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In the last decade, both scholars and practitioners have sought novel ways to address the problem of cybersecurity. Innovative outcomes have included applications such as blockchain as well as creative methods for cyber forensics, software development, and intrusion prevention. Accompanying these technological advancements, discussion on cyber matters at national and international levels has focused primarily on the topics of law, policy, and strategy. The objective of these efforts is typically to promote security by establishing agreements among stakeholders on regulatory activities. Varying levels of investment in cyberspace, however, comes with varying levels of risk; in some ways, this can translate directly to the degree of emphasis for pushing substantial change. At the very foundation or root of cyberspace systems and processes are tenets and rules governed by principles in mathematics. Topics such as encrypting or decrypting file transmissions, modeling networks, performing data analysis, quantifying uncertainty, measuring risk, and weighing decisions or adversarial courses of action represent a very small subset of activities highlighted by mathematics. To facilitate education and a greater awareness of the role of mathematics in cyber systems and processes, a description of research in this area is needed. Mathematics in Cyber Research aims to familiarize educators and young researchers with the breadth of mathematics in cyber-related research. Each chapter introduces a mathematical sub-field, describes relevant work in this field associated with the cyber domain, provides methods and tools, as well as details cyber research examples or case studies. Features One of the only books to bring together such a diverse and comprehensive range of topics within mathematics and apply them to cyber research. Suitable for college undergraduate students or educators that are either interested in learning about cyber-related mathematics or intend to perform research within the cyber domain. The book may also appeal to practitioners within the commercial or government industry sectors. Most national and international venues for collaboration and discussion on cyber matters have focused primarily on the topics of law, policy, strategy, and technology. This book is among the first to address the underpinning mathematics.
Cybersecurity and Applied Mathematics explores the mathematical concepts necessary for effective cybersecurity research and practice, taking an applied approach for practitioners and students entering the field. This book covers methods of statistical exploratory data analysis and visualization as a type of model for driving decisions, also discussing key topics, such as graph theory, topological complexes, and persistent homology. Defending the Internet is a complex effort, but applying the right techniques from mathematics can make this task more manageable. This book is essential reading for creating useful and replicable methods for analyzing data. - Describes mathematical tools for solving cybersecurity problems, enabling analysts to pick the most optimal tool for the task at hand - Contains numerous cybersecurity examples and exercises using real world data - Written by mathematicians and statisticians with hands-on practitioner experience
Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. /divGraduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.
Research Methods for Cyber Security teaches scientific methods for generating impactful knowledge, validating theories, and adding critical rigor to the cyber security field. This book shows how to develop a research plan, beginning by starting research with a question, then offers an introduction to the broad range of useful research methods for cyber security research: observational, mathematical, experimental, and applied. Each research method chapter concludes with recommended outlines and suggested templates for submission to peer reviewed venues. This book concludes with information on cross-cutting issues within cyber security research. Cyber security research contends with numerous unique issues, such as an extremely fast environment evolution, adversarial behavior, and the merging of natural and social science phenomena. Research Methods for Cyber Security addresses these concerns and much more by teaching readers not only the process of science in the context of cyber security research, but providing assistance in execution of research as well. - Presents research methods from a cyber security science perspective - Catalyzes the rigorous research necessary to propel the cyber security field forward - Provides a guided method selection for the type of research being conducted, presented in the context of real-world usage
A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.
Mathematical techniques pervade current research in computer networking, yet are not taught to most computer science undergraduates. This self-contained, highly-accessible book bridges the gap, providing the mathematical grounding students and professionals need to successfully design or evaluate networking systems. The only book of its kind, it brings together information previously scattered amongst multiple texts. It first provides crucial background in basic mathematical tools, and then illuminates the specific theories that underlie computer networking. Coverage includes: * Basic probability * Statistics * Linear Algebra * Optimization * Signals, Systems, and Transforms, including Fourier series and transforms, Laplace transforms, DFT, FFT, and Z transforms * Queuing theory * Game Theory * Control theory * Information theory
Advances in Mathematics for Industry 4.0 examines key tools, techniques, strategies, and methods in engineering applications. By covering the latest knowledge in technology for engineering design and manufacture, chapters provide systematic and comprehensive coverage of key drivers in rapid economic development. Written by leading industry experts, chapter authors explore managing big data in processing information and helping in decision-making, including mathematical and optimization techniques for dealing with large amounts of data in short periods. - Focuses on recent research in mathematics applications for Industry 4.0 - Provides insights on international and transnational scales - Identifies mathematics knowledge gaps for Industry 4.0 - Describes fruitful areas for further research in industrial mathematics, including forthcoming international studies and research
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Attaining meaningful cybersecurity presents a broad societal challenge. Its complexity and the range of systems and sectors in which it is needed mean that successful approaches are necessarily multifaceted. Moreover, cybersecurity is a dynamic process involving human attackers who continue to adapt. Despite considerable investments of resources and intellect, cybersecurity continues to poses serious challenges to national security, business performance, and public well-being. Modern developments in computation, storage and connectivity to the Internet have brought into even sharper focus the need for a better understanding of the overall security of the systems we depend on. Foundational Cybersecurity Research focuses on foundational research strategies for organizing people, technologies, and governance. These strategies seek to ensure the sustained support needed to create an agile, effective research community, with collaborative links across disciplines and between research and practice. This report is aimed primarily at the cybersecurity research community, but takes a broad view that efforts to improve foundational cybersecurity research will need to include many disciplines working together to achieve common goals.
A variety of modern research methods in a number of innovating cyber-security techniques and information management technologies are provided in this book along with new related mathematical developments and support applications from engineering. This allows for the exploration of new approaches, useful practices and related problems for further investigation.Distinguished researchers and scientists coming from different scientific origins present their research and views concerning cyber-security, information warfare and communications systems.Graduate students, scientists and engineers interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.Topics covered include: Electronic crime and ethics in cyberspace, new technologies in security systems/systems interfaces, economic information warfare, digital security in the economy, human factor evaluation of military security systems, cyber warfare, military communications, operational analysis and information warfare, and engineering applications to security systems/detection theory.