Cybersecurity and applied 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.

Machine generated contents note: 2.1. Introduction to Set Theory -- 2.2. Operations on Sets -- 2.2.1.Complement -- 2.2.2. Intersection -- 2.2.3. Union -- 2.2.4. Difference -- 2.2.5. Symmetric Difference -- 2.2.6. Cross Product -- 2.3. Set Theory Laws -- 2.4. Functions -- 2.5. Metrics -- 2.6. Distance Variations -- 2.6.1. Pseudometric -- 2.6.2. Quasimetric -- 2.6.3. Semimetric -- 2.7. Similarities -- 2.8. Metrics and Similarities of Numbers -- 2.8.1. Lp Metrics -- 2.8.2. Gaussian Kernel -- 2.9. Metrics and Similarities of Strings -- 2.9.1. Levenshtein Distance -- 2.9.2. Hamming Distance -- 2.10. Metrics and Similarities of Sets of Sets -- 2.10.1. Jaccard Index -- 2.10.2. Tanimoto Distance -- 2.10.3. Overlap Coefficient -- 2.10.4. Hausdorff Metric -- 2.10.5. Kendall's Tau -- 2.11. Mahalanobis Distance -- 2.12. Internet Metrics -- 2.12.1. Great Circle Distance -- 2.12.2. Hop Distance -- 2.12.3. Keyword Distance -- 3.1. Basic Probability Review -- 3.1.1. Language and Axioms of Probability

Note continued: 3.1.2.Combinatorics Aka Parlor Tricks -- 3.1.3. Joint and Conditional Probability -- 3.1.4. Independence and Bayes Rule -- 3.2. From Parlor Tricks to Random Variables -- 3.2.1. Types…