This module will provide a solid background in the mathematical description of fluid dynamics. They will cover the derivation of the conservation laws (mass, momentum, energy) that describe the dynamics of fluids and their application to a remarkable range of phenomena including water waves, sound propagation, atmospheric dynamics and aerodynamics. The focus will be on deriving approximate expressions using known mathematical techniques that yield analytic solutions.
This module introduces the basic concepts of Partial Differential Equations by concrete Examples. PDEs are used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatistics, electrodynamics, fluid dynamics, electricity, gravitation and quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Partial differential Equations are used in modelling of multidimensional systems.
This course will permit the users to work in industry. Environmental modelling is also tackled using PDEs. Climate change, Chemical reactions, competitions between species, modelling of dynamics of infectious diseases, among others are described using PDEs.
At the end of the module, the learner should be able to explain confidently basic concepts used in financial mathematics, to simulate the prices of financial products (fixed income products and derivatives) using available IT software (R, Python). The contents of this module to include arbitrage theory, pricing derivatives, martingales and martingale representations, differentiation in stochastic environments, the Wiener process, Levy processes and rare events in financial markets, Integration in stochastic environments and Ito's formula and its usage in financial mathematics.
The module general objective is to introduce the leaners to survival and clinical data analysis. The contents for the module shall include survival, hazard and cumulative hazard functions, censoring, Kaplan Meier survival curve, parametric models and estimation of parameters in these models, nonparametric models, comparison of two groups including log-rank test, Inclusion of the covariates. Proportional hazard model including application of model checking, computation of risks and extensions, clinical trials, uncontrolled and blind trials, forms of data and data management. Some computer labs will also be organized where R or Stata can be used.
Actuarial mathematics is a field of financial mathematics which focus on risks measurements particularly insurance industry. Students undertaking this module are thus trained to apply financial mathematics in insurance industry. It is thus reasonable in the contents of the course to have some reviews of financial mathematics, mortality concepts and mortality tables, some annuities computation, life insurance, premium computations and reinsurance.
This module focuses on analysis of problems in biology by applying the techniques of mathematical modelling mainly using differential equations along with numerical solution techniques. The module presents models of population dynamics, epidemics, biochemical reaction networks and molecular networks (metabolic reactions and gene regulation).
This module is intended to provide students with the theoretical understanding needed to underpin econometric work in the business area. It will create an improved awareness, through the analysis of economic data, of the econometric techniques available to decision makers, and use practical applications to explore the value of econometric methods in decision support and evaluate their limitations.
The aims of this course is to enable students to acquire active knowledge and understanding of some basic concepts in Decision analysis, It gives a mathematical description of the decision analysis under certain circumstances. Decision under Certainty, uncertainty and under risk. Decision tree and ends with the decision making in light of competitive actions (game theory).
During the teaching sessions, the following will be covered: Introduction to Decision Analysis, Decision making under Certainty, Decision making under uncertainty, Decision making under risk, Decision making with perfect information, Decision making with imperfect information, Decision tree, Decision making and utility, Decision making criteria. Decision making in light of competitive actions, Network analysis and Game theory.
Learning Outcomes
- Should have a reasonable understanding of the definitions and terms related to the Module aims at as well as the Course Contents.
- Should have a reasonable understanding of the statements, proofs and implications of the basic results.
- should be able to practice the application of theoretical results using SAS
- should be able to present simple arguments and conclusions using Decision analysis in making decisions
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.
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.
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.
This course covers the basic tools for the collection, analysis, and presentation of data in health sciences. Central to these skills is assessing the impact of chance and variability on the interpretation of research findings and subsequent recommendations for public health practice and policy.