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Advances in Mathematical and Computational Sciences
This volume documents the contributions presented at The ICRTMPCS II International Conference on Advances in Mathematical and Computational Sciences. Entries focus on modern trends and techniques in branches of pure and applied mathematics, statistics, and computer science. Highlighting applications in coding theory, cryptography, graph theory, fuzzy theory, variance analysis, data analysis, and sampling theory.
Combinatorial Number Theory
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics.
Combinatorial Set Theory
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
The Landman
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Walk Through Combinatorics, A: An Introduction To Enumeration, Graph Theory, And Selected Other Topics (Fifth Edition)
The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.
Ergodic Theory and Dynamical Systems
This book grew out of the 2021 Chapel Hill Ergodic Theory Workshop (https://ergwork.web.unc.edu/schedule-of-talks-201/) during which young and senior researchers presented recent advances in ergodic theory and dynamical systems. Included are original research and survey articles devoted to various topics in Ergodic Theory and Dynamical Systems. Some are from presenters at this workshop. This book attracts young and senior researchers alike.
Ramsey Theory on the Integers
Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics...
Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition)
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the oth...
A Deep Danger
A Deep Danger is a powerfully realistic, sweeping, exciting and entertaining novel. It offers thoughtful analyses and spins a good yarn, has the intrigue and intellectual adroitness of a thriller, combined with an exquisite lyricism that turns it into a novel that refuses to stay shut. Breathtaking in scope and painfully human, written with passion and controlled power, A Deep Danger is a kind of contemporary novel, which is worth to be read, enjoyed and savored long after the last page is turned.
Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Fourth Edition)
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the o...
