Advance Mathematics In Software Engineering

This course will cover the fundamentals of the techniques of statistical testing and software simulation. After familiarizing ourselves with the fundamentals like Monte Carlo simulation and markov chains as well as the fundamentals of combined techniques such as MCMC and HMM, we will dig into applications that illustrate the use of these techniques. The applications covered will be from computer systems, simulation and some topics in machine learning and data mining. We will also study computational techniques to complement analytical performance evaluation.

Course References
1 Computer Modeling and Simulation (In Persian)M. Vafaei Jahan, Islamic Azad University – Mashhad Branch Press, 2011.
2 Bayesian Artificial Intelligence, K.B. Korb, A.E. Nicholson – CRC Press, 2011.
3 Finite Markov Chain and Algorithmic Application, O. Haggstrom, Cambridge University Press, 2002.
Course Topics
 1 ‌Bayes Theory and Bayesian Network – (Matalb Tools: Tools, Manual, Example)
 2 Computer Simulation Definition and Fundamental – (Slide pdf) – (4 hours)
 3 Random Numbers / Random Number Generations / Chaos Functions (6 hours)
 4 Statistical Analysis and Tests: (6 hours)
 5 –  Correlation Test-  Entropy Test-  Chi-Square Test-  Kolmogrov – Semirnov Test-  Fractal Dimension Test
Read & Discuss these Papers:
 1 1) Z. Ghezelbiglo; M. Vafaei Jahan, “Pseudo Random Number Generation Based on Chaos Logistic Map and Midproduct Method“, 9th International ISC Conference on Information Security and Cryptology 2012 (ISCISC), Tabriz, Iran.
 2 2) H. Karimi, S. M. Hosseini, M. Vafaei Jahan, “On the Combination of Self-Organized Systems to Generate Pseudo-Random Numbers,“ Information Sciences, 2012.
#1 Paper Presentation
Baysian Networks (4 hours)
Markov Chain Monte Carlo (MCMC) – (Slide pdf) (4 hours)
#2 Paper Presentation
 Exams and Practices
1 Optimization Methods Exam, Create By Dr. Majid Vafaei Jahan 2012.
Reading List Papers and Book Chapters
1 On Clustering Using Random Walks, D. Harel, Y. Koren, (2001).
2 Fastest Mixing Markov Chain on a Graph, S.Boyd, P. Diaconis, L. Xiao, SIAM Review, Vol. 46, No. 4, pp. 667–689, (2004).
3 Link Prediction and Path Analysis Using Markov Chains, R. Sarukkai, Computer Networks, Volume 33, Issues 1–6, pp:377–386, (2000).
Course Evaluation
Each Exercise = +0.5
* Paper Presentation = 2 / 20
* Final Exam = 14 / 20
* Take Home and Represent as Paper Format = 3 / 20
Conference Paper = 2 / 20 (+1)