## FACULTY OF ARTS AND SCIENCES

## Department of Mathematics

# Courses

This course aims at preparing students to use academic skills in English.

Presentation of Administrative Units, Academic Units and Student Clubs

Functions, limits and continuity, derivatives and its applications. extreme values, Intermediate Value Theorem, Rolle’s Theorem, The Mean Value Theorem and its applications, inverse functions and their derivatives, related rates problems.

Students will be taught how to use the written and verbal communication tools accurately and efficiently in this course. Various types of verbal and written statements will be examined through a critical point of view by doing exercises on understanding, telling, reading, and writing. Punctuation and spelling rules, which are basis of written statement, will be taught and accurate usage of these rules for efficient and strong expression will be provided. As for verbal statement, students will be taught how to use the body language, use accent and intonation elaborately, and use presentation techniques.

In this course symbolic logic, set theory, cartesian product, relations, functions, equivalence relations, equivalence classes and partitions, order relations: partial order, total order and well ordering will be discussed. Mathematical induction will be taught.

This course provides a general information of the events from the end of the 19. century until the end of the Turkish War of Independence and the signing of the Treaty of Lausanne in 1923 and the following period until 1990’s.

The course will focus on the concepts and principles of Euclidean geometry. Conic sections, their classifications, focal properties, and their geometry will be discussed in detail.

ENG 102 is a compulsory course for first year students. ENG 102 focuses on the cognitive skills of listening, reading, writing and speaking. Students' academic listening skills will be improved by listening to important / relevant information from lectures or discussions and reading skills by reading recent academic texts and then using this information to create an output task. Speaking focuses on giving presentations and students get prepared to express their ideas and opinions by speaking persuasively and coherently. The writing component is a consolidation of the speaking activities.

Areas as limits of sums, Riemann sums, definite and indefinite integrals, improper integrals, integration techniques, volumes of solids, arc length and surface area.

This course aims to cover basic theory and applications of linear optimization.

This course studies basic properties of finite and countable Markov chains. The accent is made on their asymptotic properties. The course also discusses branching process and Poisson process and their various applications. The last mention of this course is birth and death processes and their applications in queueing theory.

In this course basic concepts of complex numbers will be discussed. Elementary functions; Derivative and CauchyRiemann equations; Cauchy’s integral theorem; Morera’s theorem; Zeroes of analytic functions; Maximum and minimum principle; Fundamental theorem of algebra; Laurent series; Classification of singular isolated points; residue theorem.

The main subjects of the course are the vector and matrix operations, linear independence and dependence of vectors, linear vector spaces and subspaces, dimensions and basis vectors for vector spaces, linear transformations, determinants, solution methods for first order and second order ordinary differential equations and their engineering applications, eigenvalues eigenvectors analysis and diagonalization

This course aims to provide basic theory and applications of Probability Theory.

In this course series; power series, limits and partial derivatives of functions of several variables, Taylor series, applications of partial derivatives, multiple integrals and their applications will be covered

In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed.

Each student is given a topic of research by an appointed supervisor.

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

This course aims to cover basic theory and applications of Topology.

In this course the numerical solution of nonlinear equations will be discussed. Several interpolation methods will be given. Least squares problems will be solved.

This course is designed to equip students with the necessary skills and knowledge that they will need when they start their professional lives. The course simulates all stages of the job application process, including topics like finding job openings, CVs, job application forms, cover letters, job interviews, and following up, as well as handling job offers and rejection.

In this course vector fields and vector calculus will be discussed. Line integrals, surface integrals, flux integrals will be calculated. Green's theorem, divergence theorem and Stokes' theorem will be discussed and some physical applications will be solved.

In this course basic concepts and classification of partial differential equations will be discussed.The heat, wave and Laplace equation will be given and the solution methods will be taught.

In this course, the concepts of bases, dimensions, linear transformations, orthogonality, inner product spaces, eigenvalues, eigenvectors and diagonalization are discussed.

This course aims to provide basic theory and applications of Probability Theory.

ENG 310 is a compulsory course for third year students and is designed to enable them to speak more effectively while expressing themselves in a variety of areas, such as business related and academic related topics. These areas range from participating in discusiions to presenting information in the form of short presentations, known as Pecha Kuchas. Students will also take part in role plays and formal debates.

In this course, the basic pillars of modern mathematics will be introduced and analyzed. These structures include groups, rings, fields, any mapping between them and their substructures.

In this course, the concepts of the sample population, lthe ikelihood and invariance princeples, point estimation, hypothesis testing, interval estimation and the decision theory are discussed.

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

Internship, covers field experience at any work place for 3 weeks. Students should follow the instructions stated in IUE Internship Guide in order to successfully complete their internships.

# Elective Courses

BA 205 Financial Accounting I

This course is designed as an introductory accounting course in which the aim is to initiate the students in the use and preparation of financial statements.As aspiring managers,the students need to recognize the need for accounting principles,procedures and the financial statements in companies' decision making process.In so doing, the topics covered include the basic principles and recording process to prepare useful financial statements.In the second half of the semester,selected topics will be discussed in detail.

CE 223 Database Systems

Topics related to both database design and database programming are covered.

CE 308 Computing Theory

The following topics will be included: regular expressions and contextfree languages, finite and pushdown automata, Turing machines, computability, undecidability, and complexity of problems.

CE 380 Computational Geometry

Wellknown computational geometry problems, their algorithmic solutions and computational geometry problem solving techniques.

CE 390 Analysis of Algorithms

Greedy algorithms, divideandconquer type of algorithms, dynamic programming and approximation algorithms.

CE 401 Algorithms Design

The course covers basics of Algorithms Analysis, graph theoretic concepts, greedy algorithms, divide and conquer algorithms, dynamic programming, and approximation algorithms.

CE 470 Introduction to Neural Networks

The following topics will be included in the course: The main neural network architectures and learning algorithms, perceptrons and the LMS algorithm, back propagation learning, radial basis function networks, support vector machines, Kohonen’s self organizing feature maps, Hopfield networks, artificial neural networks for signal processing, pattern recognition and control.

CE 490 Introduction to Digital Image Processing

The following topics will be included: Digital images as twodimensional signals; twodimensional convolution, Fourier transform, and discrete cosine transform; Image processing basics; Image enhancement; Image restoration; Wavelets and Multiresolution processing; Image coding and compression.

ECON 213 Mathematical Economics I

This course will extensively use algebra and basic calculus. The course focuses mainly on the following; static analysis, linear models and matrix algebra, comparative static models, optimization problems with equality constraints.

ECON 214 Mathematical Economics II

The following topics will be covered: First order differential and difference equations, higher order differential and difference equations, simultaneous systems of higher order equations, stability analysis.

ECON 301 Econometrics

Econometrics can be defined as the “application of statistics to the analysis of economic phenomena”. The knowledge of econometrics is essential to test economic theories and to understand empirical work being done in Economics. The course will teach how to do empirical work by using examples drawn from various fields in economics. It will also focus on various types of economic data, how one can obtain them, and how they may be used. Topics include regression analysis, ordinary least squares, hypothesis testing, choosing independent variables and functional form, multicollinearity, serial correlation and heteroskedasticity.To aid in empirical work the regression package EViews will be used.

ECON 303 Money and Banking

In this course money and monetary issues are explained. Foreign exchange is duly introduced with all experimental equations and practices. The scope and structures of all banking activities are taught and exemplified, and commercial banks’ role in the foreign trade are accentuated.

ECON 304 Monetary Theory and Policy

This course will explore the theoretical and empirical analysis of the effect of money on economy. The effect of money, credit and liquidity on income, employment, economic growth and inflation will be analyzed. The goals of monetary policy, the methods used to obtain these goals, and the effects of these methods will be discussed. Moreover, issues such as the functioning of monetary policy in international financial system; the relationship of the financial system with the real economy, monetary policy channels (money, bank credit, and balance sheet channels), and reasons and outcomes of inflation will be undertaken.

ECON 324 Applied Econometrics

The course will teach advanced techniques that are required for empirical work in economics. Emphasis will be on the use and interpretation of single equation and system estimation techniques rather than on their derivation. The purpose of the course is to help students understand how to interpret economic data and conduct empirical tests of economic theories. It will focus on issues that arise in using such data, and the methodology for solving these problems. Specific topics include limited dependent variables, simultaneous equations, time series models, nonstationarity and cointegration and panel data analysis. The regression package EVIEWS will be used for empirical work.

ECON 407 Applied Economic Topics

The course starts with an introduction to quantitative macroeconomics. We then discuss the benchmark deterministic model and competitive equilibrium. We then discuss steady state. The course continues with introduction to Matlab and Dynare programs in the Lab. It concludes with the discussion of calibration and simulation of a simple real business cycle (RBC) model.

ECON 416 Time Series Analysis

The class covers the theory behind a variety of topics in time series econometrics, and introduces the student to a large number of time series applications. Class exposition is evenly divided between theory and applications, but applications are given priority in assignements and exams. After a brief review of statistical and econometric basics, we discuss the use of difference equations and lag operators. Stationary ARMA models are covered in great detail, and so are ARCH, GARCH, and VAR techniques. The student is also exposed to nonstationary time series, unit roots, and ARIMA models. The class ends with discussions on cointegration and forecasting.

ECON 418 Game Theory

The course covers the analysis of strategic behaviors in everyday life. Most of the times, people and firms are in competition and have to behave strategically to maintain their best interests. Behaving strategically means that an agent must accept other’s existence and consider their decisions as well when deciding. Our best interest may harm others whom we are living with. The merit is to find a (the) best solution maximizing the utility under given conditions.

IE 334 Quality Assurance and Reliability

The field of quality control underwent major changes over the last two decades of the 20th century. These changes made quality control an important course in the curriculum of all major industrial engineering departments in the world. This course is designed to explain this evolutionary change in the understanding of quality concepts from different perspectives with the help of statistical methods.

IE 338 Stochastic Models in Manufacturing Systems

This course deals with the following topics: Models of manufacturing systems, including transfer lines and flexible manufacturing systems; Calculation of performance measures, including throughput, inprocess inventory, and meeting production commitments; Realtime control of scheduling; Effects of machine failure, setups, and other disruptions on system performance.

IE 342 Decision Theory

This course is one of the basic sections of Operations Research, which studies a rational process for selecting the best of several alternatives. The “goodness” of a selected alternative depends on the quality of the data used in describing the decision situation. From this standpoint, a decisionmaking process can fall into one of three categories. 1. Decisionmaking under uncertainty in which the data cannot be assigned relative weights that represent their degree of relevance in the decision process. 2. Decisionmaking under risk in which the data can be described by probability distributions. 3. Decisionmaking under certainty in which the data are known deterministically. 4. Decision making in multicriteria environment. The main subjects of the course are the decision situation, decision rule, decision trees, information and the cost of additional information, utility theory, multiobjective problems, solution notions for such problems and methods for calculations efficient solutions for multiobjective problems, goal programming and the methods of analyzing solutions for goal programming problems.

IE 354 Combinatorial Optimization

The course covers a broad range of topics in combinatorial modeling and the systematic analysis. The topics include basic counting rules, generating functions, recurrence relations, some famous combinatorial optimization problems and related mathematical techniques.

IE 357 Special Topics in Optimization

In this course, students will have the chance to learn certain optimization subjects, methods and models which are not covered in compulsory courses. At the end students will also have the chance to learn applications of these models and methods.

IE 358 Heuristics in Optimization

This course introduces the concept of heuristics to students who 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.

IE 375 Financial Engineering

Students will learn to make decisions by taking into account such features as interest rates, and rates of return. They will learn about the concept of arbitrage, and when consideration of such is sufficient to price different investments. Applications to call and put options will be given. Students will learn when arbitrage arguments are not sufficient to evaluate investment opportunities. They will learn to make use of utility theory and mathematical optimization models to determine optimal decisions. Dynamic programming will be introduced and used to solve sequential optimization problems. The use of simulation in financial engineering will be explored.

INS 401 Introduction to Insurance and Actuarial Mathematics

Interest Theory, Life Table, Life Annuity, Life Insurance, Premiums, Rezerves, Multiple Life Theory and Multiple Decrement Model.

ISE 336 Art of Mathematical Modelling

Topics of this course include developing mathematical models and heuristic solution algorithms for essential Industrial Systems Engineering problems. During the course, IBM ILOG OPL Development Studio will be used to code and solve mathematical models and heuristic algorithms.

ITF 301 International Finance

The main objective is to explore the primary theoretical and practical concepts that dominate international financial markets and those that should be taken into consideration during international risk management and investment decisions.

ITF 304 Quantitative Methods in Finance

This lecture guides the students through a wide array of mathematics, ranging from elementary basic mathematics, limit, derivative and integral, linear algebra and differential calculus to optimization and linear regression. These quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income securities and equities.

ITF 403 Financial Risk Management

This course covers, the evolution of risk management, enterprise risk management approach, fundamental concepts of risk management, goals and strategies in risk management, design and application of risk management systems.

ITF 410 Financial Institutions and Markets

The content of this course will be comprised of mainly examining the structure of financial institutions and markets in developed countries and emerging markets as well as their interactions. The basic topics to be covered in this course are; the evolution of financial institutions, their role within the financial system, the operation of financial markets, their impact on economy, their future role and possible development strategies for financial markets.

MATH 150 Research Methods and Biostatistics

The course content is designed in twofold. In the first part the theoretical background of statistical analysis will be discussed. In the second part of the semester, demographic distribution, public health and the analysis and grouping of thee data in the healthcare sector will be discussed with examples.

MATH 308 Introduction to Stochastic Processes II

This course studies the analysis of Martingales and Stationary Processes. The course analyzes the Poisson process in detail and extends it to renewal processes. The Brownian Motion and stochastic integration are also studied in the framework of this course.

MATH 309 Equations of Mathematical Physics

Smoothing of partial differential equations, modeling of displacement equation, wire oscillation and diffusion equations, Fourier transforms and applications, Fourier integral representations, Fourier transform method to wave and heat equation, Fourier cosine and sine transforms, solutions of problems in the semi-infinite range.

MATH 311 Discrete Mathematics

Topics include cartesian products, relations and functions, the pigeonhole principle, partition of integers, the exponential generating function, first and second-order linear recurrence relations, nonhomogeneous recurrence relations nonlinear recurrence relations.

MATH 314 Measure Theory

The Riemann integral; Measure, null sets, outer measure; Lebesque measurable sets and Lebesque measure; Monotone convergence theorems; Integrable functions, The Dominated Convergence Theorem.

MATH 317 Elementary Number Theory

In this course, divisibility algorithm, Diaphontine equations, prime numbers and distributions, conjugate theory, number-theoretical functions, Fermat's theorem and its generalization, prime roots, indices will be discussed.

MATH 321 Introduction fo Mathematical Finance

In this course, students will learn about interest rates and income. In the course, when the arbitrage and its applications and economic evaluations are insufficient, the lessons will be taught. Mathematical modeling methods in finance are also among the topics of the course.

MATH 336 Engineering Statistics II

Chi-square distribution and applications, goodness of fit test, simple linear regression and correlation analysis, multiple regression analysis, non-linear regression analysis, defining model in multiple regression, single and multi-factor analysis of variance.

MATH 400 Biomathematics

Biological applications of difference and differantial equations. Biological applications of nonlinear differantial equations. Biological applications of graph theaory.

MATH 402 Topology II

This course aims to cover basic theory and applications of topology.

MATH 404 Numerical Analysis II

In this course the solution of linear systems of equations will be discussed using direct and iterative methods. Overdetermined linear systems will be solved using least squares method. Eigenvalues and eigenvectors will be discussed. Functions will be approximated using orthogonal polynomials

MATH 407 Introduction to Spectral Analysis I

This course aims to cover basic theory and applications of spectral analysis.

MATH 408 Introduction to Spectral Analysis

This course aims to cover basic theory and applications of spectral analysis.

MATH 410 Linear Integral Equations

In this course, basic issues of Green's functions will be discussed. Solution applications of ordinary differential equations, Fredholm and Volterra equations of 1st and 2nd type, separable kernel and Fredholm equations will be studied.

MATH 420 Seminar: Introduction to Quaternionic and Clifford Calculus

In this course, basic issues of quaternions will be discussed. Clifford valued functions and forms; Clifford operator algebra; Boundary value problems will be studied.

MATH 425 Mathematical Computing and Simulation I

In this course, the concepts of different computational methods are discussed. Student solve equations numerically and constract plots. As the application to probability theory and statistics, different simulation tethniques are studied.

MATH 426 Mathematical Computing and Simulation II

In this course, various calculation methods are discussed. Students solve the equations numerically and draw graphs. Different simulation techniques are studied as probability theory and application of statistics.

MATH 437 Fuzzy Set Theory

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

MATH 440 Numerical Solutions of Partial Differential Equations

This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear partial differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods.

MATH 450 Game Theory

Elements of a Game and Payoffs Games, Prisoner's dilemma,Intro to ComlabGames Software, Strategies, Sequential Move Games, Risk and Probabilities, Simultaneous Move Games, Nash Theory, Incomplete Information Games

MATH 455 Graph Theory

Graphs notations, Varieties of graphs, Walks and distance, paths, cycles, and trees, colorability, chromatic numbers, five color theorem, four color conjecture,

MATH 460 Additional Topics in Algebra

The focus of the course will be the applications of abstract structures such as group actions, Sylow theorems, Gröbner bases, Galois theory, homology computations. This course is a complement of abstract algebra and enables students to understand abstract notions as solid structures.

MATH 462 Applied Statistics

This course provides several basic methods for analyzing statistical data appear in various fields of science.

MATH 470 Introduction to 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; simple cryptosystems, publickey cryptosystems, practical applications such as authentication, key exchange and sharing.

MATH 472 Introduction to Computational Commutative Algebra

The main subjects of the course are monomial orders, Groebner basis, elimination theory, dimension theory, resultants, Zariski topology and geometry-algebra bridge, affine and projective varieties, and invariant theory.

MATH 480 Algebraic Number Theory

In this course, algebraic numbers are defined and their properties are investigated with motivations and roots from classical problems. Also, it makes abstract topics from algebra easier to understand. Nevertheless, the approach will be elementary and all necessary topics will be covered at the very beginning. Geometric methods will also be discussed with an applications of Minkowski's theorem.

MATH 485 Exploratory Data Analysis

MATH 488 Introduction to Invariant Theory

This course provides an introduction to the theory of polynomial invariants with topics; linear representations, algebras, ring of invariants, permutation invariants, generators, bounds on generators, constructing invariants, system of parameters, and if possible, rational invariants. This course is a perfect chance to learn why abstract mathematics is a fundamental topic. It is intended for students planning professional career in various areas.

MATH 490 Introduction to Algebraic Geometry

This course covers some fundamental topics about algebraic varieties. Projective geometry is also introduced and as a final topic homogeneous invariants of finite groups are studied. Algebraic geometry is a central topic which has tight connections with number theory, singularity theory, Diophantine problems. Prerequisites for this course are abstract algebra and multivariate calculus.

MATH 499 Introduction to Coding Theory

This course provides an introduction to error correcting codes by which it is possible to communicate on noisy channels, such as satellite communications. In this course, an introduction revealing the theory and also an introduction providing important classes of codes is aimed. Topics include: linear codes, Hamming codes as perfect codes, nonlinear codes, Hadamard codes, dual codes and weight distributions, cyclic codes, and BCH codes. Requirements for the course are basic linear algebra and an elementary number theory.

PHYS 100 General Physics I

Through lectures and labs we aim to introduces the following classical mechanics and thermodynamics topic: space and time; straight line kinematics; motion in a plane; forces and static equilibrium; particle dynamics with force and conservation of momentum; relative inertial frames and noninertial force; work, potential energy and conservation of energy; rigid bodies and rotational dynamics; vibrational motion; conservation of angular momentum; central force motions

RM 401 Fundamentals of Risk Management

Topics covered are: identification, classification, measurement and management of different types of financial risks.

RM 402 Statistical Foundations of Risk Management

RM 403 Applied Risk Analysis

Data and portfolio risk analysis will be learnt by using several approaches. Learning techniques requires an extensive use of Excelbased applications. JP Morgan’s RiskMetricsTM will also be covered during the course as a benchmark source for risk analysis and modeling.

SE 330 Advanced Game Development

In this course, students learn about the advanced topics in the process of video game development and use this information to develop their own computer games.

SE 420 Artificial Intelligence and Expert Systems

This course provides an introduction to Artificial Intelligence (AI). In this course we will study a number of theories, mathematical formalisms, and algorithms, that capture some of the core elements of computational intelligence. We will cover some of the following topics: search, logical representations and reasoning, automated planning, representing and reasoning with uncertainty, decision making under uncertainty, and learning.

## NEWS | ALL NEWS

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### Mathematics Olympics 2005

The mathematicians of future compute at the 4. International Mathematics Olympiad with science consultancy of Izmir University of Economics Department of Mathematics