In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on "doing" mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word 'separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

The abstract branch of theoretical computer science known as Computation Theory typically appears in undergraduate academic curricula in a form that obscures both the mathematical concepts that are central to the various components of the theory and the relevance of the theory to the typical student. This regrettable situation is due largely to the thematic tension among three main competing principles for organizing the material in the course.

This book is motivated by the belief that a deep understanding of, and operational control over, the few "big" mathematical ideas that underlie Computation Theory is the best way to enable the typical student to assimilate the "big" ideas of Computation Theory into her daily computational life.

Computation theory is a discipline that uses mathematical concepts and tools to expose the nature of "computation" and to explain a broad range of computational phenomena: Why is it harder to perform some computations than others?  Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations?  How does one reason about such questions? This unique textbook strives to endow students with conceptual and manipulative tools necessary to make computation theory part of their professional lives. The work achieves this goal by means of three stratagems that set its approach apart from most other texts on the subject. For starters, it develops the necessary mathematical concepts and tools from the concepts' simplest instances, thereby helping students gain operational control over the required mathematics. Secondly, it organizes development of theory around four "pillars," enabling students to see computational topics that have the same intellectual origins in physical proximity to one another. Finally, the text illustrates the "big ideas" that computation theory is built upon with applications of these ideas within "practical" domains in mathematics, computer science, computer engineering, and even further afield. Suitable for advanced undergraduate students and beginning graduates, this textbook augments the "classical" models that traditionally support courses on computation theory with novel models inspired by "real, modern" computational topics,such as  crowd-sourced computing, mobile computing, robotic path planning, and volunteer computing. Arnold L. Rosenberg is Distinguished Univ. Professor Emeritus at University of Massachusetts, Amherst, USA. Lenwood S. Heath is Professor at Virgina Tech, Blacksburg, USA.            

This volume commemorates Shimon Even, one of founding fathers of Computer Science in Israel, who passed away on May 1, 2004. This Festschrift contains research contributions, surveys and educational essays in theoretical computer science, written by former students and close collaborators of Shimon. The essays address natural computational problems and are accessible to most researchers in theoretical computer science.

Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

Research in the field of parallel computer architectures and parallel algorithms has been very successful in recent years, and further progress isto be expected. On the other hand, the question of basic principles of the architecture of universal parallel computers and their realizations is still wide open. The answer to this question must be regarded as mostimportant for the further development of parallel computing and especially for user acceptance. The First Heinz Nixdorf Symposium brought together leading experts in the field of parallel computing and its applications to discuss the state of the art, promising directions of research, and future perspectives. It was the first in a series of Heinz Nixdorf Symposia, intended to cover varying subjects from the research spectrum of the Heinz Nixdorf Institute of the University of Paderborn. This volume presents the proceedings of the symposium, which was held in Paderborn in November 1992. The contributions are grouped into four parts: parallel computation models and simulations, existing parallel machines, communication and programming paradigms, and parallel algorithms.

Computation theory is a discipline that uses mathematical concepts and tools to expose the nature of "computation" and to explain a broad range of computational phenomena: Why is it harder to perform some computations than others? Are the differences in difficulty that we observe inherent, or are they artifacts of the way we try to perform the computations? How does one reason about such questions? This unique textbook strives to endow students with conceptual and manipulative tools necessary to make computation theory part of their professional lives. The work achieves this goal by means of three stratagems that set its approach apart from most other texts on the subject. For starters, it develops the necessary mathematical concepts and tools from the concepts' simplest instances, thereby helping students gain operational control over the required mathematics. Secondly, it organizes development of theory around four "pillars," enabling students to see computational topics that have the same intellectual origins in physical proximity to one another. Finally, the text illustrates the "big ideas" that computation theory is built upon with applications of these ideas within "practical" domains in mathematics, computer science, computer engineering, and even further afield. Suitable for advanced undergraduate students and beginning graduates, this textbook augments the "classical" models that traditionally support courses on computation theory with novel models inspired by "real, modern" computational topics,such as crowd-sourced computing, mobile computing, robotic path planning, and volunteer computing. Arnold L. Rosenberg is Distinguished Univ. Professor Emeritus at University of Massachusetts, Amherst, USA. Lenwood S. Heath is Professor at Virgina Tech, Blacksburg, USA.

In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on "doing" mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Topics in Parallel and Distributed Computing provides resources and guidance for those learning PDC as well as those teaching students new to the discipline. The pervasiveness of computing devices containing multicore CPUs and GPUs, including home and office PCs, laptops, and mobile devices, is making even common users dependent on parallel processing. Certainly, it is no longer sufficient for even basic programmers to acquire only the traditional sequential programming skills. The preceding trends point to the need for imparting a broad-based skill set in PDC technology. However, the rapid changes in computing hardware platforms and devices, languages, supporting programming environments, and research advances, poses a challenge both for newcomers and seasoned computer scientists. This edited collection has been developed over the past several years in conjunction with the IEEE technical committee on parallel processing (TCPP), which held several workshops and discussions on learning parallel computing and integrating parallel concepts into courses throughout computer science curricula.