## Courses

##### Last Updated:

All Courses @ IAM Actuarial Science Cryptography Financial Mathematics Scientific Computing

### Selected Courses for Scientific Computing

**Credit: **
0(0-0); **ECTS: **
50.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.

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**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Mathematical modelling of stochastic reaction systems. Deterministic approach: ODE models, Reaction Rate Equations. Stochastic Models: Chemical Master Equation, Chapman-Kolmogorov Equations, Gillespie Algorithms, Explicit Solution Formulas, Hybrid Methods, Tau-Leaping method. Lotka-Volterra Models, Michaelis-Menten Models.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Computer Arithmetic; Linear Equations: Gauss elimination, LU decomposition; Linear Least Squares: data fitting, normal equations, orthogonal transformations; Eigenvalue Problems; Singular Value Decomposition; Nonlinear Equations: bisection, fixed-point iteration, Newton’s method, optimization; Interpolation: polynomials, piecewise polynomials; Numerical Differentiation and Integration.

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**Credit: **
3(3-0); **ECTS: **
8.0

Ordinary Differential Equations: Euler’s method, multistep methods, Runge-Kutta methods, stiff equations, adaptivity; Boundary Value Problems: shooting, collocation, Galerkin; Partial Differential Equations: parabolic, elliptic, and hyperbolic equations; Iterative Methods for Sparse Linear Systems: splitting methods, descent methods, conjugate gradients, preconditioners, multigrid methods.

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**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
0(0-4); **ECTS: **
4.0

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**Credit: **
3(2-2); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Unconstrained Optimization: steepest descent, line search methods, trust-region methods, conjugate gradient methods, Newton and quasi-Newton methods, large-scale unconstrained optimization, least-square problems; Theory of Constrained Optimization; Linear Programming: simplex method, interior point method; Quadratic Programming; Active Set Methods; Interior Point Methods; Penalty, Barrier and Augmented Lagrangian Methods; Sequential Quadratic Programming.

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**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(2-2); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Abstract Finite Element Analysis: weak derivatives, Sobolev spaces, Lax-Milgram lemma; Piecewise Polynomials Approximations 1D and 2D: interpolation, projection; Finite Element Method 1D and 2D: weak formulation, derivation of linear system of equations, a priori estimates; Time Dependent Problems: finite differences for systems of ODE, stability estimates; Semi-elliptic equations; a posteriori Error Analysis: estimator, mesh Refinement

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
2(2-0); **ECTS: **
6.0

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.

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**Credit: **
2(2-0); **ECTS: **
6.0

Review of Programming and Toolboxes, Packages, Modules; Iterative Linear Algebra Problems; Root Finding Programs; Recursive Functions and Algorithms; Optimisation Algorithms; Data Fitting and Interpolation; Extrapolation; Numerical Integration; Numerical Solutions of Differential Equations: IVPs and BVPs; Selected Topics (algorithms and coding in different fields).

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**Credit: **
0(0-0); **ECTS: **
130.0

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**Credit: **
3(3-0); **ECTS: **
8.0

**Numerical Methods for Discrete Time Models:**binomial method for options; discrete time optimal control problems.

**Reminders on Continuous Models:**Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile.

**Monte Carlo Method for Options:**generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method.

**Finite Difference Methods for Options:**explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options.

**Finite Difference Methods for Control Problems:**Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.

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**Credit: **
3(3-0); **ECTS: **
8.0

Classification of inverse problems, linear regression, discretizing continuous inverse problems, rank-deficiency, Tikhonov regularization, iterative methods, other regularization techniques, Fourier techniques, nonlinear inverse problems, Bayesian methods. Computer applications and MATLAB exercises are important elements of the course.

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**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Generating Random Numbers; Basic Principles of Monte Carlo; Numerical Schemes for Stochastic Differential Equations; Simulating Financial Models; Jump-Diffusion and Levy Type Models; Simulating Actuarial Models; Markov Chain Monte Carlo Methods.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

Reduced Order Modeling: proper orthogonal decomposition (POD), evolution problems; Active Subspaces: parametrized models in physics and engineering, discover the active subspaces, exploit the active subspaces, active subspaces in action; Dynamic Mode Decomposition: introduction, Koopman analysis; PDE-constrained optimization: elliptic and parabolic linear optimal control problems; equality and inequality constraints; numerical algorithms for PDE-constrained optimization; reduced order modeling.

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

See the course in IAM Catalogue or METU Catalogue

**Credit: **
3(3-0); **ECTS: **
8.0

DG in One Spatial Dimension: linear system, implementation in MATLAB; Higher Dimensional Elliptic Problems: interior penalty methods, variational formulation, a priori error estimates, implementation in MATLAB, local discontinuous Galerkin method; DG for Convection Diffusion Problems: upwind scheme; Construction of Finite Element Spaces: Lagrange, Hermite, etc.; A Posteriori Error Analysis: residual-based, goal-oriented, hierarchical, equilibrated error estimators; Hybrid Discontinuous Galerkin Methods.

See the course in IAM Catalogue or METU Catalogue