsDiscrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics,

Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this areaPearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relation

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he

Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references. The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks. Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and