(Between the 2013-2019 Academic Years) Courses

MATH 505 Advanced Mathematical Analysis

This course aims to teach basic theory and applications of Functional Analysis

MATH 601 Differential Equations

This course contains the results of linear equations and systems, perturbations of linear systems, the existence and uniqueness of nonlinear initial value problems and the stability theory of linear and nonlinear equations. It also includes the boundary value problems.

MATH 602 Advanced Linear Algebra and Optimization

This course provides essential materials for analyzing advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts.

MATH 695 Seminar

Conduct and present a research investigation or an experimental research investigation

MATH 697 Individual Studies in Applied Mathematics and Statistics

Compulsary course subjects of the department and the selective subjects choosen from the students course profile.

MATH 699 Thesis

To determine original problems which have not been studied previously through a detailed literature review. Analysis of approach methods towards the determined problems. Obtainment of new methods and results.

STAT 601 Probability Theory and Mathematical Statistics

Axioms of Probability, Conditional Probability and Independence, Random variables, Joint distribution functions, Order statistics, Sufficiency Principles, Limit Theorems, Principles of Data Reduction, Point Estimation, Hypothesis Testing, Interval Estimations

ECON 517 Financial Econometrics

The course will mostly be based on Time Series econometric methods. While this is the ideal approach for an introduction to the fundamental methods of quantitative finance, the student should keep in mind that the range of econometric methods that can be used to answer questions related to finance and financial economics spans almost the entire spectrum of econometrics. The course starts by reviewing basic tools of statistics and econometrics, and makes brief introductions to regression analysis, least squares methods, and some extensions of these topics. Then, numerous time series methods are discussed, including the estimation and forecasting of ARMA and ARIMA models, models of conditional heteroscedasticity (ARCH/GARCH), vector autoregressions, and cointegration. Each topic is discussed along with its applications in finance, keeping in mind the peculiarities of financial data and methods that are designed to work with such data.

FM 506 Stochastic Processes in Finance

The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales.

IE 502 Probabilistic Systems Analysis

The course involves defining and modelling a stochastic process and solving the problems related to the stochastic process being investigated. The underlying theory will be taught, followed by applications that illustrate the use of a stochastic process.

IES 503 Artificial Intelligence

Common LISP and Prolog; Intelligent Agents; Problemsolving and Search: uninformed and heuristic search, A*, local search and optimization; Constraint satisfaction problems; Game playing and adversarial search; Logical reasoning. Propositional Logic. Firstorder logic. Inference in firstorder logic; Planning; Reasoning under uncertainty. Bayes rule. Belief networks. Using beliefs to make decisions. Learning beliefs; Special topics: Robotics, Natural Language Processing, Game Theory, other AI applications.

IES 508 System Simulation and Modeling

This course covers Basic Simulation Modeling; Random Number, Random Variate Generation; Model Verification and Validation; Input Modeling;Output Analysis; VarianceReduction Techniques; Experimental Design.

IES 509 Heuristics

This course introduces the concept of heuristics to the students who have already know about mathematical optimization. The topics include basic heuristic constructs (greedy, improvement, construction); meta heuristics such as simulated annealing, tabu search, genetic algorithms, ant algorithms and their hybrids. The basic material on the heuristic will be covered in regular lectures The students will be required to present a variety of application papers on different subjects related to the course. In addition, as a project assignment the students will design a heuristic, write a code of an appropriate algorithm for the problem and evaluate its performance.

IES 511 Machine Learning

Supervised Learning: Decision trees, nearest neighbors, linear classifiers and kernels, neural networks, linear regression; learning theory. Unsupervised Learning: Clustering, graphical models, EM, PCA, factor analysis. Reinforcement Learning: Value iteration, policy iteration, TD learning, Q learning. Bayesian learning, online learning.

IES 513 Mathematical Programming and Applications

Topics of this course include theory, algorithms, and computational aspects of linear programming; formulation of problems as linear programs; duality and sensitivity analysis; primaldual simplex methods; the transportation, transshipment and assignment algorithms; extensions of linear programming; integer programming formulations and solution methods.

IES 534 Nonlinear Programming

The course emphasizes the unifying themes such that convex sets and convex functions, their topological properties, separation theorems and optimality conditions for convex optimization problems.

IES 570 Criptology and Computer Security

To acquaint students with advanced cryptography algorithms, systems, principals, functions, and development techniques of network security mechanisms. Make students to go into research and development within this field.

MATH 504 Statistics

This course provides an introduction to statistics with financial applications. Statistical estimation and analysis techniques are provided and illustrated with financial problems.

MATH 508 Partial Differential Equations

In this course the subjects such as canonical forms of partial differential equations, solution methods of parabolic, hyperbolic and elliptic equations in different regions will be discussed.

MATH 552 Copula Theory and Its Application in Finance

Bivariate copula functions, Frechet bounds, Sklar’s theorem, Independence, Measures of association, Parametric families of bivariate copula, Multivariate copulas are the main subjects will be discussed in this course.

MATH 553 Optimization

Linear Programming: Modeling, Solution Methods, Duality in linear programming; Nonlinear programming: First and second order optimality conditions for unconstrained problems, Lagrange multipliers, convexity in mathematical programming, The KuhnTucker theorem; Discrete optimization.

MATH 554 Basic Topics in Mathematics

This course will both review and extend a number of basic mathematical tools which are generally useful in applications and are typically assumed as prerequisites for many of the current courses.

MATH 555 Financial Mathematics

The first half of the course begins with an introduction to basic financial mathematics covering the computation of simple interest and discount rates, deriving the compound interest, and applications of different rates of interest in determining the present and future values of different types of annuities for different time periods. The second part of the course mainly concerns the classical quantitative finance i.e. derivatives, specifically the option pricing . The probability and stochastic theory, optimization models, the Black-Scholes Option Model, partial differential equations and numerical methods are covered.

MATH 600 Mathematics Softwares and Research Methods

The course will focus on the concepts and principles underlying MAGMA computational algebra system and LaTeX, especially the notion of functional programming and pattern matching. This core knowledge will enable attendees to apply researching program system more effectively, and write their papers/course materials with LaTeX. Graduate students will also learn how to use digital databases for research, techniques of mathematical paper writing.

MATH 654 Discrete Optimization and Heuristic Methods

This course aims to cover the classification of the optimization problems and wellknown heuristic methods.

MATH 655 Fuzzy Set Theory and Its Applications

This course aims to cover the fundemental fuzzy theory and its applications of fuzzy logic.

MATH 656 Complex Analysis

This course contains the questions of existence of holomorphic and meromorphic functions with prescribed properties on plane domains, viz., those that are doubly‐periodic with respect to a lattice. This includes the construction of elliptic functions and of theta functions, and the representation of elliptic functions in terms of translates of the sigma function.

MATH 657 Time Scales

The time scales calculus. Second order linear dynamic equations. Selfadjoint dynamic equations. Linear systems of dynamic equations. Dynamic inequalities on time scales. Dynamical systems on time scales..

MATH 658 Advanced Data Analysis

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MATH 659 Graph Theory

Graphs, some special graphs, connectivity, blocks, trees, linear paths, planarity, Kuratowsky theorem, coloring, cromatic numbers, five color theorem, four color theorem, petri nets.

MATH 660 Algebraic Geometry

In this course, the many uses of algebraic geometry will be illustrated and the more recent applications of Gröbner bases and resultants will be highlighted.

MATH 661 Finite Fields and Its Applications

This course basically introduces algebra over finite fields and analyses its structure in detail to obtain solutions of general equations.

MATH 662 Cryptography

Cryptography is one of the popular topics with direct applications to daily life. Topics include: congruences, factoring, quadratic residues as preliminaries from number theory and continue with cryptography and algebraic geometry.

MATH 663 Biomathematics

Biological applications of linear/nonlinear Difference Equations, theory and examples. Biological applications of  Linear/Nonlinear differential equations. Biological applications of partial differential equations. Biological applications of graph theory.

MATH 664 Invariant Theory

This course provides an introduction to the theory of invariants of finite groups. Topics are based both on classical methods and also on new computational methods.

MATH 665 Algebraic Coding Theory

This course provides an introduction to the theory of algebraic codes. Topics are based on algebraic function fields and geometric methods.

MATH 666 Integral Equations

Classification of Integral Equations, Connection with differential equations, kernels, special types of kernels, Fredholm and Volterra equations of the first and second kind, Method of successive approximations, Integral equations with singular kernels, Hilbert space, kernel and transforms. Linear integral operators in Hilbert spaces. The resolvent, Fredholm theory, degenerate kernels.

MATH 667 Theory of Finite Elements

In this course variational formulation of boundary value problems, an introduction to Sobolev spaces and finite element concepts will be taught. Also includes classification of finite elements in onedimensional and twodimensional models.

MATH 668 Spectral Analysis of Differential Operators

This course aims to cover an advanced theory and applications of Spectral Analysis.

MATH 669 Applied Homology, Computational Approach

The course will focus on the concepts and principles homology, especially on the computaitonal side. This core knowledge will enable attendees to apply homological methods to nonlinear problems, and provide sufficient characterization. Students will also learn how to use appropriate software.

MATH 670 Set Theoretic Topology

This course aims to cover fundamentals of Set Theoretic Topology and its applications.

MATH 671 Fuzzy Optimization

The course covers basic concepts and applications of Fuzzy Set Theory.

MATH 672 Algebra

The course will focus on the concepts and principles of algebra. This core knowledge will enable attendees to understand the abstract structures in detail. Moreover, attendees will also learn computations of algebraic structures.

MATH 673 Computational Commutative Algebra

The course will focus on the concepts and principles of commutative algebra. This core knowledge will enable attendees to apply algebraic methods to various problems involving polynomials in many variables. Students will also learn how to use appropriate software.

MATH 674 Group Theory and Its Applications

The course will focus on the concepts and principles of fundamental topics of group theory. This core knowledge will enable attendees to understand the groups in general. Moreover, attendees will also learn the types of groups and how to identify these types.

MATH 675 Applications of Modules and Representation Theory

The course will focus on the concepts and principles of representation theory of finite groups, especially on the computational side of the modular case. This core knowledge will enable attendees to apply algebraic methods to compute modular representations. Students will also learn how to use appropriate software.

STAT 501 Theory of Statistics

The topics covered in this course include basic notations and definitions of statistics, data reduction, point estimation, methods of evaluating estimators, and hypothesis testing.

STAT 502 Stochastic Processes

The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales and Brownian motion process.

STAT 503 Probability Theory

In this course, a short introduction to the combinatorial analysis is given. The axioms of probability theory and historical background is discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered.

STAT 504 Nonparametric Statistics

Most of the nonparametric techniques are based on order statistics, runs, and ranks. Therefore the theory of order statistics, runs, and rank statistics is extensively studied.

STAT 505 Applied Statistical Analysis

This course provides essential materials for analyzing statistical data appear in various fields of science.

STAT 506 Multivariate Statistics and the Theory of Copulas

The course is designed to provide graduate students in mathematics and statistics with a strong grasp of the multivariate statistical theory, particularly emphasizing the connection with the theory of copulas.

STAT 551 Actuaria

This course provides essential materials for analyzing acturatial concepts.

STAT 552 Ordered Random Variables

Order statistics: distributions, approximations, bound, moments, parametric and nonparametric inference. Records: distribution, moments, asymptotic results, representations, correlation coefficients, nonstationary cases.

STAT 553 Reliability

System reliability models and their properties are the focus of this course.

STAT 554 Statistical Process Control

Basic topics of this course are: Basics of statistics, Quality control systems,methods of stochastics processes.

STAT 555 Risk Analysis

This course provides essential materials for analyzing risk analysis concepts.

STAT 556 Linear Statistical Models

This course studies the following topics:
Linear difference equations, forecasting and linear prediction, AR and MA processes, estimators of parameters in linear models, best linear unbiased estimators, linear rank tests, different tests for scaling.

STAT 557 Time Series Analysis

Different tests on randomness are discussed. Difference Equations and Lag Operators are considered. Analysis of ARMA processes is done. Moment estimators and Maximum Likelihood Estimatords are investigated. Forecasting for linear and nonlinear models is applied.

STAT 558 Design of Experiment

The course includes analysis of different types of statistical experiments. Randomized Experiments and Fixed Designs are also discussed. Analysis of covariates and incomplete samples are presented.

STAT 559 Advanced Probability Theory

The axioms of probability theory and historical probability backgrood are discussed. Random events, random variables as well as their basic characteristics are studied. Limit theorems for sums of independent random variables are also considered. Dependent random variables are studied. Bivariate random variables are discussed.

STAT 560 Statistical Methods in Biology and Medical Sciences

The course program includes: Comparative and Screening Studies, Measuring Rates, Different Statistical and Biastatistical Tests, Regression and Survival Analysis.

STAT 561 Statistical Softwares and Simulation

The course includes. Description of statistical software. Basic commands and operations in Matlab. Various simulation techniques of Matlab. Codes and commands of Arena.

STAT 562 Combinatorial Analysis and Discrete Distributions

Pigeonhole Principle, Permutations, Combinations, The Binomial Coefficients, Discrete random variables with their probability distributions, The inclusionExclusion Principle and Applications, Recurrence Relations and Generating Functions.

STAT 563 Statistical Decision Theory

The topics covered in this course include elements of decision theory, risk, estimation and hypothesis testing in a setup of decision theory, Bayes risk and decision, and optimal stopping rules.

STAT 602 Probability and Statistics for Business

Confidence interval estimation: one and two populations, Hypothesis Tests of single and double populations, Simple and multiple regression analysis, Nonparametric statistics