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Mathematics and Modeling III (Spring 2013)

Course code : ME-MAM3-U1
ECTS Credits : 10 Status : Compulsory
Placement : 3. & 4. semester Hours per week : 4
Length : 1 semester Teaching Language : English
Principal Content : Axioms of probability theory, elements of combinatorial analysis, conditional probability, independence, Bayes" rule, random variables, expectation, the binomial distribution, normal approximation to the binomial distribution, sampling with and without replacement, the hypergeometric distribution, the geometric and negative binomial distributions, the Poisson distribution, , cumulative distribution function, the normal, exponential, and gamma distributions, the chi-squared distribution, random number generation, Markov and Chebychev inequalities, generating functions, law of large numbers, functions of random variables, joint distributions, the central limit theorem. Hypothesis testing, estimation of parameters, and construction of confidence intervals in common situations (especially mean values, variances, and proportions). Model formulation. Model control: goodness-of-fit test and test for independence. Introduction to operations research and linear programming. Simplex methods. Optimization techniques and nonlinear programming. Introduction to numerical analysis. Examples of applications in the engineering sciences.
Teaching method : The pedagogy of the course is “problem-based learning”. Approximately half of the time allocated to the course will be used in guided project work in groups. The course projects will give the students an opportunity to apply basic concepts learned in the class to real-life problems, and to learn new topics in mathematics that are not covered in the lectures.
There will be introductory and summing up lectures and students will work in small groups with projects, problem solving, computer simulations and case studies.
Required prequisites : ME-MAM2 or equivalent.
Responsible teacher : Imad Abou-Hayt , iabo@dtu.dk