Markov Chains, Queueing, Martingales :
The Poisson process, the compound Poisson process, discrete time Markov chains: classification of states, stationary distributions, time reversibility. Continuous time Markov chains. Markov queueing systems (M/M/c/K), Markovian queueing systems (M/Er/1, Er/M/1), Markov networks, M/G/1 queueing systems, Pollaczek-Khinchin transform equation. Discrete time martingales: Conditional expectation, martingale convergence theorems, Doob’s inequality, optional stopping Theorems. Birkhoff’s ergodic theorem.
Time Series :
Basic forecasting Tools (Time pots and time series patterns, Seasonal plots, Scatter plots, Auto correlation, Prediction intervals, Least Square estimation), Time series models (Auto regressive (AR) models, Moving Average models (MA), Auto Regressive Moving Average (ARMA), Auto Regressive Integrated Moving Average (ARIMA), Exponential Smoothing), Box-Jenkins methodology for ARIMA models, Assumptions in Box-Jenkins fitting models, Forecasting using ARIMA models, Introduction to Non –Linear time series model.
The current course is designed to initiate and train students in statistics option who are keen is acquiring skills in designs and analysis of experiment. This entire material for this course is extracted from Douglas C. Montgomery, Design and Analysis of Experiments, Eight edition, John Wiley & Sons, Inc; USA, 2013. At the end of this course, students are expected to be able to:
- Design an experiment in various fields, including agriculture, health, pharmacology, clinical drug tests, industry, etc.
- Conduct effectively the analysis of variance (ANOVA);
- Replicate the experiment conducted for validation and robustness of results.
Computer labs shall be organized, and this will be done following the reference of John Lawson, Design and Analysis of Experiments with R, CRC Press, Taylor and Francis group, USA, Chapman and Hall Book, 2015.
This module is destined for students of level two of the bachelor programs in applied mathematics. Its purpose is to provide them the opportunities to apply classroom concepts to the work environment; that is to work real problems and to create a network of contacts outside university environment.
The student is responsible for selecting the attachment. He will meet with the host supervisor to the internship to clarify expectations and responsabilities. The school supervisor, appointed by the department, is responsible for visiting and addressing issues raised by the site supervisor based on the student's performance.