Various Studies on Split and Non- Split Dominating Sets of an Interval
Square-Free Factorizations. Some Cryptological and Other Mathematical Aspects
Set Dynamic Equations on Time Scales
The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.
Graph-Theoretic Concepts in Computer Science
This book constitutes the refereed proceedings of the 50th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2024, held in Gozd Martuljek, Slovenia in June 2024, The 31 papers presented in this volume were carefully reviewed and selected from 89 submissions. Additionally, this volume also contains a survey on approximation algorithms for tree-width, path-width, and tree-depth prepared by Hans Bodlander, who delivered the Test of Time Award talk at WG 2024. The WG 2024 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science or by extracting new graph-theoretic problems from applications.
Geometry by Its Transformations
This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid's Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the M繹bius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.
Almost Periodicity and Almost Automorphy
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an "ordinary differential equation" with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Introduction to Enumerative and Analytic Combinatorics
This award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.Updates to the Third Edition include: Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter. A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book. An extended section on multivariate generating functions. Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation. The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.
Discrete Mathematics
Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the "bridge" course for math majors. Features Uses problem-oriented and inquiry-based methods to teach the concepts. Suitable for undergraduates in mathematics and computer science. New to the 4th edition Large scale restructuring. Contains more than 750 exercises and examples. New sections on probability, relations, and discrete structures and their proofs.
Advances in Fuzzy Logic and Artificial Neural Networks
In a world where uncertainty and complexity dominate decision-making processes, Advances in Neural Networks and Fuzzy Logic presents groundbreaking studies exploring the potential of these Artificial Intelligence approaches to solve real-world problems. The chapters cover applications across various fields, such as robust galaxy classification, simulations in weighted finite automata, stock price prediction, large-scale water purification selection, speech deficiency detection in children, and supply chain management. Advanced techniques such as deep neural networks, fuzzy clustering, SHAP, LIME, and Hesitant Fuzzy Linguistic Term Sets are explored. This reprint is helpful for researchers, engineers, and students who wish to understand the latest advancements in and practical applications of neural networks and fuzzy logic. Within these pages, you will discover how these technologies solve complex problems and foster more transparent and reliable decision-support systems, as well as the state of the art in Artificial Intelligence, where neural networks and fuzzy logic converge to tackle modern challenges with innovation and precision.
The calculating engine
The calculating engine" is a classic book, that has held significant value throughout history, and to ensure its timeless wisdom is never lost, Alpha Editions has carefully preserved it by republishing it in a modern, accessible format for both present and future generations. Thoughtfully reformatted, retyped, and newly designed, this edition offers a clear and readable text-free from scanned copies of the original work. Alpha Editions is dedicated to breathing new life into antique and classic books, making these literary treasures available once again for readers who cherish history, culture, and timeless knowledge.
A Beginner's Guide to Mathematical Proof
A Beginner's Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics. The text is designed to be easily utilized by both instructor and student, with an accessible, step-by-step approach requiring minimal mathematical prerequisites. The book builds towards more complex ideas as it progresses but never makes assumptions of the reader beyond the material already covered. Features- No mathematical prerequisites beyond high school mathematics- Suitable for an Introduction to Proofs course for mathematics majors and other students of quantitative sciences, such as engineering- Replete with exercises and examples.Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency as an applied mathematician of machine learning. He is at present working for the US Department of Energy at Sandia National Lab. His research interests include machine learning, statistics, and computational algebra.
The Math Book
Math's infinite mysteries unfold in this updated edition of the award-winning The Math Book. Beginning millions of years ago with ancient "ant odometers," and moving through time to our modern-day quest for higher dimensions, prolific polymath Clifford Pickover covers major milestones in mathematical history. Among the numerous concepts readers will encounter as they dip into this inviting anthology: cicada-generated prime numbers, magic squares, and the butterfly effect. Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems. This reissue includes four new entries: 2013 (Bounded Gaps Between Primes), 2015 (Erdős Discrepancy Problem Solved), 2016 (Sphere Packing in Dimension 8), and 2023 (Einstein Tiles and Beyond). Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems.
