COURSE SUMMARY
Course Title: 
Mathematical Foundations for Cyber Security Systems
Course Code: 
18MA612
Year Taught: 
2018
Degree: 
Postgraduate (PG)
School: 
School of Engineering
Center: 
Cyber Security
Campus: 
Amritapuri

"Mathematical Foundations for Cyber Security Systems" is an elective course offered in M. Tech. in Cyber Security Systems & Networks program at School of Engineering, Amrita Vishwa Vidyapeetham, Amritapuri.

Logic, Mathematical reasoning, Sets, Basics of counting, Relations.

Graph Theory: Euler graphs, Hamiltonian paths and circuits, planar graphs, trees, rooted and binary trees, distance and centres in a tree, fundamental circuits and cut sets, graph coloringsand applications, chromatic number, chromatic partitioning, chromatic polynomial, matching, vector spaces of a graph.

Analytic Number Theory: Euclid’s lemma, Euclidean algorithm, basic properties of congruences, residue classes and complete residue systems, Euler-Fermat theorem, Lagrange’s theorem and its applications, Chinese remainder theorem, primitive roots. Algebra: groups, cyclic groups, rings, fields, finite fields and their applications to cryptography.

Linear Algebra: vector spaces and subspaces, linear independence, basis and dimensions, linear transformations and applications.

Probability and Statistics: introduction to probability concepts, random variables, probability distributions (continuous and discrete), Bayesian approach to distributions, mean and variance of a distribution, joint probability distributions, theory of estimation,

Bayesian methods of estimation. Random Processes: general concepts, power spectrum, discrete-time processes, random walks and other applications, Markov chains, transition probabilities.

  1. R.P.Grimaldi, ”Discrete and Combinatorial Mathematics”, Fifth edition, Pearson Education, 2007.
  2. K. H. Rosen, “Discrete Mathematics and its applications”, Seventh Edition, Tata MCGraw-Hill Publishing company limited, New Delhi, 2007.
  3. H. Anton, “Elementary Linear Algebra”, John Wiley & Sons, 2010.
  4. N. Deo, “Graph theory with applications to Engineering and Computer Science”, Prentice Hall of India, New Delhi, 1974.
  5. T. M. Apostol, “Introduction to Analytic Number Theory”, Springer, 1976.
  6. Douglas C. Montgomery and George C. Runger, “Applied Statistics and Probability forEngineers”, Third Edition, John Wiley & Sons Inc., 2003.
  7. A. Papoulis and U. Pillai, Probability, “Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.
  8. Ronald E. Walpole, Raymond H Myres, Sharon.L.Myres and Kying Ye, “Probability andStatistics for Engineers and Scientists”, Seventh Edition, Pearson Education, 2002.