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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.
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
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Partial differential Equations (PDEs) are used to construct models of the most basic theories underlying physics and engineering. In general, the construction of a mathematical model is based on two main ingredients: general laws and constitutive relations. This module presents methods of solving first order linear equations and IV/BVP for the well-known second order PDEs. The module presents also numerical methods of solving IV/BVP for PDEs: Finite difference methods and Finite elements methods. Part I: This part begins with an introduction to PDEs, their definitions, classifications and their use. It gives the three origins of some PDEs (Diffusion equation, wave equation). The second part deals with the Boundary value problems and well - posedness of introducing function spaces. The third part deals with Laplace’s and Poisson’s equation (a maximum principle, Uniqueness for the Dirichlet problem). The fourth chapter deals with the heat and wave equations. Part II: Numerical solutions for PDEs Chapter 5: This chapter describes the finite difference methods for solutions of PDEs: Finite differences, Approximating solution to the diffusion equation, order, stability and convergence, the crank-Nicholson scheme, Approximation of Laplace’s equation, the discrete mean value property, stability analysis. Chapter 6: This chapter describes the Finite element methods for solving IV/BVP for PDEs: Galerkin method, Approximation of elliptic problems. Finite approximation of initial boundary value problems. Energy dissipation, conservation and stability. Analysis of finite element methods for evolution problems. |
This module aims to equip students with the ability to use computer-based simulations in studying how fluids move and interact with their surroundings, helping researchers and engineers make better, faster, and more cost-effective decisions in design and analysis. Students will also be able to use different CFD techniques, numerical analysis and data structures to solve problems that involve fluid flow.
This module aims at providing students with the general techniques needed to analyse mathematical models in biology. It introduces dynamical mathematical models in terms of ordinary differential equations using population dynamics, age-structured population and infectious and chronic disease as case studies. The module presents models biochemical reaction networks and reaction diffusion, chemotaxis, stochastic modeling of population growth. The students will be provided with the general techniques to compute the solution numerically with the aid of a computer.
Optimization problems arise in various fields ranging from economics to physics and in many aspects of our daily lives. For example, airlines arrange their schedules to maximize their profit subject to constraints imposed by limited resources such as the number of crew-members and planes. Ray of light follows a path to minimize the travel time. Two main ingredients of an optimization problem are: an objective function which we want to minimize or maximize, and a set of constraints which determines the set of allowable points over which the objective function must be minimized or maximized. The main purpose of this course is to learn an algorithmic approach to continuous numerical optimization, constrained and unconstrained. Emphasis on practical methods with enough practical examples and enough theory to make them work.
Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.
This module aims to provide you with basic knowledge and skills that help you to solve real life problems (problems from physics, engineering,...) formulated using mathematical concepts.
This module is designed in such a way that the knowledge acquired by the students will enable them to perform calculus operations for recording and managing engineering operations such as writing some phenomena in mathematically models. Therefore, it contains powerful tools for handling physics models, engineering models, and analyzing the solutions after resolution the models.
The Module aims to introduce students to the various techniques of numerical analysis applied to transcendental equations, mathematical functions, matrix algebra and differential equations. The module will deal with these topics at a basic level, leaving more advanced techniques to the specialist courses in Engineering.
Having successfully completed the module, students should be able to demonstrate knowledge and understanding of:
- Numerical analysis as applied to simple mathematical topics.
- The implications of basic numerical analysis.
- Presenting simple arguments and conclusions using numerical analysis.
- Analyzing and evaluating problems in mathematics and engineering.
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Apply the mathematical knowledge to solve problems in range of Engineering situations.
- Carry out mathematical and numerical manipulation with confidence and accuracy.
- Solve open-ended problems and problems with well-defined solutions by formulating problems in precise terms, identifying key issues and trying different approaches in order to make progress.
- Carry out an independent investigation using textbooks and other available literature, searching databases and interacting with colleagues and staff to extract important information.
Dear Students,
You are invited to this platform so that you can partake in online learning the Research Methodology module. Please note that it is important for each one of you to do all exercises and assignment and submit on time.
The following will be the facilitators:
Prof Bideri Ishuheri Nyamulinda (for Part One); Email: drnbideri@gmail.com; Mob Tel: 0788716140 and Dr Ndikubwimana Phillip (for Part Two); Email: ndiphil2000@gmail.com ; Mob Tel 0788615066
Learning outcomes
Having suceesfully completed this module, students should be able to:
Explain the nature marketing research
Explain the marketing process
Describe the marketing research sampling design
Explain the data collect and data analysis
General Introduction
This module is composed of two parts namely the theoretical part and the practical part that will require your participation in performing various practical activities.
Part One comprises of 7 topics including: An Introduction to Research Methodology, The Language of Research, Dimensions of Social Research, Research Design, Measurement, Sampling Design and Data Collection.
Part Two includes topics such as;………
This module will offer to the students with opportunity to gain an enhanced understanding of leadership applications in the business context. Whilst not intended for those interested in the more technical aspects of business management, the module aims to develop knowledge and understanding of both theoretical and practical systems applications. The study area would include management analysis and design, leadership styles systems, leadership modelling and development.
This course introduces students to the basic accounting procedures involved in the production of a business entity's financial statements. Enable the student to understand the basic concepts of accounting science, recording the business transactions, measurement of business performance and the assessment of the financial position of the organization.
Advanced Financial Analysis aimed at providing students with good understanding of practical financial management and enabling them to apply relevant knowledge, skills and exercise professional judgment as expected of a senior financial executive or advisor, in taking or recommending decisions relating to the financial management of an organization.
This module will offer to the students with opportunity to gain an understanding of the key concepts, techniques, and decision tools used by managers in the business context. Whilst not intended for those interested in more technical aspects of business management, the module aims to develop knowledge and understanding of both theoretical and practical systems applications. The study area would include planning, scheduling, analyzing and implementing projects - e,g., product development, construction, information systems, new business, and special events.
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