## Courses Offered

##### Last Updated:

### 2018-2019 Spring

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

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

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

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

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

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: **
0(0-2); **ECTS: **
20.0

See the course in IAM Catalogue or METU Catalogue

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

See the course in IAM Catalogue or METU Catalogue

**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

See the course in IAM Catalogue or METU Catalogue

**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: **
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.

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**Credit: **
0(0-0); **ECTS: **
0.0

This course is a fundamental course for any kind of graduate program since its focus is on the scientific research methods. It provides an introduction to the research design as well as ethical issues in scientific research. More specifically, the course provides students with an integrated framework for doing research. Students will gain methodological skills which will assist them in applying to the research process, such as defining the research questions, design and define the research methods, survey design, data inquiries. In this way, the students learn to manage their thesis writing process independently, writing their own research paper. The role of ethics in research, ethical issues in conducting research will be emphasized to assure ethical aspects in scientific research.

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

Quantum Information Theory: density matrix, composite systems, Shannon entropy; Quantum Data Compression; Decoherence: decoherence models for a single qubit, quantum black box; Quantum Error Correction: general properties of quantum error correction; Experimental Implementations: NMR quantum computation, cavity quantum electro dynamics.

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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

Public Key Cryptosystems; Pairing-based Cryptography; Hashed-based Cryptography; Zero Knowledge Proofs; Bitcoin; Cryptocurrencies; Blockchain; Distributed Ledger Technologies; Security; Privacy.

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

This course is an introduction to the mathematical formulation and treatment of problems arising from trade execution in financial markets. When there are costs and constraints imposed on the execution of trades, how to best execute them? The course studies mathematical formulations and solutions of these types of problems.

See the course in IAM Catalogue or METU Catalogue

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

Please, ask Secretary to IAM, or your advisor/supervisor about the details.

See the course in IAM Catalogue or METU Catalogue

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

Please, ask Secretary to IAM, or your advisor/supervisor about the details.

See the course in IAM Catalogue or METU Catalogue