Cybersecurity and Applied Mathematics
- 1st Edition - June 8, 2016
- Authors: Leigh Metcalf, William Casey
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 0 4 4 5 2 - 0
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 4 4 9 9 - 5
Cybersecurity and Applied Mathematics explores the mathematical concepts necessary for effective cybersecurity research and practice, taking an applied approach for practitio… Read more
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
Computer Security Architects, Engineers, Analysts, Software Developers, Incident Responders, System and Network Engineers, Penetration Testers, and Vulnerability Assessors. Advanced Undergraduate and Graduate students in Cybersecurity, Network Security, Information Technology, Computer Science, and Applied Mathematics
- Biography
- Chapter 1: Introduction
- Abstract
- Chapter 2: Metrics, similarity, and sets
- Abstract
- 2.1 Introduction to Set Theory
- 2.2 Operations on Sets
- 2.3 Set Theory Laws
- 2.4 Functions
- 2.5 Metrics
- 2.6 Distance Variations
- 2.7 Similarities
- 2.8 Metrics and Similarities of Numbers
- 2.9 Metrics and Similarities of Strings
- 2.10 Metrics and Similarities of Sets of Sets
- 2.11 Mahalanobis Distance
- 2.12 Internet Metrics
- Chapter 3: Probability models
- Abstract
- 3.1 Basic Probability Review
- 3.2 From Parlor Tricks to Random Variables
- 3.3 The Random Variable as a Model
- 3.4 Multiple Random Variables
- 3.5 Using Probability and Random Distributions
- 3.6 Conclusion
- Chapter 4: Introduction to data analysis
- Abstract
- 4.1 The Language of Data Analysis
- 4.2 Units, Variables, and Repeated Measures
- 4.3 Distributions of Data
- 4.4 Visualizing Distributions
- 4.5 Data Outliers
- 4.6 Log Transformation
- 4.7 Parametric Families
- 4.8 Bivariate Analysis
- 4.9 Time Series
- 4.10 Classification
- 4.11 Generating Hypotheses
- 4.12 Conclusion
- Chapter 5: Graph theory
- Abstract
- 5.1 An Introduction to Graph Theory
- 5.2 Varieties of Graphs
- 5.3 Properties of Graphs
- 5.4 Paths, Cycles and Trees
- 5.5 Varieties of Graphs Revisited
- 5.6 Representing Graphs
- 5.7 Triangles, the Smallest Cycle
- 5.8 Distances on Graphs
- 5.9 More properties of graphs
- 5.10 Centrality
- 5.11 Covering
- 5.12 Creating New Graphs from Old
- 5.13 Conclusion
- Chapter 6: Game theory
- Abstract
- 6.1 The Prisoner’s Dilemma
- 6.2 The Mathematical Definition of a Game
- 6.3 Snowdrift Game
- 6.4 Stag Hunt Game
- 6.5 Iterative Prisoner’s Dilemma
- 6.6 Game Solutions
- 6.7 Partially Informed Games
- 6.8 Leader-Follower Game
- 6.9 Signaling Games
- Chapter 7: Visualizing cybersecurity data
- Abstract
- 7.1 Why visualize?
- 7.2 What we visualize
- 7.3 Visualizing IP addresses
- 7.4 Plotting higher dimensional data
- 7.5 Graph plotting
- 7.6 Visualizing malware
- 7.7 Visualizing strings
- 7.8 Visualization with a purpose
- Chapter 8: String analysis for cyber strings
- Abstract
- 8.1 String Analysis and Cyber Data
- 8.2 Discrete String Matching
- 8.3 Affine alignment string similarity
- 8.4 Summary
- Chapter 9: Persistent homology
- Abstract
- 9.1 Triangulations
- 9.2 α Shapes
- 9.3 Holes
- 9.4 Homology
- 9.5 Persistent homology
- 9.6 Visualizing Persistent Homology
- 9.7 Conclusions
- Appendix: Introduction to linear algebra
- A.1 Vector Algebra
- A.2 Eigenvalues
- A.3 Additional Matrix Operations
- Bibliography
- Index
- Edition: 1
- Published: June 8, 2016
- Language: English
LM
Leigh Metcalf
Leigh Metcalf research’s network security, game theory, formal languages, and dynamical systems. She is Editor in Chief of the Journal on Digital Threats and has a PhD in Mathematics.
Affiliations and expertise
PhD (Mathematics), Co-Editor in Chief, ACM Digital ThreatsWC
William Casey
Will Casey works in threat analysis, code analysis, natural language processing, genomics, bioinformatics, and applied mathematics. He has a MS and MA in Mathematics and a PhD in Applied Mathematics.
Affiliations and expertise
PhD (Applied Mathematics)Read Cybersecurity and Applied Mathematics on ScienceDirect