## Course Detail

 Course Name Mathematical Foundation for Cybersecurity Course Code 21MA612 Program M. Tech. in Cyber Security Systems & Networks Credits 3

### Overview

Unit 1: Sets, subsets, and their respective properties. Relations and their properties, functions, bijective function, inverse functions, domain, and range.

Unit 2: Matrix Theory: Basic Matrix algebra, determinant of a matrix, inverse of a matrix, finding solution of a linear system, geometry representation of matrices, Subspace, Vector Space, Solution Space of a Matrix, Null- Space, Basis, Linear independent, Spanning set.

Unit 3: Probability Theory: Permutations and combinations, basic probability theory, probability threes, conditional probability, Independence, Bayes Theorem, Random variable definition, discrete random variables and their properties, Bernoulli, Binomial, Uniform, probability mass function, Cumulative distribution function, expectation and Variance.

Unit 4: Continuous random variables, normal distribution, exponential, geometric, PDF, CDF, Marginal distribution, Independent Random Variables, Joint Random Variable.

Unit 5: Random process: general concept, power spectrum, discrete-time processes, random walks and other applications, Markov chains, transition probabilities.Unit 6: Introduction to Game Theory, basic game theory games and their application to Cyber Security

### TEXTBOOKS / REFERENCES:

1. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th Edition, Wiley ISBN: ES8-0-470-91361-1
2. Kenneth Rosen, “Discrete Mathematics and Its Applications”, 8th Edition, 2019
3. Sheldon Ross, “A First Course in Probability”, 10th Edition, Pearson, 2019
4. Peter Morris, “Introduction to Game Theory”, Springer,1994
5. A. Papoulis and U. Pillai, Probability, “Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.

### Course Outcomes

• CO1 : Understand the basic mathematical functions for cyber security
• CO2 : Understand basics of matrix algebra and vector spaces
• CO3 : Understand basics of probability theory and distributions
• CO4: Understand usage of random variables for cryptography
• CO5 : Understand usage of random and stochastic processes for cyber security
• CO6: Understand basics of game theory for cyber security

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