Undergraduate Program (before September 2016) Course List

Compulsory Departmental Courses

Elective Courses

Service Courses Given to Other Departments

Service Courses Taken From Other Departments



Compulsory Departmental Courses

MATH111 - Basic Logic and Algebra
Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Elementary Examples of Groups, Rings and Fields, The Real Numbers

MATH112 - Discrete Mathematics and Combinatorics
Numbers and Counting. Countable and Uncountable Sets. Continuum. The Pigeonhole Principle and its Applications. Permutations and Combinations. Combinatorial Formulas. Recurrence Relations. Principle Of Inclusion and Exclusion. Binary Relations. Elementary Graph Theory.

MATH121 - Analytic Geometry I
Fundamental Principles of Analytic Geometry, Cartesian Coordinates, Lines in Plane, Trigonometry, Polar Coordinates, Rotation and Translation in Plane, Conics.

MATH122 - Analytic Geometry II
Cartesian Coordinates in 3-Space, Vectors, Lines and Planes in 3-Space, Basic Surfaces in 3-Space; Cylinders, Surface of Revolutions

MATH135 - Mathematical Analysis I
Preliminaries, Functions and Graphs, Limits and Continuity, Derivatives, Mean Value Theorem, Applications of Derivatives: Monotonicity, Local and Absolute Extrema, Concavity, L’Hospital’s Rule, Graphs of Functions.

MATH136 - Mathematical Analysis II
Riemann Integral, The Fundamental Theorem of Calculus, Integration Techniques, Applications of Integrals: Area, Volume, Arc Length, Improper Integrals, Sequences, Infinite Series, Tests For Convergence, Functional Sequences and Series, Interval of Convergence, Power Series, Taylor Series and Its Applications.

MATH231 - Linear Algebra I
Matrices and Linear Equations, Determinants, Vector Spaces, Linear Transformations. ● Prerequisite: None

MATH232 - Linear Algebra II
Eigenvalues and Eigenvectors, Elementary Canonical Forms, The Rational and Jordan Forms, Inner Product Spaces, Operators on Inner Product Spaces, Bilinear Forms. ● Prerequisite: Math 231

MATH247 - Introduction To Object-Oriented Programming
Object-Oriented Thinking, Review of Programming Paradigms, Abstract Data Type, Scope Rules and Access Controls, Classes, Constructors and Destructors, Operator Overloading, Introduction to Object Oriented Concepts: Inheritance, Polymorphism. Templates.

MATH251 - Advanced Calculus I
Vector and Matrix Algebra. Functions of Several Variables. Limit. Continuity. Partial Derivatives. Chain Rule. Implicit Functions. Inverse Functions. Directional Derivatives. Maxima and minima of functions of several variables. Extrema for functions with side conditions.

MATH252 - Advanced Calculus II
Vector and Scalar Fields. Double Integrals. Triple Integrals. Integral of Vector Functions. Improper Integrals. Line Integrals. Green’s Theorem. Surface Integrals. The Divergence Theorem. Stoke’s Theorem

MATH262 - Ordinary Differential Equations
First Order, Higher Order Linear Ordinary Differential Equations, Applications of First Order Differential Equations, Series Solutions of Differential Equations, Laplace Transforms, Linear Systems of Ordinary Differential Equations.

MATH331 - Abstract Algebra
Groups: Subgroups, Cyclic Groups, Permutation groups, Lagrange Theorem, Normal subgroups and Factor Groups, Homomorphisms, Isomorphism Theorems, Rings and Fields: Subrings, Integral Domains, Ideals and Factor Rings, Maximal and Prime Ideals, Homomorphisms of Rings, Field of Quotients, Polynomial Rings, Principal Ideal Domain (PID), Irreducibility of Polynomials (Eisenstein Irr. Criterion), Unique Factorization, Euclidean Domains

MATH346 - Complex Analysis
Complex Numbers and Elementary Functions, Analytic Functions and Integration, Sequences, Series and Singularities of Complex Functions, Residue Calculus and Applications of Contour Integration, Conformal Mappings and Applications.

MATH347 - Data Structures
Static and Dynamic Memory Allocation, Recursion, Algorithms, Stacks, Queues, Linked Lists, Circular Linked Lists, Trees, Binary Trees, Hash Tables, Searching and Sorting Algorithms.

MATH351 - Introduction to Real Analysis
A review of Sets and Functions, The Real numbers (or system), Countable and uncountable Sets, Sequences of Real Numbers ( Cauchy Sequences), Uniform Convergence of Sequences of functions, Metric Spaces, Compactness and Connectedness, Contraction Mapping Theorem, Arzela-Ascoli Theorem, Extension Theorem fo Tietze, Baire’s Theorem. ●Prerequisite: MATH 136

MATH374 - Differential Geometry
Curves in the Plane and Space, Curvature and Torsion, Global Properties of Plane Curves, Surfaces in Space, The First Fundamental Form, Curvatures of Surfaces, Gaussian Curvature and the Gauss Map, Geodesics, Minimal Surfaces, Gauss's Theorema Egregium, The Gauss-Bonnet Theorem. ●Prerequisite: MATH 251

MATH392 - Probability Theory and Statistics
Probability Spaces, Conditional Probability and Independence, Random Variables and Probability Distributions, Numerical Characteristics of Random Variables, Classical Probability Distributions, Random Vectors, Descriptive Statistics, Sampling, Point Estimation, Interval Estimation, Testing Hypotheses.

MATH411 - Seminar Studies
The course is designed for senior Mathematics students. The purpose of the course is to introduce students to the activities of reading and doing research on advanced Mathematics topics and presenting them in class. Each student is required to work individually on a topic assigned by his/her supervisor and to make atleast one presentation to the class and the faculty.

MCS115 - Introduction to Computer Science
Introduction to Computers, Overview of Computer Hardware Components, Programming Essentials, Algorithm Design, Data Handling and Networking, Problem Solving Using Computers and Principles of C Programming.

MCS116 - Computer Programming in C
Algorithms and Flowcharts, Variable Declarations and Data Types, Arithmetic Expressions, Pointers, Library Functions, Selection Structures, Repetition and Loop Statements, Arrays, Strings, Recursion.

Elective Courses

MATH313 - Introduction to Mathematical Finance
Introduction to theory of interest: Simple and compound interest, time value of money, rate of interest, rate of discount, Nominal rates, effective rates, compound interest functions, Generalized cash flow modelling, Loans, Present value analysis, accumulated profit, and internal rate of return for investment projects, annuities, perpetuities, Measurement of investment performance, bonds, probability, geometric Brownian motion, term structure of interest rates, stochastic interest rate models

MATH316 - Mathematics of Financial Derivatives
Introduction to options and markets, European Call and Put Options, Arbitrage, Put call parity, Asset price random walks, Brownian Motion, Ito’s Lemma, Derivation of Black-Scholes formula for European options, Greeks, Options for dividend paying assets, Multi-step binomial models, American call and put options, Early exercise on calls and puts on a non-dividend-paying stocks, American option pricing as the free boundary value problems, Exotic options, Forwards and Futures, Interest rate models.

MATH318 - History of Mathematics I
Prehistoric mathematics Ancient Near East mathematics ( Mesopotamia-Egypt,3rd millenium BC–500 BC ) Greek and Hellenistic mathematics (c. 600 BC–300 AD) Chinese mathematics (c. 2nd millenium BC–1300 AD) Indian mathematics (c. 800 BC–1600 AD) Islamic mathematics (c. 800–1500)

MATH325 - Elementary Number Theory
Divisibility, Congruences , Euler, Chinese Remainder and Wilson’s Theorems, Arithmetical Functions, Primitive Roots, Quadratic Residues and Quadratic Reciprocity, Diophantine Equations.

MATH326 - Coding Theory
Error Detection, Correction and Decoding, Finite Fields, Linear Codes, Bounds In Coding Theory, Construction of Linear Codes, Cyclic Codes.

MATH332 - Finite Fields
Characterization of Finite Fields, Roots of Irreducible Polynomials, Trace, Norm, Roots of Unity and Cyclotomic Polynomials, Order of Polynomials and Primitive Polynomials, Irreducible Polynomials, Construction of Irreducible Polynomials, Factorization of Polynomials

MATH333 - Matrix Analysis
Preliminaries, Eigenvalues, Eigenvectors, and Similarity, Unitary Equivalence and Normal Matrices, Canonical Forms, Hermitian and Symmetric Matrices, Norms for Vectors and Matrices, Location and Perturbation of Eigenvalues, Positive Definite Matrices, Nonnegative Matrices. ●Prerequisite: MATH 231

MATH357 - Functional Analysis
Vector Spaces, Hamel Basis, Linear Operators, Equations in Operators, Ordered Vector Spaces, Extension of Positive Linear Functionals, Convex Functions, Hahn-Banach Theorem, The Minkowski Functional, Seperation Theorem, Metric Spaces, Continuity and Uniform Continuity, Completeness, Baire Theorem, Normed Spaces, Banach Spaces, The Algebra of Bounded Linear Operators on Banach Spaces, Hilbert Spaces and basic concepts.●Prerequisite: Math 235

MATH360 - Introduction to Theory of Ordinary Differential Equations
First Order Ordinary Differential Equations, The Existence and Uniqueness Theorem, Systems and Higher Order Ordinary Differential Equations, Linear Differential Equations, Boundary Value Problems and Eigenvalue Problems, Oscillation and Comparison Theorems.

MATH363 - Calculus on Time Scales
The h-derivative and The q-derivative, The concept of a time scale, Differentiation on Time Scales, Integration on Time Scales, Taylor’s Formula on Time Scales. ●Prerequisite: MATH 136

MATH365 - Approximation Theory
Preliminaries, Convexity, Chebychev Solution of Inconsistent Linear Systems, Interpolation, Approximation of Functions by Polynomials, Least-Squares Approximation.

MATH372 - Topology
Fundamental Concepts, Functions, Relations, Sets and Axiom of Choice, Well-ordered Sets, Topological Spaces, Basis, The Order Topology, The Subspace Topology, Closed Sets and Limit Points, Continuous Functions, The Product Topology, Metric Topology, The Quotient Topology, Connectedness and Compactness, Countability and Separation Axioms, The Fundamental Group, Classification of Surfaces.

MATH378 - Partial Differential Equations
Basic Concepts. First Order Partial Differential Equations. Types and Normal Forms of Second Order Linear Partial Equations. Separation of Variables. Fourier Series. Hyperbolic, Parabolic, and Elliptic Equations. Solution of the Wave Equation.

MATH381 - Numerical Analysis
Computational and Mathematical Preliminaries, Numerical Solution of Nonlinear Equations and Systems of Nonlinear Equations, Numerical Solution of Systems of Linear Equations, Direct and Iterative Methods, The Algebraic Eigenvalue Problem, Interpolation and Approximation, Numerical Differentiation and Integration, Numerical solution of ODEs

MATH409 - Summer Training
In the “Mathematical Finance Certificate” program, the students have to do a 4-weeks practice in financial institutions after taking the courses Math 313 and Math 316. The main objectives of summer training include implementing the theoretical knowledge into various applications, improving teamwork abilities, observation of the various aspects of the financial systems and getting real life experience. After summer training, students are expected to submit a written report.

MATH417 - Computational Methods of Mathematical Finance
Introduction to MATLAB, Finite difference formulae, The explicit and implicit finite difference methods, The Crank-Nicolson method, European option pricing by the heat equation, pricıng by the Black-Scholes equation, Pricing by an explicit, an implicit and Crank-Nicolson method, Pricing American options, Projected SOR and tree methods, Pseudo-Random numbers, Inverse transform, Acceptance-Rejection and Box-Muller methods, The polar method of Marsaglia, Monte Carlo integration, Option pricing by Monte Carlo simulation.

MATH419 - History of Mathematics II
Early Middle Ages European mathematics (c. 500–1100) Mathematics of the Renaissance: Rebirth of mathematics in Europe (1100–1400) Early modern European mathematics (c. 1400–1600): Solution of the cubic equation and consequences. Invention of logarithms. Time of Fermat and Descartes. Development of the limit concept. Newton and Leibniz. The age of Euler. Contributions of Gauss and Cauchy. Non-Euclidean geometries. The arithmetization of analysis. The rise of abstract algebra. Aspects of the twentieth century.

MATH425 - Final Project
Students will be given planned projects based on either Coding Theory or Cryptography courses taken in the program. Students will be working (either individually or in small teams) under close supervision of a faculty member as an advisor of the project. The projects will be reviewed by a committee of instructors in related disciplines.

MATH427 - Introduction to Crytopgraphy
Basics of Cryptography, Classical Cryptosystems, Substitution, Review of Number Theory and Algebra, Public-key and Private-key Cryptosystems, RSA Cryptosystem, Diffie-Hellman Key Exchange, El-Gamal Cryptosystem, Digital Signatures, Basic Cryptographic Protocols.

MATH437 - Statistical Methods and Financial Applications
Central Tendency/Dispersion Measures, Moments, Maximum Likelihood Estimation, Correlation and Simple Linear Regression, Multi Regression Model, Autocorrelation and Multi Collinearity on Regression Models, Portfolio Theory, CAPM and ARMA Approaches

MATH463 - Applied Mathematics
Calculus of Variations and Applications, Integral Equations and Applications.

MATH467 - Dynamical Systems and Chaos
One-dimensional dynamic systems. Stability of equilibria. Bifurcation. Linear systems and its stability. two-dimensional dynamic systems. Liapunov’s direct method and method of linearization. 3-dimensional dynamic systems.

MATH482 - Numerical Methods for Ordinary Differential Equations
Existence, Uniqueness and Stability Theory. IVP: Euler’s Method, Taylor Series Method, Runge-Kutta Methods, Explicit and Implicit methods. Multistep methods based on Integration and Differentiation. Predictor–Corrector methods. Stability, convergence and error estimates of the methods. Boundary Value Problems: Finite Difference Methods, Shooting Methods, Collocation methods.

MATH483 - Special Functions of Applied Mathematics
Gamma and Beta functions. Pochhammer's symbol. Hypergeometric series. Hypergeometric differential equation. Generalized hypergeometric functions. Bessel function; the functional relationships, Bessel's differential equation. Orthogonality of Bessel functions. ● Prerequisite: Math 262 or Math 276 or Consent of the instructor

MATH484 - Classical Orthogonal Polynomials
Generating Functions. Orthogonal Polynomials. Legendre polynomials. Hermite polynomials. Laguerre polynomials. Tchebicheff polynomials. Gegenbauer polynomials. ● Prerequisite: Math 262 or Math 276 or Consent of the instructor

MATH485 - Theory of Difference Equations
The Difference Calculus, Linear Difference Equations, Linear Systems of Difference Equations, Self-adjoint Second Order Linear Equations, The Sturm-Liouville Eigenvalue Problem, Boundary Value Problems for Nonlinear Equations.

MATH486 - Mathematical Modeling
Differetial Equations and Solutions, Models of Vertical Motion, Single-Species Population Models, Multiple-Species Population Models, Mechanical Oscillators, Modeling Electric Circuits, Diffusion Models.

MATH495 - Stochastic Processes
Basic notions of probability theory. Reliability theory. Notion of a stochastic process. Poisson processes. Markov chains. Markov decision processes.

MCS401 - Algorithms
Design and Analysis of Algorithms, O,o,ω,Ω,Θ Notations, Lower and Upper Bound Theory, Divide and Conquer Algorithms, Recurrences, Dynamic Programming, Complexity of Sorting and Searching Algorithms, Greedy Algorithms, Greedy Algorithms vs. Dynamic Programming, Elementary Graph Algorithms, NP-Completeness

Service Courses Given to Other Departments

MATH101 - Introduction to Calculus
Course Description : Basic algebra, Graphs, Functions and Their Graphs, Equations and Inequalities, Polynomials and Rational Functions, Exponential and Logarithmic Functions, System of Equations, Matrices, Determinants.

MATH102 - Calculus for Management and Economics Students
Limits and Continuity, Derivative, Applications of Derivative, Integration, Applications of Integral, Functions of Several Variables, Partial Derivatives, Extrema of Functions of Several Variables. ●Prerequisite:Math101

MATH103 - General Mathematics
Sets, numbers and their properties, identities, equations and inequalities, polinomials, coordinate system in plane, graphs of lines and quadratic equations, functions, trigonometry, polar coordinates, complex numbers, systems of linear equations, matrices and determinants.

MATH104 - Single Variable Calculus
Review of Functions, Trigonometric Functions, Exponential and Logarithmic Functions, Limit and Continuity, Derivative, Applications of the Derivative, Definite and Indefinite Integrals, Techniques of Integration, Areas and Volumes.

MATH105 - Introduction to Calculus
Basic algebra, Graphs, Functions and Their Graphs, Equations and Inequalities, Polynomials and Rational Functions, Exponential and Logarithmic Functions, System of Equations, Matrices, Determinants.

MATH106 - Calculus for Management and Economics Students
Limits and Continuity, Derivative, Applications of Derivative, Integration, Applications of Integral, Functions of Several Variables, Partial Derivatives, Extrema of Functions of Several Variables.

MATH107 - Basic Mathematics I
Sets, numbers, intervals, absolute value, exponential and radicals, equations and inequalities, polynomials, coordinate system in the plane, equations of line and conics in the plane and their graphs, systems of linear equations, matrices and determinants.

MATH108 - Basic Mathematics II
Functions, trigonometric functions, exponential and logarithmic functions, Limits and continuity, Derivative, applications of derivative, Definite and indefinite integrals, integration techniques, Area and volume computation.

MATH151 - Calculus I
Preliminaries, Limits and Continuity, Differentiation, Applications of Derivatives, L'Hopital’s Rule, Integration, Applications of Integrals, Integrals and Transcendental Functions, Integration Techniques, and Improper Integrals.

MATH152 - Calculus II
Sequences, Infinite Series, Vectors in the Plane and Polar Coordinates, Vectors and Motions in Space, Multivariable Functions and Their Derivatives, Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular, Cylindrical and Spherical Coordinates.

MATH157 - Extended Calculus I
Preliminaries, Limits and Continuity, Differentiation, Applications of Derivatives, L'Hopital’s Rule, Integration, Applications of Integrals, Integrals and Transcendental Functions, Integration Techniques, and Improper Integrals, Sequences.

MATH158 - Extended Calculus II
Infinite Series, Vectors in the plane and Polar Coordinates. Vectors and Motions in Space, Multivariable Functions and Their Derivatives, Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Coordinates, Triple Integrals in Rectangular, Cylindrical and Spherical Coordinates, Line Integrals, Independence of path, Green’s Theorem.

MATH211 - Discrete Mathematics with Applications
Analysis and Complexity of Algorithms, Elements of Discrete Probability Theory, Recursive and Iterative Implementations, Sorting and Searching Algorithms, Graphs, Trees and Paths.

MATH274 - Complex Variables and Applications
Complex Numbers and Functions. Analytic Functions. Elementary Functions. Line Integral and Cauchy Theorem. Power, Taylor, Maclaurin Series and Laurent series. Residues and Poles. Conformal Mapping.

MATH275 - Linear Algebra
Linear Equations and Matrices, Real Vector Spaces, Inner Product Spaces, Linear Transformations and Matrices, Determinants, Eigenvalues and Eigenvectors.

MATH276 - Differential Equations
First Order, Higher Order Linear Ordinary Differential Equations, Series Solutions of Differential Equations, Laplace Transforms, Linear Systems of Ordinary Differential Equations, Fourier Analysis and Partial Differential Equations.

STAT201 - Introduction to Probability and Statistics -I
Basic Definitions, Tables and Graphs, Central Tendency Measures, Central Dispersion Measures, Probability Concept, Conditional Probability, Bayesian Approach, Random Variables, Expected Value, Binomial and Normal Distributions.

STAT201T - Introduction to Probability and Statistics-I
Basic Definitions, Tables and Graphs, Central Tendency Measures, Central Dispersion Measures, Probability Concept, Conditional Probability, Bayesian Approach, Random Variables, Expected Value, Binomial and Normal Distributions.

STAT202 - Introduction to Probability and Statistics-II
Sampling and Sampling Distributions, Central Limit Theorem, Point Estimation, Confidence Interval, Hypothesis Testing, Regression and Correlation, Variance Analysis

STAT202T - Introduction to Probability and Statistics-II
Sampling and Sampling Distributions, Central Limit Theorem, Point Estimation, Confidence Interval, Hypothesis Testing, Regression and Correlation, Variance Analysis

STAT211 - Elementary Statistics
Descriptive Statistics such as mean, median mode and standard deviation, The Notion of Probability, Random Event/ Experiment, Conditional Probability, Statistical Independency, Random Variables, Probability Distribution Table, Binomial Distribution and Normal Distribution.

Service Courses Taken From Other Departments

ENG101 - English for Academic Purposes I
ENG101 consists of academic skills, such as reading comprehension, vocabulary building and critical analysis of texts. In this frame, listening and note-taking, class discussions, presentations, writing, research assignments and use of technology are some of the important activities.

ENG102 - English for Academic Purposes II
ENG102 elaborates on academic skills such as reading comprehension, listening, class discussions about the topic of the unit, vocabulary building and critical analysis of texts. It also includes research assignments and response paper and graph writing. Skills like listening and note-taking, analysis of written products, portfolio keeping and use of technology are elaborated in this course, as well.

ENG201 - English for Academic Purposes III
The course consists of mainly advanced reading and writing skills, applying critical reading skills and strategies, identifying the organization of a reading text, main ideas of the texts, and the author’s main purpose, summarizing a given text, outlining and writing an argumentative essay. Some parts of the input are in flipped learning mode.

ENG204 - Report Writing Skills
This course includes research-based report writing skills. The content includes types of reports and models; the choice of topics, formation of thesis statements, writing paraphrases and summaries, preparation of report outlines, evaluation of print and electronic sources, in-text and end-of-text citation, report presentation in oral and written format. Flipped learning method is utilised to a great extent.

HIST101 - Principles of Atatürk and History of Turkish Revolution I
The decline of the Ottoman Empire and the developments leading to the Turkish Revolution.

HIST102 - Principles of Atatürk and History of Turkish Revolution II
Foundation of the Turkish Republic and principles of Mustafa Kemal Atatürk

ORY 400 - Participation in Social and Cultural Activities
Students must attend at least one social/cultural activity in each semester or at least two activities in each academic year. The activities are announced on the webpage of the departments. The students get an attendance certificate for the participation of each activity. To get a passing grade from this course, students should submit these certificates to their advisors.

PHYS 101 - General Physics I
Measurement; Motion Along a Straight Line; Vectors; Motion in Two and Three Dimensions; Force and Motion I; Force and Motion II; Kinetic Energy and Work; Potential Energy and Conservation of Energy; Center of Mass and Linear Momentum; Rotation; Rolling, Torque, and Angular Momentum; Equilibrium and Elasticity.

PHYS 102 - General Physics II
Electric Charge; Electric Fields; Gauss' Law; Electric Potential; Capacitance; Current and Resistance; Circuits; Magnetic Fields; Magnetic Field due to Currents; Induction and Inductance

TURK 101 - Turkish Language I
Historical development, structure, and usage of Turkish language, Practice on texts.

TURK 102 - Turkish Language II
Historical development, structure, and usage of Turkish language, Practice on texts