INSTITUTE OF APPLIED MATHEMATICS

Integrated PhD in Scientific Computing

  • Compulsory Courses

    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.

    See the course in IAM Catalogue or METU Catalogue

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

    Introduction to statistical learning, simulation and supervised learning. Linear methods of regression and classification. Model assessment and selection. Model inference and averaging. Additive models, trees and related methods. Prototype methods and nearest neighbors. Cluster algorithms and support vector machines. Unsupervised learning. Computer applications and MATLAB exercises are important elements of the course.

    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.

    See the course in IAM Catalogue or METU Catalogue

    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.

    See the course in IAM Catalogue or METU Catalogue

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

    Unconstrained optimization: line search methods, steepest descent, Newton and quasi Newton methods, the conjugate gradient method constrained optimization: equality and inequality constraints, linear constraints and duality, linear programming, the simplex method, Lagrange multiplier algorithms, interior point methods, penalty methods, large scale optimization.

    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

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    Credit: 0(0-2); ECTS: 10.0

    This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice.

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

    Program of research leading to Ph.D. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write up of thesis is in progress.

    See the course in IAM Catalogue or METU Catalogue

    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.

    See the course in IAM Catalogue or METU Catalogue

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

    Globalization techniques, semidefinite and conic optimization, derivative free optimization, semi-infinite optimization methods, Newton Krylov methods, nonlinear parameter estimation and advanced spline regression, multi-objective optimization, nonsmooth optimization, optimization in support vector machines.

    See the course in IAM Catalogue or METU Catalogue

    Credit: 0(0-2); ECTS: 10.0

    This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice. Students can work independently in issues that require expertise; they can share and make presentations of their research both verbally and in written form.

    See the course in IAM Catalogue or METU Catalogue

    3 of Compulsory Courses are to be chosen, excluding IAM600, IAM561, IAM562, IAM566, IAM590, are chosen

    8 Elective Courses (Total 42 credits)

See IAM Catalogue for possible elective courses.

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