Cybersecurity and Applied Mathematics 1st Edition by Leigh Metcalf 0128044995 9780128044995

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Product details:

ISBN-10 :  0128044995 

ISBN-13 : 9780128044995

Author:  Leigh Metcalf 

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.

Cybersecurity and Applied Mathematics 1st Table of contents:

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

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Tags: Cybersecurity, Applied Mathematics, Leigh Metcalf, mathematical concepts