(Between the 2013-2019 Academic Years) Courses

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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

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.

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..

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

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.

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

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.

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.

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.

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

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.

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.

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

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.

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

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

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.

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.

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.

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.

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

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.

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.

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.

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

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.

This course provides essential materials for analyzing acturatial concepts.

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

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

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

This course provides essential materials for analyzing risk analysis concepts.

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.

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.

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.

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.

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

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

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

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.

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