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Mathematics 3 (Spring 2013) |
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| Course code : | M-MAT3-U5 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Placement : | 4. sem | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | Danish and English |
| Principal Content : | A student who has met the objectives of the course will be able to: • Apply basic definitions and axioms of probability in problem solving. • Apply the concepts of conditional probability and conditional distribution. • Formulate simple probability models from verbal descriptions. • Identify and describe probability distributions, including Poisson, binomial, exponential and the normal distribution. • Choose a suitable probabilistic model for a real world phenomenon. • Perform calculations involving distributions, expectations, moments and correlations. • Estimate and interpret simple summary statistics, such as mean, standard deviation, variance, median and quartiles. • Apply simple graphical techniques, including histograms. • Apply and interpret important statistical concepts, such as the formulation of models, parameter estimation, construction of confidence intervals and hypothesis testing. • Understand and interpret output from some commonly used statistical software. 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. Simple methods for graphical and tabular assessments of collected or measured data. 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. Examples of applications in the engineering sciences. |
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| Teaching method : | The pedagogy of the course is “problem-based learning”. Some of the time allocated to the course will be used in working with guided assignment. The course assignments will give the students an opportunity to apply basic concepts learned in the class to real-life problems, and to learn new concepts 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. |
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| Required prequisites : | Mathematics 1 and Mathematics 2 (or equivalent). | ||
| Responsible teacher : | Jørgen Sand
, jsan@win.dtu.dk |
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