• Elements of Probability and Statistics

    Part I: Probability spaces, random variables, probability distributions and probability densities, conditional probability, Bayes' formula, mathematical expectation, moments. Part II: Sampling distributions, decision theory, estimation (theory and applications), hypothesis testing (theory and applications), regression and correlation, analysis of variance, non-parametric tests.

    For further information see the academic catalog: IAM530

  • Special Topics: Methods and Applications of Uncertainty Quantification

    Probability, Random Processes, and Statistics; Markov Chains; Sampling and Monte Carlo Methods; Parameter Estimation; Uncertainty Propagation in Models; Stochastic Spectral Methods; Surrogate Models and Advanced Topics.

    For further information see the academic catalog: IAM768

  • Finite Element Methods for Partial Differential Equations: Theory and Applications

    FEM for one dimensional problems. Variational formulation and weak solutions. FEM for elliptic equations. FEM spaces. Error analysis and adaptivity. Diffusion-convection equations. Time dependent problems. Iterative solution techniques and preconditioning.

    For further information see the academic catalog: IAM572

  • Programming Techniques in Applied Mathematics I

    \( \LaTeX \) and Matlab; Basic Commands and Syntax of \( \LaTeX \) and Matlab; Working within a Research Group via Subversion; Arrays and Matrices; Scripts and Function in Matlab; Commands and Environments in \( \LaTeX \); More on Matlab Functions; Toolboxes of Matlab; Packages in \( \LaTeX \); Graphics in Matlab; Handling Graphics and Plotting in \( \LaTeX \); Advanced Techniques in Matlab: memory allocation, vectoristaion, object orientation, scoping, structures, strings, file streams.

    For further information see the academic catalog: IAM591

  • Advanced Calculus and Integration

    Review of linear algebra and multivariate calculus, sequences of series and functions, Reimann-Stieltjes and Lebesgue integration.

    For further information see the academic catalog: IAM527