Mathematics and Computer Science

Department of Mathematics was established as one of the first departments shortly after the foundation of EMU. At the beginning, its mission was just to provide service courses in Mathematics and Computer Science. Over the past 30 years, the department has been evolving to one of the biggest and most international departments of EMU. The Department has become one of the most scholarly and competitive mathematics departments in the Turkish-speaking region and the Middle East. The main aim of the department is to educate students in becoming competitive at the international arena and providing high quality educational and research services in their own countries. The Mathematics and Computer Sciences Program is offered by the Mathematics Department.

General Information

Students attending the undergraduate program specialise in the areas of mathematics and computer science. The department’s tendency of offering these two programs is not only a preferred system in today’s world but also provides the graduates better employment opportunities. In order to provide its students with opportunities at international standards, the department continuously updates its curriculum according to developments and changing trends in the area.

Education

Along with core courses in the areas of mathematics and computer science, every undergraduate student during his/her study in the department has the opportunity to choose from among the elective courses leading to the certificate programs in Managerial Economics and Financial Management offered by the Departments of Economics and Finance. Successful completion of the requirements of these certificate programs allows the student to receive the respective certificate. Students studying this undergraduate program may also take pedagogical formation courses and become Mathematics or Mathematics/Computer teachers.

Facilities

Academic staff at the Department of Mathematics consists of 19 prominent academicians who have devoted themselves to teaching and research. More specifically, the academic staff members consist of 4 professors, 5 associate professors and 10 assistant professors. All full time academic staff are PhD holders, granted the degrees from various prominent international institutions. Besides, 11 part time staff and 19 full time research assistants are also employed at the department.

Career Opportunities

Program graduates successfully pursue postgraduate study opportunities in Eastern Mediterranean University and other prominent universities in Turkey, Europe and North America. Graduates of the department have the following career opportunities:

  • Scientific Research, Design and Development
  • Teaching
  • Statistical Work
  • Risk Management
  • Financial Management
  • Managerial Economics
  • Management Services
  • Software Development
  • Tax Inspectorate
  • Banking
  • Accountancy

Contact

Tel: +90 392 630 1227
Fax: +90 392 365 1314
E-mail: math@emu.edu.tr
Web: http://math.emu.edu.tr

* You can contact the department and / or faculty for detailed information about elective courses.

Semester 1

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Sets, set operations and numbers. Polynomials, factorization, equations and root finding. Real axis, labeling integers, rationals and some irrationals on the number axis. Cartesian coordinates. Lines. Graphs of equations and quadratic curves. Functions and graphs of functions. Limits and continuity. Derivatives. Rules of differentiation. Higher order derivatives. Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals. Fundamental Theorem. Techniques of integration. Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Infinite series. Geometric series. Power series. Taylor series and binomial series.

Calculus - I (MATH151)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): 1 | Tutorial (hrs/week): - | ECTS: 6
Limits and continuity. Derivatives. Rules of differentiation. Higher order derivatives. Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals. Fundamental Theorem. Techniques of integration. Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Infinite series. Geometric series. Power series. Taylor series and binomial series.

Analytic Geometry (MATH131)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Cartesian coordinates in 2 and 3 dimensional spaces. Vectors. Equations of lines and planes. Conics. Cylindrical and spherical coordinates. Identifying and sketching some elementary curves and surfaces.
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Set theory, functions and relations; introduction to set theory, functions and relations, inductive proofs and recursive definitions. Combinatorics; basic counting rules, permutations, combinations, allocation problems, selection problems, the pigeonhole principle, the principle of inclusion and exclusion. Generating functions; ordinary generating functions and their applications. Recurrence relations; homogeneous recurrence relations, inhomogeneous recurrence relations, recurrence relations and generating functions, analysis of algorithms. Propositional calculus and boolean algebra; basic boolean functions, digital logic gates, minterm and maxterm expansions, the basic theorems of boolean algebra, simplifying boolean function with karnaugh maps. Graphs and trees; adjacency matrices, incidence matrices, eulerian graphs, hamiltonian graphs, colored graphs, planar graphs, spanning trees, minimal spanning trees, Prim's algorithm, shortest path problems, Dijkstra's algorithms .
Credit: 4 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 2 | ECTS: 6
Organization of a digital computer. Number systems. Algorithmic approach to problem solving. Flowcharting. Concepts of structured programming. Programming in at least one of the programming languages. Data types, constants and variable declarations. Expressions. Input/output statements. Control structures, loops, arrays.
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
ENGL191 is a first-semester freshman academic English course. It is designed to help students improve the level of their English to B1+ level, as specified in the Common European Framework of Reference for Languages. The course connects critical thinking with language skills and incorporates learning technologies such as IQ Online. The purpose of the course is to consolidate students’ knowledge and awareness of academic discourse, language structures, and lexis. The main focus will be on the development of productive (writing and speaking) and receptive (reading) skills in academic settings.
Credit: 3 | Lecture Hour (hrs/week): 5 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
ENGL 181 is a first-semester freshman academic English course. It is designed to help students improve the level of their English to B1+ level, as specified in the Common European Framework of Reference for Languages. The course connects critical thinking with language skills and incorporates learning technologies such as IQ Online. The purpose of the course is to consolidate students’ knowledge and awareness of academic discourse, language structures, and lexis. The main focus will be on the development of productive (writing and speaking) and receptive (reading) skills in academic settings.

Atatürk İlkeleri ve İnkilap Tarihi (HIST280)

Credit: 2 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 3

Turkish as a Second Language (TUSL181)

Credit: 2 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 3

Semester 2

Calculus - II (MATH152)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Vectors in R3. Lines and Planes. Functions of several variables. Limit and continuity. Partial differentiation. Chain rule. Tangent plane. Critical Points. Global and local extrema. Lagrange multipliers. Directional derivative. Gradient, Divergence and Curl. Multiple integrals with applications. Triple integrals with applications. Triple integral in cylindrical and spherical coordinates. Line, surface and volume integrals. Independence of path. Green's Theorem. Conservative vector fields. Divergence Theorem. Stokes' Theorem.

Geometry (MATH124)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -

Linear Algebra (MATH106)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Cartesian coordinate system; Linear equations and lines, system of linear equations, quadratic equations, functionsSelected application to economics and accounting. Matrices, determinants, systems of linear equations and their solutions using Cramer's Rule. . Set theory, counting theory, discrete probability. Descriptive statistics
Credit: 4 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 2 | ECTS: 6
Advanced programming concepts, strings and string processing. Record structures. Modular programming. Procedures, subroutines and functions. Communication between program modules. Scopes of variables. Recursive programs. Introduction to file processing. Applications in the programming languages.
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): 1 | Tutorial (hrs/week): - | ECTS: 6
ENGL192 is a second-semester freshman academic English course. It is designed to help students improve the level of their English to B2 level, as specified in the Common European Framework of Reference for Languages. The course connects critical thinking with language skills and incorporates learning technologies such as IQ Online. The purpose of the course is to consolidate students’ knowledge and awareness of academic discourse, language structures, and lexis. The main focus will be on the development of productive (writing and speaking) and receptive (reading) skills in academic settings.
Credit: 3 | Lecture Hour (hrs/week): 5 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
ENGL182 is a second-semester freshman academic English course. It is designed to help students improve the level of their English to B2 level, as specified in the Common European Framework of Reference for Languages (CEFR). The course connects critical thinking with language skills and incorporates learning technologies such as IQ Online. The purpose of the course is to consolidate students’ knowledge and awareness of academic discourse, language structures, and lexis. The main focus will be on the development of productive (writing and speaking) and receptive (reading) skills in academic settings.

Semester 3

Real Analysis - I (MATH209)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Review on sets and functions, review on proof techniques, finite and infinite sets, natural numbers system, countable and uncountable sets, rational numbers system, real numbers system and its properties, supremum and infimum, sequences and limits, monotone sequences, subsequences, Bolzano-Weierstrass theorem, limit supremum, limit infimum, Cauchy criterion for convergence, divergence to infinity, continuous functions, examples of discontinuity, combinations of continuous functions, continuous functions on intervals, boundedness theorem, maximum-minimum theorem, Bolzano intermediate value theorem, uniform continuity, uniform continuity theorem, monotone and inverse functions, continuous inverse theorem, derivative and its properties, example of continuous and nowhere differentiable function, chain rule, derivative of inverse function, mean value theorems and their applications, intermediate value property of derivatives., L?Hospital?s rules, Taylor?s theorem, Riemann integration, partitions and integral sums, properties of Riemann integrals, integrability of continuous and monotone functions, fundamental theorem of calculus.
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Vector spaces, subspaces, basis and dimension, coordinates, row equivalence. Linear transformations, representation by matrices, linear functionals, dual. Algebras, algebra and factorization of polynomials. Commutative rings, determinant function, permutations and properties of determinants. Characteristic values, the Cayley-Hamilton theorem, invariant subspaces, direct-sum decompositions, the primary decomposition theorem, cyclic decompositions and rational form, the jordan form, inner product spaces.

Algorihms and Data Structure (COMP211)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -

Physics - I (PHYS101)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Physical quantities and units. Vector calculus. Kinematics of motion. Newton`s laws of motion and their applications. Work-energy theorem. Impulse and momentum. Rotational kinematics and dynamics. Static equilibrium.

Logic (MATH231)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -

Semester 4

Real Analysis - II (MATH210)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Ordinary differential equations of the first order; separation of variables, exact equations, integrating factors, linear and homogeneous equations. Special first order equations; Bernoulli, Riccati, Clairaut equations. Homogeneous higher order equations with constant coefficients. Nonhomogeneous linear equations; variation of parameters, operator method. Power series solution of differential equations. Laplace transforms. Systems of linear differential equations.
Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Number and counting; odometer principle, principle of induction, order of magnitude, handshaking lemma, set notation. Subsets, partitions, permutations; subset, subset of fixed size, the binomial theorem, pascal's triangle, Lucas' theorem, permutations, estimates for factorials, Cayley's theorem on trees, Bell numbers, generating combinatorial objects. Recurrence relations and generating functions; Fibonacci numbers, linear recurrence relations with constant coefficients, derangements and involutions, Catalan and Bell numbers. The principle of inclusion and exclusion; PIE and its generalization, Stirling numbers and exponentials, even add odd permutations. System of distinct representatives; Hall's theorem. Extremal set theory; intersecting families, Erdos-Ko-Rado theorem, Sperner's theorem, the de Brujin-Erdos theorem. Graphs; trees and forests, Cayley's theorem, minimal spanning tree, Eulerian graphs, Hamiltonian graphs, Ore's theorem, gray codes, the traveling salesman, digraphs, networks, max-flow min-cut theorem , integrity theorem, Menger's theorem, Könsg's theorem, Hall's theorem, diameter and girth. Ramsey's theoremlthe pigeonhole principle, bounds for Ramsey's theorem, Applications, infinite version.
Credit: 3 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): 2 | ECTS: 6
COMP302 Computer Networks and Communications Foundations of Computer Networks and Its Architecture, topologies and types of Computer Network, Protocols and Procedures of Computer Network Systems and OSI model, Network connection devices active and passive devices, LAN communication technologies (802.X and Ethernet, token ring FDDI), WAN communication technologies (x25, DSL, ISDN, FR etc.), Network Operating Systems, Communication on Network Systems, Management of Network System, communication on internet: E-Mail, instant message programs, sending and receiving files on internet, using FTP programs, Network security, set up web servers like DHCP, DNS (domain name system), Web server, database server.

Physics - II (PHYS102)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Kinetic theory of ideal gases. Equipartition of energy. Heat, heat transfer and heat conduction. Laws of thermodynamics, applications to engine cycles. Coulombs law and electrostatic fields. Gauss's law. Electric potential. Magnetic field. Amperes law. Faradays law.

University Elective - I (UE01)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

Semester 5

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Introduction to probability and statistics. Operations on sets. Counting problems. Conditional probability and total probability formula, Bayes' theorem. Introduction to random variables, density and distribution functions. Expectation, variance and covariance. Basic distributions. Joint density and distribution function. Descriptive statistics. Estimation of parameters, maximum likelihood estimator. Hypothesis testing.
Credit: 3 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): 3 | ECTS: 6
Introduction to object technology; objects, attributes, methods, classes, constructor. Basic C++ types and programs; integer objects, and simple expressions, C++ input and output, character objects, real number objects, string objects. Describing and declaring classes; class description, declaring and using objects, class declaration, function prototypes, with default values. Selection statements; logical expressions, if statement, nested selection statements. Loop structures. Developing your own classes; implementing classes, organizing program source code, error checking. Additional C++ control structures; multiple selection, enumeration types, date class, for loop, advanced loop concepts, argument passing. Arrays; array storage, initializing arrays, arrays as arguments, arrays of objects, arrays of class data members, string objects, multidimensional arrays.

Internet Programming and Web Design (COMP311)

Credit: 3 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): 3 | ECTS: -

Complex Analysis (MATH236)

Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Complex numbers and complex plane. Analytic functions. Cauchy-Riemann equations, harmonic functions. Elementary functions: exponential and trigonometric functions, logarithmic functions. Contours, contour integrals, Cauchy-Goursat theorem. Liouville?s theorem and the fundamental theorem of algebra. Power series, Taylor series, Laurent series, residues and poles, residue theorems, applications of residues. Linear transformations.

University Elective - II (UE02)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

Programming Languages (COMP436)

Credit: 3 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): 2 | ECTS: -

Semester 6

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Numerical error. Solution of nonlinear equations, and linear systems of equations. Interpolation and extrapolation. Curve fitting. Numerical differentiation and integration. Numerical solution of ordinary differential equations.
Credit: 4 | Lecture Hour (hrs/week): 4 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
First-Order Partial Differential Equations. The method of characteristics for solving linear first-order IVP. Nonlinear First-Order PDEs, Compatible Systems and Charpit’s Method. Second-Order Partial Differential. Canonical Forms. Fourier Series. Heat Equation, The Maximum and Minimum Principle. Method of Separation of Variables. The Wave Equation. The Inhomogeneous Wave Equation. The Laplace Equation. The Dirichlet BVP for a Rectangle.

Security and Information Assurance (COMP322)

Credit: 4 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): 21 | Tutorial (hrs/week): - | ECTS: -
Credit: 3 | Lecture Hour (hrs/week): 2 | Lab (hrs/week): - | Tutorial (hrs/week): 3 | ECTS: 6
Introduction to the evolution of database concepts. Data abstraction. Entity relationship model. Relational model. Relational algebra. Relational calculus. Integrity constraints. File and system structure, mapping relational data to files. Relational database design. Distributed databases. Database security. Cryptography, encryption and decryption.

Area Elective I (AE01)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

Semester 7

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: -
Groups, subgroups, cyclic groups, homomorphisms and isomorphisms, permutations and Cayley's Theorem, cosets and Lagrange's Theorem, quotient groups and the isomorphism theorems, Sylow's Theorem; Rings and fields, ideals and quotient rings, integral domains, prime and maximal ideals, the field of quotients, properties of integers; rings of polynomials, polynomials over C, R and Q, basic ideas of field extensions.

Big Data (COMP413)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: -

Operating Systems (COMP483)

Credit: 4 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 2 | ECTS: -
View and functions of operating systems. Interprocess communication, process scheduling. Memory management, multiprogramming, swapping, paging, virtual memory. File system, its security and protection mechanisms. Deadlocks. Study of operating systems introducing MS DOS, UNIX.

Statistics (MATH324)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): 1 | ECTS: 6
Introduction to statistics. Basic methods of working with observation data, histogram and ogive Descriptive statistics. Estimation of parameters, maximum likelihood estimator. Hypothesis testing. Linear regression.

Area Elective II (AE02)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

Semester 8

Data Analytics (COMP414)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: -

Applied Functional Analysis (MATH302)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: -

Area Elective III (AE03)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

University Elecitive - III (UE03)

Credit: 3 | Lecture Hour (hrs/week): 3 | Lab (hrs/week): - | Tutorial (hrs/week): - | ECTS: 6

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