Over the last 30 years graph theory has evolved into an important math- ematical tool in the solution of a wide variety of problems in many areas of society.
Discrete probability theory and the theory of algorithms have become close partners over the last ten years, though the roots of this partnership go back much longer.
Structured adaptive mesh refinement (SAMR) methods have matured over the past 20 years and are now the method of choice for certain difficult problems, such as compressible flow.
The idea for this book was conceived over the second bottle of Villa Maria's Caber- net Medot '89, at the dinner of the Australasian Combinatorics Conference held at Palmerston North, New Zealand in December 1990, where the authors first met and discovered they had a number of interests in common.
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities.
Developments in mathematical physics during the second half of the 20th century influenced a number of mathematical areas, among the more significant being representation theory, differential equations, combinatorics, and algebraic geometry.
This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets.
This book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the "e;combinatorial spirit"e;.
Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to prac- tical problems.
Computer and Information Security Handbook, Fourth Edition offers deep coverage of an extremely wide range of issues in computer and cybersecurity theory, along with applications and best practices, offering the latest insights into established and emerging technologies and advancements.
Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems.
In the spectrum of mathematics, graph theory which studies a mathe- matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer.
The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations.
The second edition of this 5-volume handbook is intended to be a basic yet comprehensive reference work in combinatorial optimization that will benefit newcomers and researchers for years to come.
A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas.
A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds.
"e;Proofs and Fundamentals: A First Course in Abstract Mathematics"e; 2nd edition is designed as a "e;transition"e; course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality.
Emphasizes a Problem Solving ApproachA first course in combinatoricsCompletely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems.
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity.
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields.
The Star and the Whole: Gian-Carlo Rota on Mathematics and Phenomenology, authored by Fabrizio Palombi, is the first book to study Rota's philosophical reflection.
Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus focuses on the life and accomplishments of one of the seventeenth century's most influential mathematicians and philosophers.
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Godel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory.
Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems.
This book is a tribute to Paul Erd\H{o}s, the wandering mathematician once described as the "e;prince of problem solvers and the absolute monarch of problem posers.
