Cybersecurity and applied mathematics / Leigh Metcalf, William Casey.

Includes bibliographical references (pages 179-182) and index.

Print version record.

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 of Random Variables -- 3.2.2.Properties of Random Variables -- 3.3.The Random Variable as a Model -- 3.3.1.Bernoulli and Geometric Distributions -- 3.3.2.Binomial Distribution -- 3.3.3.Poisson Distribution -- 3.3.4.Normal Distribution -- 3.3.5.Pareto Distributions -- 3.3.6.Uniform Distribution -- 3.4.Multiple Random Variables -- 3.5.Using Probability and Random Distributions -- 3.6.Conclusion -- 4.1.The Language of Data Analysis -- 4.1.1.Producing Data -- 4.1.2.Exploratory Data Analysis -- 4.1.3.Inference -- 4.2.Units, Variables, and Repeated Measures -- 4.2.1.Measurement Error and Random Variation -- 4.3.Distributions of Data -- 4.4.Visualizing Distributions -- 4.4.1.Bar Plot -- 4.4.2.Histogram -- 4.4.3.Box Plots -- 4.4.4.Density Plot -- 4.5.Data Outliers

Note continued: 4.6.Log Transformation -- 4.7.Parametric Families -- 4.8.Bivariate Analysis -- 4.8.1.Visualizing Bipartite Variables -- 4.8.2.Correlation -- 4.9.Time Series -- 4.10.Classification -- 4.11.Generating Hypotheses -- 4.12.Conclusion -- 5.1.An Introduction to Graph Theory -- 5.2.Varieties of Graphs -- 5.2.1.Undirected Graph -- 5.2.2.Directed Graph -- 5.2.3.Multigraph -- 5.2.4.Bipartite Graph -- 5.2.5.Subgraph -- 5.2.6.Graph Complement -- 5.3.Properties of Graphs -- 5.3.1.Graph Sizes -- 5.3.2.Vertices and Their Edges -- 5.3.3.Degree -- 5.3.4.Directed Graphs and Degrees -- 5.3.5.Scale Free Graphs -- 5.4.Paths, Cycles and Trees -- 5.4.1.Paths and Cycles -- 5.4.2.Shortest Paths -- 5.4.3.Connected and Disconnected Graphs -- 5.4.4.Trees -- 5.4.5.Cycles and Their Properties -- 5.4.6.Spanning Trees -- 5.5.Varieties of Graphs Revisited -- 5.5.1.Graph Density, Sparse and Dense Graphs -- 5.5.2.Complete and Regular Graphs -- 5.5.3.Weighted Graph

Note continued: 5.5.4.And Yet More Graphs! -- 5.6.Representing Graphs -- 5.6.1.Adjacency Matrix -- 5.6.2.Incidence Matrix -- 5.7.Triangles, the Smallest Cycle -- 5.7.1.Introduction and Counting -- 5.7.2.Triangle Free Graphs -- 5.7.3.The Local Clustering Coefficient -- 5.8.Distances on Graphs -- 5.8.1.Eccentricity -- 5.8.2.Cycle Length Properties -- 5.9.More Properties of Graphs -- 5.9.1.Cut -- 5.9.2.Bridge -- 5.9.3.Partitions -- 5.9.4.Vertex Separators -- 5.9.5.Cliques -- 5.10.Centrality -- 5.10.1.Betweenness -- 5.10.2.Degree Centrality -- 5.10.3.Closeness and Farness -- 5.10.4.Cross-Clique Centrality -- 5.11.Covering -- 5.11.1.Vertex Covering -- 5.11.2.Edge Cover -- 5.12.Creating New Graphs from Old -- 5.12.1.Union Graphs -- 5.12.2.Intersection Graphs -- 5.12.3.Uniting Graphs -- 5.12.4.The Intersection Graph -- 5.12.5.Modifying Existing Graphs -- 5.13.Conclusion -- 6.1.The Prisoner's Dilemma -- 6.2.The Mathematical Definition of a Game

Note continued: 6.2.1.Strategies, Payoffs and Normal Form -- 6.2.2.Normal Form -- 6.2.3.Extensive Form -- 6.3.Snowdrift Game -- 6.4.Stag Hunt Game -- 6.5.Iterative Prisoner's Dilemma -- 6.6.Game Solutions -- 6.6.1.Cooperative and Non-Cooperative Games -- 6.6.2.Zero Sum Game -- 6.6.3.Dominant Strategy -- 6.6.4.Nash Equilibrium -- 6.6.5.Mixed Strategy Nash Equilibrium -- 6.7.Partially Informed Games -- 6.8.Leader-Follower Game -- 6.8.1.Stackelberg Game -- 6.8.2.Colonel Blotto -- 6.9.Signaling Games -- 7.1.Why Visualize? -- 7.2.What We Visualize -- 7.2.1.Considering the Efficacy of a Visualization -- 7.2.2.Data Collection and Visualization -- 7.2.3.Visualizing Malware Features -- 7.2.4.Existence Plots -- 7.2.5.Combining Plots -- 7.3.Visualizing IP Addresses -- 7.3.1.Hilbert Curve -- 7.3.2.Heat Map -- 7.4.Plotting Higher Dimensional Data -- 7.4.1.Principal Component Analysis -- 7.4.2.Sammon Mapping -- 7.5.Graph Plotting -- 7.6.Visualizing Malware