· Web viewCode Term Level Type Language Credit hours/week Lecture Lab Credit ECTS Credit Mat 540 Spring MS Elective Turkish 3 0 3 10 Course Prerequisites None Name of Instructors

FACULTY OF ARTS AND SCIENCES

Course Title Real and Complex Analysis IDepartment MathematicsDivision in the Dept. Analysis and Function Theory

Code Term Level Type LanguageCredit hours/week

Lecture Lab Credit ECTS CreditMAT501 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors Assoc. Prof. Dr. İbrahim Çanak

Instructor Information

Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09010 AydınTel: 256 21284 98 -2115 [email protected]

Course Objective and brief Description

This course aims to acquaint students with the fundamental notions of Real and Complex analysis including abstract integration, positive Borel measures, -spaces, elementary Hilbert theory, examples of Banach spaces techniques, complex measures, differentiation and integration on product spaces.

Textbook and Supplementary readings1 Real and Complex Analysis, by Walter Rudin, 1987.234

COURSE CALANDER / SCHEDULEWeek Lecture topics Practice/Lab/Field

1 Abstract integration

2 Abstract integration

3 Positive Borel measures

4 Positive Borel measures

5 -spaces

6 -spaces

7 Elementary Hilbert theory

8 Elementary Hilbert theory

9 Examples of Banach spaces techniques

10 Examples of Banach spaces techniques

11 Complex measures

12 Complex measures

13 Differentiation and integration on product spaces

14 Final ExamCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Algebra I Department Mathematics Division in the Dept. Algebra and Number Theory


Lecture Lab Credit ECTS Credit

MAT503 Fall MS Obligatory Turkish 3 0 3 10Course Prerequisites None

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın


Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


This course gives the fundamental concepts of groups

Textbook and Supplementary readings1 Algebra,T.W.Hungerfort

2 Contemporary Abstract Algebra, J.A.Gallian 3 Basic Algebra I-II, N. Jacobson4 Basic Abstract Algebra, P.B. Bhattacharya, S.K.Jain, S.R. Nagpaul, Cambridge University Pres5 Fundamentals of Abstract Algebra, D.S.Malik, John M.Mordeson, M.K.Sen, , The McGraw-Hill Companies


1 Semigroups, Monoids and Groups

2 Homorphisms and Subgroups

3 Cyclic Groups, Coset and Counting

4 Normal altgruplar , Quotient Groups

5 Isomorphism theorems

6 Symmetric,

7 Alternating and Dihedral Groups

8 Categories

9 Product, Coproduct and Free Objects-EXAM

10 Direct Products and Direct Sums

11 Free Abelian Group

12 Finitely Generated Abelian Groups

13 The Action of Group on a set

14 The Sylow Theorems

Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


mailto:[email protected]






Course Title TopologyDepartment MathematicsDivision in the Dept. Topology


Lecture Lab Credit ECTS creditMAT 505 Fall MS Obligatory Turkish 3 0 3 10

Course Prerequisites None

Name of Instructors Assist. Prof. Dr. Adnan MELEKOĞLU


Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDINTel: 256 2128498 [email protected]

Course Objective and Brief Description

The aim of this course is to provide basic knowledge on General Topology.

Textbook and Supplementary Readings1 Gemignani, M., (1990) Elementary Topology, Dover Publications2 Munkres, J.R. (1999) Topology, Prentice Hall

COURSE CALENDAR / SCHEDULEWeek Lecture Topics

1 Metric spaces

2 Topological spaces

3 Bases and sub bases

4 Continuous functions

5 Subspaces

6 Product spaces

7 Quotient spaces

8 Midterm Exam

9 Sequences

10 Nets

11 Filters

12 Separation axioms

13 Compactness

14 ConnectednessCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Commutative Rings

Department Mathematics Division in the Dept. Algebra and Number Theory



MAT507 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Assist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Assist Prof. Dr. Hülya İnceboz


[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


In order to study open problems in Algebraic Geometry, commutative rings must be studied. This course’s aim is to introduce the fundmental concepts of Commutative Rings.

Textbook and Supplementary readings1 Commutative ring theory, H. Matsumura, Cambridge Unv. Press, 1997


1 Rings and ıdeals

2 Localization of rings

3 Modules

4 Exact sequences

5 Prime and Primary ideals

6 Primary decomposition

7 Noetherian rings and modules

8 Noetherian rings and modules

9 Artinian rings and modules Ara sınav

10 Extension of rings

11 Hilbert Nullstellensats

12 Hilbert Nullstellensats

13 Dimension theory

14 Dimension theoryCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Field Extensions







Department MathematicsDivision in the Dept. Algebra and Number Theory




Name of Instructors Prof. Dr. Hatice Kandamar, Yrd. Doç. Dr. Selma Altınok


Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 [email protected], [email protected]


This course gives the fundamental concepts of field extensions.

Textbook and Supplementary Readings1 Algebraic Extension of Fields, Paul J. McCarty2


1 Algebraic Extensions: Seperability of extensions, normal extensions, Finite Fields2 Algebraically Closed Fields, Norm and Traces3 Galois Theory: Automorphisms of extensions, the Fundamental Theorem of Galois theory4 Cyclotomic Fields, Cyclic Extensions

5 Multiplicative Kummer Theory, Additive Kummer Theory, Solution of Polynomial Equations by Radicals

6 Infinite Galois Extensions, Introduction to Valuation Theory7 Value Groups and Residue Class Fields8 Midterm Exam

9 Relatively Complete Fields10 Extension of Valued Fields11 Ramification and Residue Class Degree, Unramified and Tamely Ramified Extensions12 The Different, Extension with Seperable, Ramification Groups13 Dedekind Fields: The Fundamental Theorem of Dedekind Fields14 Extension of Dedekind Fields, Factoring of Ideals in Extensions.

Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Number TheoryDepartment Mathematics



Division in the Dept. Algebra and Number Theory




Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Assist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Asist. Prof. Hülya İnceboz


[email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


Number Theory is a branch of science which investigate intigers and things related to them. Its aim is to teach students fundamental concepts of Number Theory

Textbook and Supplementary readings1 Number Theory, Z. I. Borevich and I.R. Shafarevich, Academic Press, 1967


1 Congruencies and P-adic numbers

2 Quadratic forms and Rational quadratic forms

3 Decomposition of forms and representations of numbers

4 Classification of modules

5 Representation of numbers by binary quadratic forms

6 Divisors

7 Değerler

8 Dedekind halkalar

9 Dedekind halkalarAra sınav

10 Quadratic fields

11 Extension of fields by valuations

12 Extension of fields by valuations

13 Numbers of divisor class and their Formula

14 Numbers of divisor class and their FormulaCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Differentiable ManifoldsDepartment MathematicDivision in the Dept. Geometry









Name of Instructors Assist. Prof. Dr. Leyla Onat


Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AdınTel:02562128498 [email protected]


The main goal is this course to provide a working knowledge of manifolds, tensors and differential forms.

Textbook and Supplementary readings1 Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry Academic

Press, New York,1975COURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 Define manifold

2 Construct the topology of a manifolds

3 Define the tangent vectors

4 D,ifferentiable maps between manifolds

5 Define the Riemannian metric and Riemannian manifold

6 Define the Lie Bracket

7 Solve the problem about what he has learned

8 Observe the Koszul Formulas

9 Define tensors and tensor fields

10 Take derivative on the tensor field

11 Define spaces of constant curvature

12 Define spaces of constant curvature Define the Ricci tensor and scalar curvature




Course Title Mathematical Statistics IDepartment MathematicsDivision in the Dept. Application Mathematic

tel:02562128498


Lecture Lab Credit ECTC Credit


Name of Instructors Assist. Prof. Dr. Hüsnü Barutoğlu


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected]


This course introduces fundamental probability and mathematical statistical theory

Textbook and Supplementary readings1 İnal C. Olasılıksal ve Matematiksel İstatistik,Hacettepe Üniv. Fen Fak yayınları No: 16, 19822 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.3 Alexander, W.H. –Elements of Mathematical Statistics John Wiley and Sons, NewYork,1961.4 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.

NewYork,1963COURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 Permutation, Combination

2 Probability

3 Discrete distribution functions

4 Continuous distribution function

5 Expected value

6 Arithmetic mean, Variance

7 Moment generation function

8 Characteristic function

9 QUIZ

10 Maping of variable

11 Estimations Theory

12 Point Estimation

13 Interval Estimation

14 ExercisesCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Foundation StatisticsDepartment MathematicsDivision in the Dept. Application Mathematic









This course introduces fundamental probability and mathematical statistical theory

Textbook and Supplementary readings1 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.2 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.

NewYork,1963.34


1 Measures of location

2 Measures of distribution

3 Moments

4 Regression

5 Correlation

6 Normal distribution

7 Standard normal distribution

8 Confidence intervals

9 QUIZ

10 Student-t distribution

11 Chi-square distribution

12 Test of hypothesis.

13 Test of hypothesis.

14 Test of hypothesis.Final Exam



Course Title Regression AnalysisDepartment MathematicsDivision in the Dept. Applied Mathematics






InstuctorsInformation



This course introduces fundamental experiment design and analysis of variance.

Textbook and Supplementary readings1 Mood A.M.,GraybillF.G., An Indroduction to Statistics Theory Çeviri Prof.Dr. Süeda Moralı Özarkadaş

Matbaası İstanbul 1973.2 Kendal M.,Stuart A., Ord J.K., The Advanced Theory of Statistics. Charles griffin com. London 1983.3 Graybill F.A., An Indroduction to Linear Statistical Models, McGraw-Hill Book Com. İnc. NewYork 1961.

COURSE CALANDER/ SCHEDULEWeek Lecture topics Prectice/Lab/Field

1 Point estimation and interval estimation

2 Testing hypothesis

3 The multivariate normal distribution

4 Distribution of quadratic forms

5 Linear models

6 The general linear of full rank

7 Functional relationships

8 Regression models

9 Experimental design models

10 Factorial models

11 Analysis of varians

12 Incomplete block models

13 Latin squares

14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.


Course Title Mathematical ModellingDepartment MathematicsDivision in the Dept. Applied Mathematics

Code Term Level Type Language Credit hours/week



Name of Instructors Assist. Prof. Dr. Ali Filiz, Assist. Prof. Dr. Ali IŞIK


Adnan Menderes Üniversity, Faculty of arts and science 09100 AydınTel:256 2128498 [email protected], [email protected]


This course aims to acquaint students with the basic knowledge of numerical solution of some kinds of integral equations and ODEs. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.

Textbook and Supplementary readings1 Paul Davis, (1999), Differential Equations : Modeling with MATLAB, Prentice Hall.2 G. A Turskey, F. Yuan, D. K. Katz, (2004), Tranport Phenomena in Biological Systems3 S. M. Dunn, A. Constantides, P. V. Moghe, (2006) Numerical methods in Biomedical Engineer, Academic

pres. 4


1 Introduction to mathematical modelling

2 Applications in real life

3 Finite difference methods for ODEs,

4 Finite difference methods for PDEs

5 Numerical solution and stability of differential equations

6 Cauchy- Riemann equations

7 Local truncation errors

8 Midterm exam

9 Linear and non-linear differential equations

10 Population and logistic equations

11 Harvesting and toxicity

12 Time depend phenomena

13 Toxicity term via integral terms



Coerce Title Numerical solution of Differential EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMat 527 Fall MS Elective Turkish 3 0 3 10





This course aims to acquaint students with the basic knowledge of numerical solution of some differential equations. Students will be familiar with classification of equations initial and boundary value problems and relation between Volterra and Fredholm integrals. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.

Textbook and Supplementary readings1 Clay C. Rose, (2004), Differential Equations, Springer, second edition.2 B. R. Hunt, R. L. Lipsman, J. E. Osborn, J. M. Rosenberg, (2005), Differential Equations with MATLAB34


1 Introduction of MATLAB and differential equations

2 Ordinary differential equations., Initial and boundary value problems and solution of methods,

3 Numerical methods and their stabilities

4 Numerical solution of IVP and Volterra integral equations

5 Local truncation errors and order of convergence

6 Linear and non-linear differential equations

7 Single step methods for differential equations

8 Midterm exam

9 Linear and Nonlinear Volterra integral equations of the second kind

10 Numerical stability of Single step methods

11 Taylor series and Runge-Kutta methods

12 Butcher table and Runge-Kutta method And Adams methods

13 Numerical stability of Multi-step methods



Course Title Academic Software Department MathematicsDivision in the Dept. Applied Mathematics



Name of Instructors Assist. Prof. Dr. Ali Filiz




This course aims to acquaint students with the fundamentals of academic software. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing

Textbook and Supplementary readings1 LaTeX: A Document Preparation System, Leslie Lamport, 1992.234


1 Matematiksel yazılımın tarihi The history of academic software

2 İnternet and knowledge source

3 Search in the internet

4 LaTeX and mathematical writing

5 Project with LaTeX’de

6 Project via Ms Word

7 The comparasion LaTeX and Word

8 Project I

9 Article style

10 Book style

11 Thesis style

12 LaTeX’s error Messages

13 Prepare index and reference

14 Proje IICourse assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.


Course Title Mathematical Analysis IDepartment MathematicsDivision in the Dept. Analysis and Function Theory



MAT541 Fall MS Obligatory Turkish 3 0 3 10Course Prerequisites None





This course aims to acquaint students with the fundamental notions of mathematical analysis including the real and complex number systems, basic topology, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes Integral

Textbook and Supplementary readings1 Principles of Mathematical Analysis, Walter Rudin.234


1 Real and complex number systems

2 Real and complex number systems

3 Basic topology

4 Basic topology

5 Numerical sequences and series

6 Numerical sequences and series

7 Continuity

8 Continuity

9 Differentiation

10 Differentiation

11 Riemann-Stieltjes Integral



14 Final Exam

Course assesment will be weighted 50% for one quiz and 50% for the fin al exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.


Course Title Divegent Series IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory


Lecture Lab Credit ECTS CreditMAT551 Fall MS Elective Turkish 3 0 3 10






This course aims to acquaint students with the fundamental notions of divergent series including elementary Tauberian theorems, Tauberian theorems, A tauberian theorem for Euler method, Fourier series, Convergence of Fourier series, Convergence tests, Cesaro summability of Fourier series, Abel-Poisson summability of Fourier series, Riemann’s method of summation, Absolute convergence, Fourier transforms, Applications of summability to analytic continuation, the Borel exponential method, the Okada theorem

Textbook and Supplementary readings1 Divergent Series, G. H. Hardy234


1 Elementary Tauberian theorems

2 Tauberian theorems

3 A tauberian theorem for Euler method

4 Fourier series

5 Convergence of Fourier series

6 Convergence tests

7 Cesaro summability of Fourier series

8 Abel-Poisson summability of Fourier series

9 Riemann’s method of summation

10 Absolute convergence

11 Fourier transforms

12 Applications of summability to analytic continuation

13 the Borel exponential method and the Okada theorem

14 Final Exam



Course Title Riemann surfacesDepartment MathematicsDivision in the Dept. Topology


Lecture Lab Credit ECTS credit

MAT 555 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None





The aim of this course is to provide introductory knowledge for Riemann surfaces regarding them as the quotient spaces of Fuchsian groups.

Textbook and Supplementary Readings1 Jones G.A. and Singerman D. (1987) Complex Functions, Cambridge University Press2 Katok S. (1992) Fuchsian groups, The University of Chicago Press


1 Riemann surfaces

2 The methods of obtaining Riemann surfaces

3 Lattices

4 Riemann surfaces of genus one

5 Fuchsian groups

6 Generators and geometric properties of Fuchsian groups

7 Fundamental regions and quotient spaces of Fuchsian groups

8 Midterm Exam

9 Fuchsian groups whose quotient spaces are Riemann surfaces

10 Triangle groups

11 Platonic Riemann surfaces

12 Automorphisms of Riemann surfaces

13 Hyperelliptic Riemann surfaces

14 Symmetric Riemann surfacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Algebraic Geometry IIDepartment MathematicsDivision in the Dept. Topology and Geometry








This course is a continuation of Algebraic Geometry I. Its aim is to introduce the advanced subjects of Algebraic Geometry to students.

Textbook and Supplementary Readings1 Algebraic Geometry, R. Hartshorne2


1 Sheaves2 Sheaves3 Schemes, affine Schemes, Projective Schemes4 Schemes, affine Schemes, Projective Schemes5 Morphisms6 Sheaves of Modules7 Sheaves of Modules8 Midterm Exam

9 Divisors on Varietes or Schemes10 Divisors on Curves11 Cohomology and Cohomology Sheaves 12 Cohomology of Affine Schemes13 Cech Cohomology14 Cohomology of Projective Spaces

Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination


Course Title Groups and SymmetryDepartment MathematicsDivision in the Dept. Topology


Lecture Lab Credit ECTS creditMAT 559 Fall MS Elective Turkish 3 0 3 10Course Prerequisites None







The aim of this course is to provide knowledge for the geometric properties of groups by giving concrete examples.

Textbook and Supplementary Readings1 Armstrong, M.A. (1988) Groups and Symmetry, Springer


1 Groups, cyclic and dihedral groups

2 Subgroups and generators

3 Symmetry groups of regular polygons

4 Group action

5 The orbit and the stabilizer of a point

6 Permutations

7 Symmetry groups of regular polytopes

8 Midterm Exam

9 Finite rotation groups

10 Isometries in the Euclidean plane

11 Translations and rotations

12 Reflections and glide reflections

13 Euclidean groups and their quotient spaces

14 Euclidean groups with compact quotient spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Matrix AnalysisDepartment MathematicsDivision in the Dept. Algebra and Number Theory

Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS Credit

MAT561 Fall MS Elective Turkish 3 0 3 10Course None

Prerequisites

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist Prof. Dr. Selma Altınok, Asist Prof. Dr. Erdal Özyurt, Assist Prof. Dr. Semra Doğruöz, Asist. Prof. Hülya İnceboz

InstructorsInformation

ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


This course introduces fundamental concepts of linear algebra which are indispensable in all branches of basic science.

Textbook and Supplementary readings1 Matrix Analysis and Applied Linear Algebra, Roger A. Horn, Charles R. Johnson, 2001.2 Linear Algebra, K. Hoffman and R. Kuntze, Printice Hall 2.Edition, 1971.


1 Linear equations and matrices

2 Matrix algebra, some specail matrices,row and column operations

3 Echelon form in matrices, LU-decompositions

4 Vector spaces, linear independence,basis and dimensions

5 Homojen equation systems

6 Coordinates, isomorphisms, rank of matrix

7 Linear transformations, kernel, image

8 Matrix representation, of linear transformations

9 Linear functionals, Dual, MIDTERM

10 Determinants and its aplications

11 Eigenvalues and eigenvectors,

12 Diagonalization, similar matrices

13 Inner product spaces, R^2 and R^3 standart inner product spaces

14 Gram-Schmidt method, orthonormal setsCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Visual Programming IDepartment MathematicsDivision in the Dept. Applied Mathematics






Name of Instructors Asst. Prof. Dr. Ali FİLİZ


Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTelephone Number:0 256 2128498-2114 and 2116 [email protected]


This course aims to acquaint students with the fundamentals of visual programming. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing.

Textbook and Supplementary readings1 C Dersi Proglamlamaya Giriş, N. Ercil Çağıtay, G.Tokdemir, C. Fügen Selbes, Ç. Turhan, Bizim Büro

Basımevi, 2007.234


1 Visual programming setup

2 Programming languages and user interface

3 Programming languages and user interface

4 Using form

5 Using form

6 Form events

7 Form events

8 Constants

9 Project I

10 Variables

11 Operators

12 Control structures and loop structures

13 Arrays. Menus

14 Project II



Course Title Applications of MATHEMATICA in Mathematics EducationDepartment MathematicsDivision in the Dept. Applied Mathematics







MATHEMATICA is used by scientists and engineers in disciplines ranging from astronomy to zoology; typical applications include computational number theory, ecosystem modeling, financial derivatives pricing, quantum computation, statistical analysis, and hundreds more.

Textbook and Supplementary readings1 http://www.wolfram.com/2 The Student's Introduction to Mathematica : A Handbook for Precalculus, Calculus, and Linear Algebra

(Paperback), B. F. Torrence, Eve. A. Torrence, Camb. Univ. Press, 1999.3 The Mathematica book, 3rd Edition, S, Wolfram, Camb. Univ. Press, 1999.4


1 Introduction to MATHEMATICA

2 Common errors and suggestions

3 MATHEMATICA commands

4 Application of MATHEMATICA

5 Simple calculations for different subjects

6 Plotting functions

7 Combining two or more plots,

8 Project I

9 Algebra, Calculus

10 multivariable calculus and linear algebra with mathematica,

11 Derivatives and integrals

12 Special functions with MATHEMATICA

13 Programming with MATHEMATICA

14 Project II



Course Title Normed Spaces and Inner Product Spaces

Department MathematicsDivision in the Dept. Analysis and Function Theory








This course aims to acquaint students with the fundamental notions of Normed and Inner Product Spaces including Normed linear spaces, linear subspaces, infinite series, convex sets, linear functionals, finite-dimensional spaces, dual space and second dual space, weak convergence, inner product spaces, orthogonal complements, Fourier series, Riesz representation theorem

Textbook and Supplementary readings1 Topology and Normed Spaces, G. J. O. Jameson.234


1 Normed linear spaces

2 Linear subspaces

3 Infinite series

4 Convex sets

5 Linear functionals

6 Finite-dimensional spaces

7 Dual space and second dual space

8 Weak convergence

9 Inner product spaces

10 Orthogonal complements

11 Fourier series

12 Riesz representation theorem

13 Riesz representation theorem



Course Title Natural Language ProcessingDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 569 Fall MS Elective Turkish 3 0 3 8


Name of Instructors Asst. Prof. Dr. Rıfat Aşlıyan


Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected]


This course aims to present the basics of Natura Language Processing.

Textbook and Supplementary readings1 D. Jurafsky and J. H. Martin, "Speech and Language Processing" , Prentice Hall, 2000.2 E. Ranchod and N.J. Mamede, "Advances in Natural Languge Processing", Springer-Verlag, 2002.34


1 Introduction to Natural Language Processing

2 Basics of the linguistics

3 Linguistics and languages

4 Language models

5 Syntax analysis (POS)

6 Corpora, N-gram

7 Probabilistic models of spelling

8 Hidden Markov Model-Viterbi algorithm

9 Document classification

10 Information retrieval, information retrieval systems

11 Machine learning

12 Question replying systems

13 Semantic analysis



Course Title Data MiningDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 571 Fall MS Elective Turkish 3 0 3 8



Instructor Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-


Information 09010 Aydın Tel: 256 21284 98 - 2116 [email protected]


Today, a lot of information can be collected via computer based technologies. Interpreting, evaluating the collected information is very important subject for decision systems. Data mining is useful field for many areas. The fundamentals of data mining will be mentioned in this course.

Textbook and Supplementary readings1 Data Mining Concept and Techniques , J.Han and M.Kamber2 Data Preparation for Data Mining, D.Pyle3 Advances in Data Mining, P. Perner4


1 Introduction to Data Mining

2 Survey of data mining applications, techniques and models

3 Data mining steps: Define goal, data cleaning

4 Data selection and preprocessing

5 Data reduction and data transformation

6 Select data mining algorithm, model assessment, interpretation

7 Exploration of data mining algorithms

8 Decision trees, regression

9 Association rules

10 Memory based methods

11 K-nearest neighbor method

12 Clustering

13 Artificial neural networks



Course Title Mathematical Methods of Physics IDepartment Mathematics Division in the Dept. Analysis and Function Theory



MAT 573 Fall MS Elective Turkish 3 0 3 10


Name of Instructors

Assist. Prof. Dr. İnci Ege



Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN, [email protected]


This course gives the fundamental concepts of generalized functions

Textbook and Supplementary readings1 Generalized Functions, Vol. I, I. M. Gelfand and Shilov, Academic Press, 1964

2 Distributions, Ultradistributions and Other Generalized Functions, R. Hoskins and J.S. Pinto, Ellis

Horward, Chichester, 1994


1 Test functions

2 Generalized functions

3 Local properties of generalized functions

4 Translations, rotations andother linear transformations on the independent variables of generalized functions

5 Regularization of divergent integrals

6 Convergence of generalized function sequences

7 Complex test functions and generalized functions

8 EXAM

9 Differentiation and integration of generalized functions

10 Differentiation and integration of generalized functions

11 Delta-convergent sequences

12 The generalized functions , , , ,

13 Canonical regularization

14 The generalized function Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Introduction to Homological Algebra

Department Mathematics



Lecture Lab Credit ETSC CreditMAT575 Fall MS Elective Turkish 3 0 3 10Course Prerequisites

Name of Instructors Yrd. Doç. Dr. Süleyman GÜLER

Instructor Information [email protected]



This course aims to give students the basic concepts of algebraic topology., the concept based on fundamental group and homology groups of topological spaces . Aims to develop the ability to solve problems.and to give students their use in the daily life of homological algebra topics, to develop analytical thinking and to understand abstract concepts. Aims to gain a systematic approach to define problems and to solve the problems by the topics discussed.

Textbook and Supplementary readings1 Rotman, J.J., “An Introduction to Homological Algebra”, Academic Press, 1979.2 Northcott D. G. “An Introduction to Homological Algebra”, Cambridge at the University Press, 196034


1 Abel Groups

2 Rings

3 Modules

4 Homomorphisms

5 Free Modules, Exact Sequences

6 5- Lemma ve 3x3 Lemma

7 Hom Functor

8 Projektive ve İnjektive Modules

9 Midterm Exam

10 Essential and Superfluous Submodules, Supplements

11 Category of Complexes

12 Projektive and İnjektive Resolutions

13 Derived Functor

14 Final Exam



Course Title Real and Complex Analysis IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory


Lecture Lab Credit ECTS CreditMAT502 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None





This course aims to acquaint students with the fundamental notions of Real and Complex analysis including Fourier transforms, elementary properties of Holomorphic functions, Harmonic functions, the maximum modulus principle, approximation by rational functions, conformal mapping, zeros of holomorphic functions.

Textbook and Supplementary readings1 Real and Complex Analysis, by Walter Rudin, 1987.234




3 Elementary properties of Holomorphic functions

4 Elementary properties of Holomorphic functions

5 Harmonic functions


7 The maximum modulus principle

8 The maximum modulus principle

9 Approximation by rational functions

10 Approximation by rational functions

11 Conformal mapping, zeros of holomorphic functions



14 Final Exam



Course Title Algebra IIDepartment Mathematics Division in the Dept. Algebra and Number Theory



MAT504 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Algebra I

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Doç. Dr. Erdal Özyurt, Assist. Doç. Dr. Selma Altınok, Yrd. Doç.Dr. Semra Doğruöz, Yrd. Doç.Dr. Hülya İnceboz Günaydın

Instructor Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-

Information 09010 AYDIN [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]



Textbook and Supplementary readings1 Algebra, T.W.Hungerford

2 Contemporary Abstract Algebra, J.A.Gallian 3 Basic Algebra I-II, N. Jacobson4 Basic Abstract Algebra, P.B. Bhattacharya, S.K.Jain, S.R. Nagpaul, Cambridge University Pres5 Fundamentals of Abstract Algebra, D.S.Malik, John M.Mordeson, M.K. Sen, , The McGraw-Hill Companies


1 Rings

2 Rings and Homomorphisms, Ideals

3 Some Classic Theorems(Isomorphism theorems)

4 Prime and Maximal Ideals

5 Factorization in Commutative Rings

6 Division Rings and Localization

7 Rings of Polinomials and Formal Power Series

8 Factorization in Polynomial Rings

9 Modules- EXAM

10 Homomorphism and Exact Series

11 Free Modules

12 Vector spaces

13 Projective Modules

14 Injective Modules



Course Title Algebraic TopologyDepartment MathematicsDivision in the Dept. Topology


Lecture Credit ECTS creditMAT 506 Spring MS Elective Turkish 3 3 10




Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN







Tel: 256 2128498 [email protected] Objective and Brief Description

The aim of this course is to provide introductory knowledge for Algebraic Topology.

Textbook and Supplementary Readings1 Massey, W. (1967) Algebraic Topology, Springer-Verlag2 Munkres, J.R. (1999) Topology, Prentice Hall


1 Manifolds

2 Surfaces

3 Topology of surfaces

4 Classification of compact orientable surfaces

5 Classification of compact non-orientable surfaces

6 Homotopy

7 Fundamental group

8 Midterm Exam

9 Fundamental group of circle

10 Fundamental group of product spaces

11 Fundamental group of surfaces

12 Van Kampen theorem

13 Covering spaces

14 Covering spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Noncommutaive Rings

Department Mathematics




MAT508 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Günğöroğlu, Asist. Prof. Dr. Semra DoğruözInstructor Information

ADÜ Faculty of Arts and Science, Department of Mathematics, Aydın, [email protected]


This course suggested to students who study noncommutative rings. It gives the fundemantal concepts of noncommutative rings.


Textbook and Supplementary readings1 Noncommutative Rings, I.N.Herstein2 Algebra, Hungerford3 Topics In Ring Theory, I.N.Herstein


1 Simple and primitive rings.

2 The radical of a ring, semisimple Artinian Rings.

3 Semisimple rings, The Density Theorem.

4 Semisimple rings.

5 Applications of Wedderburn’s Theorem.

6 Commutativity theorems.

7 Simple algebras.

8 The Brauer’s Groups

9 Exam

10 Maximal subfields.

11 Some classic theorems.

12 Representation of finite groups, polynomial identities.

13 The Goldie’s Theorem, Ultra-products and a theorem of Posner.

14 Final Exam



Course Title Module TheoryDepartment Mathematics Division in the Dept. Algebra and Number Theory




Name of Instructors



Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN [email protected], [email protected], [email protected],




[email protected], [email protected], [email protected] Objective and brief Description


Textbook and Supplementary readings1 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1974


1 Review of Rings and Their Homomorphisms

2 Modules and Submodules, Homomorphisms of Modules

3 Categories of Modules, Endomorphism Rings

4 Direct Summands, Direct Sums and Products of Modules

5 Decomposition of Rings

6 Generating and Cogenerating

7 Semisimple Modules-The Socle and the Radical

8 Finitely Generated and Finitely Cogenerated Modules, Chain Condations

9 Modules With Composition Series -EXAM

10 Indecompositions of Modules

11 Classical Ring, Structure Theorems(Semisimple Rings, The Density Theorem, The Radikal of a Ring, Artinian Rings)

12 The Hom Functors and Exactness

13 Projective and Injective Modules

14 The Tensor Functors and Flat Modules



Course Title Rings and RadicalsDepartment Mathematics Division in the Dept. Algebra and Number Theory




Name of Instructors Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Günğöroğlu, Asist. Prof. Dr. Semra Doğruöz


ADÜ Faculty of Arts and Science, Department of Mathematics, Aydın, [email protected]

Course Objective and brief

The goal of this course finds some properties of rings by using radicals.





DescriptionTextbook and Supplementary readings

1 Rings and Radicals, N.J.DivinskyCOURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 The general theory of radicals.

2 Rings with the descending chain condition, Nil and Nilpotent, descending chain condition ideals in nil semi-simple rings with D.C.C.

3 Central idempotent elements, I. and II. structure theorems.

4 Simple rings, radical properties, rings with ascending chain condition, relationship between A.C.C. and D.C.C.

5 Nil and Nilpotent, Bear Lower Radical.

6 Prime rings, Zorn Lemma, prime ideals, subdirect sums.

7 Semi-prime rings, prime and semi-prime rings with A.C.C.

8 The Jacobson Radical, quasi-regularity, right primitive rings.

9 Exam

10 The Jacobson Radical and general radical theory.

11 The Brown-MacCoy Radical, G-regularity, G-semi-simple rings.

12 The Brown-MacCoy Radical and general radikal theory.

13 The Levitzki Radical, local nilpotency, the eight radicals and recent results.



Course Title Minimal SubmanifoldsDepartment MathematicDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT516 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Differentiable Manifolds



Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematikj Bölümü 19010-AYDIN Tel:0262128498 [email protected]


Our aim is to give some related topics in minimalsubmanifold .

tel:0262128498

Textbook and Supplementary readings1 Xin,Yuanling, Minimal Submanifolds and Related topics, World Scientific


1 Define manifold

2 Define topologies of submanifolds

3 Second fundamental form

4 Minimal submanifold s in Euclidean spaces

5 Minimal submanifold s in the sphere

6 Examples

7 Rigidity theorems

8 Solve th problems

9 Gauss map

10 The Weierstrass representation

11 The mean curvature

12 Minimal hypersurfaces

13 Solve the problems



Course Title Non- Euclidean GeometryDepartment MathematicDivision in the Dept. Geometry



Name of Instructors Asist.Prof.Dr. Leyla Onat


Adnan Menderes Üniversitesi Fen edebiyat Fakültesi Matematik Bölümü –AydınTel:02562128498 [email protected]


Our aim is to give some definitions on non Euclidean geometry.

Textbook and Supplementary readings

tel:02562128498

1 Coxeter, H.S. Non- Euclidean Ceometry Washington. D.C.20036


1 Euclid

2 Saccheri, Gauss, Bolyai, Riemann

3 Definitions and axioms

4 Models

5 Elliptic geometry in one one dimension

6 Elliptic geometry in two dimension

7 Elliptic geometry in three dimension

8 Euclidean and hyperbolic geometry


10 Circles and triangles

11 Area

12 Euclidean models




Course Title Mathematical Statistics IIDepartment MathematicsDivision in the Dept. Applied Mathematics

Code Term Level Type Language Credit hours/Week

Lecture Lab. Credit ECTS Credit





Course Objective and brief

This course introdues fundamental probablitiy and mathematical statistical theory


DescriptionTextbook and Supplementary readings

1 İnal C. Olasılıksal ve Matematiksel İstatistik,Hacettepe Üniv. Fen Fak yayınları No: 16, 1982.2 Kendall,M, Stuart,A.,Ord J.K.-The Advanced theory of Statistics. Charles griffin com. London 1983.3 Alexander, W.H. –Elements of Mathematical Statistics John Wiley and Sons, NewYork,1961.4 Mood,A.M.,Graybill,F.A. Probabilitiy and Statistical Applications McGraw-Hill Book Com.

NewYork,1963.COURSE CALANDER/ SCHEDULE

Week Lecture Topics Practice/Lab/Field1 Permutation and combination

2 Probability

3 Discrete function of probability and function of distribution

4 Continuous function of probability and function of distribution

5 Expected value ,mean and variance

6 Transform of veriable at function of probability

7 Functions of moment generation and functions of characteristic

8 Estimation theory

9 Property of estimations

10 Least squares method

11 Maximum likelihood method

12 Bayesian estimation method

13 Moments estimation method

14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.


Course Title Nonparametric StatisticDepartment MathematicsDivision in the Dept. Applied Mathematics







Course Objective This course introduce various and important test of nonparametic statictical


and brief Description

Textbook and Supplementary readings1 Siegel S. Nonparametric Statistics for the Behavioral Sciences McGraw-Hill Kagakuska Ltd. Tokyo 1956. 2 Gamgam H. Parametrik Olmayanİstatistik Teknikleri Gazi Üniv. Yayınları No: 140 Ankara 198934

COURSE CALANDER/ SCHEDULEWeek Lecture Topics Practice/Lab/Field

1 Binomial test,khi-square test for one example

2 Kolmogorov-Smirnov test for one example

3 McNemar test for meaningfulness in variations

4 Signal test, Wilcoxon testfor degree

5 Fisher complete probability test

6 Mann-Whitney U test

7 Kolmogorov-Smirnov test for pair example

8 Moses test for extreme reactions

9 Test of rondomness

10 Cochran Q test

11 Analysis of variance whit degree . Friedman and Kruskal-Wall test

12 Spearman and Kendall, correlation coefficient of degree

13 Kendall conformity coeficient w.

14 Final Exam

Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these.

FACULTY OF ARTS AND SCİENCES

Course Title Numerical solution of Integral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics







This course aims to acquaint students with the basic knowledge of numerical solution of some kinds of integral equations. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.

Textbook and Supplementary readings1 Ram P. KANWAL (1971) Lineer integral denklemler, Academic Pres, New York and London2 Villiam Vernon LOVITT (1950) Lineer integral denklemler, Dower publications, New York3 Yavuz AKSOY (1983) İntegral Denklemler, Yıldız Üniversitesi yayınları4


1 Introduction of MATLAB and integral equations

2 Relation between linear differential equations and integral equations with Fredholm and Volterra integral equations

3 Relation between linear differential equations and integral equations with Fredholm and Volterra integral equations

4 Numerical solution and stability of Volterra integral equations

5 Numerical solution and stability of Volterra integral equations, Linear and non-linear integro-differential equations

6 Linear and non-linear integro-differential equations, Linear and Nonlinear Volterra integral equations of the second kind

7 Volterra integral equations with time lags

8 Midterm exam

9 Lotka-Volterra systems

10 Numerical solution of integro-differential equations with parabolic type.

11 Numerical error analysis

12 Numerical solution of integro-differential equations with parabolic Volterra type.

13 Numerical error analysis

14 Final Exam

Değerlendirme 1 adet ara sınavın %40 ve yarıyılsonu sınavının %60 alınarak yapılır. Sınav şekli öğretim üyesinin tercihine bağlı olarak sözlü ve/veya yazılı sınav, ödev, proje, laboratuvar denemesi, grup sunumu, veya bunların kombinasyonu şeklinde yapılabilir.



Course Title Stochastic ProcessesDepartment Matematik Division in the Dept. Applied Mathematics

Code Term Level Type LanguageCredit hour/week




ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100 [email protected],


This course intruduces fundamental stochastic processes

Textbook and Supplementary readings1 İnal C. Olasılıksal Süreçler Hacettepe Üniv. Fen-Ed Fak. Yayınları 1998.

2 Parzen E., Stochastic Processes Holden-day Inc. NewYork 1962.3 Karlin S. Taylor H.M., A first course in Stochastic processes Academic press. NewYork 1975.4 Papoulis A., Probability,Random Variable and Stochastic Processes McGraw Hill Book com. 1965

COURSE CALANDER/ SCHEDULE

Week Lecture topics Practice/Lab/Field

1 Theory of stochastic processes

2 Markov chains

3 Markov processes

4 Poisson processes

5 Birth and death processes

6 Birth and death processes

7 Random walk

8 Renewal processes

9 Renewal processes

10 Brownian motions

11 Brownian motions

12 Branching processes

13 Branching processes

14 Final Exam




Course Title Fourier AnalysisDepartment MathematicsDivision in the Dept. Analysis and Function Theory







This course aims to acquaint students with the fundamental notions of Fourier Analysis including trigonometric sums, integrability of trigonometric sums, convergence and Cesaro summability of Fourier series, convergence and summability of trigonometric series, multiple Fourier series, Fourier transform and applications, orthogonal systems, bessel functions

Textbook and Supplementary readings1 Theory and Applications of Fourier Series, C. S. Rees, S. M. Shah and C. V. Stanojevic.234


1 Trigonometric sums

2 Integrability of trigonometric sums

3 Convergence and Cesaro summability of Fourier series

4 Convergence and summability of trigonometric series

5 Convergence and summability of trigonometric series

6 Multiple Fourier series

7 Multiple Fourier series

8 Fourier transform and applications

9 Fourier transform and applications

10 Orthogonal systems

11 Orthogonal systems

12 Bessel functions

13 Bessel functions

14 Final Exam



Course Title Partial Differential EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMat 538 Spring MS Elective Turkish 3 0 3 10


Name of Instructors Assist. Prof. Ali IŞIK, Assist. Prof. Ali FİLİZ


Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTel:256 2128498 [email protected], [email protected]


This course aims to acquaint students with the fundamental structures of Partial Differential Equations first order and second order equations. Students will be familiar with classification of equations, linear first order equations, method of langrange, Cauchy problem for quasilinear first order equations, linear second order equations, hyperbolic, parabolic and elliptic equations. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.

Textbook and Supplementary readings1 Rene Denemeyer (1968) Introduction to Partial Differential Equations and Boundary Value problems,

McGraw-Hill2 V.S. Vladımırov (1971) Equations of Mathematical Physics, Marcel Dekker, inc, Newyork3 Kerim Koca (2003) Kısmi Türevli Denklemler, Gündüz yayıncılık4 Mehmet Çağlayan, Okay Çelebi (2002) Kısmi Diferensiyel Denklemler Uludağ üniversitesi


1 Introduction, Classification of partial differential equations,

2 Linear fist order equations,

3 Linear and Quasilinear equations Method of Langrange

4 Cauchy problem for first order equations

5 Types of nonlinear first order equations, Method of Charpit,

6 Linear second order equations and generalization of linear second order equations, Non-homogeneous equations

7 Classification of linear second order equations and reduction of canonical form,

8 Hyperbolic, Parabolic, and Elliptic equations,

9 Introduction to wave equations,

10 One-dimensional wave equation; Initial-value problem,

11 Two-dimensional wave equation. Initial-value problem,

12 One-dimensional heat equation. Initial-value problem.

13 One-dimensional heat equation. Initial-value problem.





Course Title Theory of Integral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMat 540 Spring MS Elective Turkish 3 0 3 10


Name of Instructors Assist. Prof. Ali IŞIK, Assist. Prof. Ali FİLİZ




This course aims to acquaint students with the basic knowledge of integral equations. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.

Textbook and Supplementary readings1 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London2 Villiam Vernon LOVITT (1950) Linear integral equations, Dower publications, New York3 Yavuz AKSOY (1983) İntegral Denklemler, Yıldız üniversitesi yayınları


1 Introduction, Classification of integral equations

2 Relation between linear differential equations and integral equations,

3 Integral equations with separable kernels,

4 Method of successive approximation,

5 Volterra integral equations,

6 Linear system of Volterra integral equations,

7 Nonlinear Volterra integral equations of the second kind,

8 Fredholm integral equations with degenerate kernel

9 Fredholm theorem for integral equations,

10 Eigenvalues of the kernel of an integral equations

11 Integral equations with continuous kernel

12 Singular Volterra integral equations.






Course Title Mathematical Analysis IIDepartment MathematicsDivision in the Dept. Analysis and Function Theory







This course aims to acquaint students with the fundamental notions of Mathematical Analysis including sequences and series of functions, some special functions, functions of several variables, integration of differential forms, the Lebesque theory

Textbook and Supplementary readings1 Principles of Mathematical Analysis, W. Rudin.234


1 Sequences and series of functions

2 Sequences and series of functions

3 Some special functions

4 Some special functions

5 Functions of several variables



8 Integration of differential forms



11 Lebesque theory

12 Lebesque theory

13 Lebesque theory

14 Final Exam



Course Title Functional Analysis









This course aims to acquaint students with the fundamental notions of Functional Analysis including normed linear spaces, linear maps, Hilbert spaces, the Hahn Banach theorem, weak topolojies, separable spaces, fixed point theorems

Textbook and Supplementary readings1 Elements of Functional Analysis, I. J. Maddox234




3 Linear maps

4 Linear maps

5 Hilbert spaces

6 Hilbert spaces

7 Hahn Banach theorem

8 Hahn Banach theorem

9 Weak topolojies

10 Weak topolojies

11 Separable spaces

12 Separable spaces

13 Fixed point theorems

14 Final Exam



Course Title Divergent Series I








This course aims to acquaint students with the fundamental notions of divergent series including Abel convergence, Cesaro convergence, Euler-Maclaurin sum Formula, Abel’s inequality, the Silverman-Toeplitz theorem, Nörlund and Nörlund type transformations, Hölder and Cesaro means, Euler, Taylor and Borel exponential transformations, Hausdorff means

Textbook and Supplementary readings1 Divergent Series, G. H. Hardy234


1 Abel convergence

2 Cesaro convergence

3 Euler-Maclaurin sum Formula

4 Abel’s inequality

5 the Silverman-Toeplitz theorem

6 the Silverman-Toeplitz theorem

7 Nörlund and Nörlund type transformations

8 Nörlund and Nörlund type transformations

9 Hölder and Cesaro means

10 Hölder and Cesaro means

11 Euler, Taylor and Borel exponential transformations

12 Euler, Taylor and Borel exponential transformations

13 Hausdorff means

14 Final Exam



Course Title Hyperbolic GeometryDepartment MathematicsDivision in the Dept. Topology



MAT 556 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None





The aim of this course is to provide introductory knowledge for Hyperbolic Geometry.

Textbook and Supplementary Readings1 Anderson J.W. (2005) Hyperbolic Geometry, Springer2 Stillwell J. (1992) Geometry of Surfaces, Springer-Verlag


1 Surfaces of negative curvature and psedosphere

2 Hyperbolic metric

3 Hyperbolic length of curves

4 Hyperbolic plane and some models

5 Upper half plane model

6 Unit disc model

7 Geodesics

8 Midterm Exam

9 Reflections and the other isometries in the hyperbolic plane

10 Classification of isometries

11 Möbius transformations

12 PSL(2,R) and its discrete subgroups

13 Hyperbolic area and Gauss-Bonnet Formula

14 Hyperbolic trigonometryCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Algebraic Geometry IDepartment MathematicsDivision in the Dept. Topology and Geometry








This course gives the study of Geometry coming from Algebra and Rings

Textbook and Supplementary Readings1 Undergraduate algebraic Geometry, M. Reid2 Algebraic Geometry, R. Hartshorne


1 Conics, cubics and group law2 Curves and genus3 Affine varieties4 Functions on Affine varieties, Projective varieties5 Tangent spaces and dimension6 Lines on Cubic spaces7 Regular functions and transformations8 Midterm Exam

9 Parametric spaces10 Rational functions and rational transformations11 Algebraic groups12 Hilbert polynomials13 Gauss transformation, tangent and dual varieties14 Singular points and tangent spaces. Parametric and moduler spaces.

Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework


Course Title CryptologyDepartment MathematicsDivision in the Dept. Applied Mathematics





Name of Instructors Assist. Prof. Dr. Ali FilizInstructor Information

Adnan Menderes University, Faculty of Art and Sciences, 09100 AydınTel: 256 2128498-2116 [email protected]


This course aims to acquaint students with Cryptography. Lectures will be given at the class. Students take notes. Some projects are given to students.

Textbook and Supplementary readings1 Applied Cryptography: Protocols, Algorithms and Source Code in C, John Wiley & Sons, 1995, ISBN 978-

04711170942 Şifreleme Matematiği: Kriptografi, Ortadoğu Teknik Üniversitesi, Toplum Bilim Merkesi, Canana Çimen,

Sedat Akleylek, Ersan Akyıldız, 2007, ISBN 978-9944-344-27-23 Lecture notes about this course are going to be given. Any book related with this course can be used for

this lesson.COURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 Introduction to cryptography

2 History of cryptography

3 Classical methods of cryptography

4 Classical methods of cryptography

5 Symmetric algorithms

6 Data encryption standard (DES)

7 Asymmetcal algorithms

8 Asymmetcal algorithms

9 Rivest, Shamir, Adleman Algorithm (RSA)

10 E1 Gamal algorithm

11 Digital Signs Standards

12 Cryptographic Protocols

13 Cryptographic Protocols



Course Title Visual Programming IIDepartment MathematicsDivision in the Dept. Applied Mathematics



Name of Instructors Asst. Prof. Dr. Ali FİLİZ


Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi 09100 AydınTelephone Number:0 256 2128498-2114 and 2116 [email protected]


This course aims to acquaint students with the fundamentals of visual programming. Classes will be held in the computer laboratory and lab computers will be used for practices during whole class hours of lecturing.

Textbook and Supplementary readings1 Borland C++ Builder, İ. Karagülle ve Z. Pala, Türkmen Kitabevi, 2002.23


1 Introduction to Visual Programming

2 Procedures

3 Procedures

4 Functions,

5 Functions,

6 Introduction to Database management systems, SQL



9 Project I

10 Debugging

11 Debugging

12 Database design and ADO.

13 Database design and ADO.

14 Project II



Course Title Linear AlgebraDepartment MathematicsDivision in the Dept. Algebra and Number Theory

Code Term Level Type Language Credit hour/week

Lecture Lab. Credit ECTS CreditMAT566 Spring MS Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. İnceboz


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın 09100, [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


This course introduces fundamental concepts of linear algebra which are indispensable in all branches of basic science. Its aim is to teach students fundamental concepts of Number Theory.

Textbook and Supplementary readings1 Linear Algebra, K. Hoffman and R. Kuntze, Printice Hall 2.Edition, 1971.2 Topics in Linear Algebra, Cemal Koç, ODTÜ Matematik Vakfı Yayınları, 2002.


1 Linear equations

2 Vector spaces

3 Linear independence, base, dimension

4 Linear transformations

5 Determınats

6 Applıcatıon of determınants

7 Characteristic and minimal polynomials

8 Eigenvalue, eigenvectors, diagonalization

9 Rational Forms MIDTERM

10 Jordan forms

11 Diogonalization in complex matrices

12 Inner products, norm, orthogonality

13 Application of iner products

14 Normal, unitary and orthogonal operations Course assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Group TheoryDepartment MathematicsDivision in the Dept. Algebra and Number Theory










Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Yrd. Doç.Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


The goal of the course is to introduce the fundamental concepts of abstract group theory. The group is defined by certain structure. Group theory is the oldest baranch of modern algebra. Its origin comes from the permutation of variable or of the roots of polynomials. All these groups were finite permutation groups. It plays an important part in all science branch, aspecially Physics and Chemstry.

Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson, Springer-Verlag New York, 1996.

2 An introduction to theory of the groups, Rotman, J.J., Springer-Verlag New York, 1995.COURSE CALANDER/ SCHEDULE

Week Lecture Topics Practice/Lab/Field1 Fundamental concepts of group theory

2 Homomorfisms and quotient groups

3 Endomorphisms and aotumorphisms of groups

4 Permutation groups and group actions

5 Generating groups, semidirect products

6 Wreath product, direct limit

7Free groups

8 Midterm

9 Sylow Theorems

10 Classification of finite groups

11 Series and composition series, Simple groups, direct decompositions

12 Abelian and central series

13 Nilpotent groups, Groups of prime power order

14 Soluble groups



Course Title Complex Variables and ApplicationsDepartment MathematicsDivision in the Dept. Mathematics













This course aims to acquaint students with the fundamental notions of Complex Variables and Applications including Complex numbers, functions, limits, continuity, complex differentiation, Cauchy- Riemann equations, complex integration, Cauchy’s theorem, Cauchy’s integral formulas, infinite series, Taylor’s and Laurent series, Residue theorem, conformal mapping, physical applications of conformal mapping.

Textbook and Supplementary readings1 Complex Variables with an introduction to conformal mapping and its applications, by M. R. Spiegel,

1991.234


1 Complex numbers

2 Functions

3 Limits

4 Continuity

5 Complex differentiation

6 Cauchy- Riemann equations

7 Complex integration

8 Cauchy’s theorem

9 Cauchy’s integral formulas

10 Infinite series

11 Taylor’s and Laurent series

12 Residue theorem

13 Conformal mapping and physical applications of conformal mapping

14 Final ExamCourse assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these


Course Title Theory and Applications of Infinite SeriesDepartment MathematicsDivision in the Dept. Mathematics







This course aims to acquaint students with the fundamental notions of Theory and Applications of Infinite Series including Principles of the theory of real numbers, sequences of real numbers, sequences of positive terms, sequences of arbitrary terms, power series, the expansions of the elementary functions, infinite products, closed and numerical expansions for the sums of series, series of positive terms, series of arbitrary terms, series of complex terms, the elementary analytic functions.

Textbook and Supplementary readings1 Theory and Applications of Infinite Series, by K. Knopp, 1990.234


1 Principles of the theory of real numbers

2 Sequences of real numbers

3 Sequences of positive terms

4 Sequences of arbitrary terms

5 Power series

6 The expansions of the elementary functions

7 Infinite products

8 Closed and numerical expansions for the sums of series

9 Series of positive terms

10 Series of arbitrary terms

11 Series of complex terms

12 The elementary analytic functions

13 The elementary analytic functions

14 Final Exam

Course assesment will be weighted 50% for one quiz and 50% for the final exam. Depending on instructor’spreference, assessment may be by written or/and oral examination, homework, Lab assay, projects, group presentation, or a combination of these


Course Title Topology and GeometryDepartment MathematicsDivision in the Dept. Geometry

Code Term Level Type LanguageCredit hour/week



Name of Instructors Prof. Dr. Hatice Kandamar, Assist. Prof. Dr. Selma Altınok


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected]


Its aim of this course inntroduces the fundamental concepts of topology and geometry, and calculates fundamental groups of differentiable manifolds and mention De Rham Cohomology of Riemannian Geometry.

Textbook and Supplementary readings1 Lecture Notes on Elementary Topology and Geometry, I. M. Singer, J. A. Thorpe, Springer, 1976.

COURSE CALANDER/ SCHEDULE

Week Lecture Topics Practice/Lab/Field

1 Topological spaces

2 Connected and compact spaces

3 Continuity, Product spcases, the Tychanoff Theorem

4 Speration axioms, complete metric spaces

5 Homotopy

6 Fundamental groups, covering spaces

7Fundamental groups, covering spaces

8 Midterm

9 Geometry of simplicial complexes and groups

10 Manifold

11 Simplicial homology, De Rham’s theorem

12 Simplicial homology, De Rham’s theorem

13 Riemann geometry of surfaces

14 Riemann geometry of surfaces



Course Title Advanced Module Theory Department Mathematics Division in the Dept. Algebra and Number Theory





MAT 576 Spring MS Elective Turkish 3 0 3 10Course Prerequisites Introduction to Module Theory

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Semra Doğruöz,




This course gives the fundamental concepts of modules


2 Moduln und Ringe, F. Kasch, B.G.Teubner Stuttgart 1977.


1 Artinian and Noetherian Modules and Homomorphisms

2 Hilbert’s Basis Theorem

3 Decomposition of Modules over Noetherien and Artinian Modules

4 Local Rings, Local Endomorphism Rings

5 Krull-Remark-Schmidt Theorem

6 Semisimple Modules and Rings

7 Socle ve Radical

8 Tensor Product and Flat Modules (EXAM)

9 Regular Rings

10 Semiperfect Modules

11 Nil Ideals and t-Nilpotent İdeals

12 Injectivity and the Cogenerator Property of Ring

13 Quasi-Frobenius Rings and Characterization of Quasi-Frobenius Rings

14 Quasi-Frobenius Algebras and Characterization of Quasi-Frobenius Algebras



Course Title Differentiable Manifolds IIDepartment MathematicDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT 578 Spring MS Elective Turkish 3 0 3 10









The main goal is this course to provide a working knowledge of Differentiable Manifold

Textbook and Supplementary readings1 Brickell,F., Clark,R. Differentiable manifolds, Windson House, Condon S.W.12 Boothby, William M. An Introduction to Differentiable Manifolds and Riemannian Geometry Academic

Press, New York,1975COURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 Submanifolds

2 Vector fiels on a manifold

3 The Lie algebra of vector fields on a manifold4 Orientation of manifolds

5 Integration on manifolds

6 Stokes Theorems


8 Differentiation on Riemannian Manifolds

9 Tangent bundle

10 Curvature

11 Gauss and mean curvature

12 Equations of structure




Course Title Artificial Neural NetworksDepartment MathematicsDivision in the Dept. Applied Mathematics




tel:02562128498





Nowadays the methods of artificial intelligence are widely used in computer science. Artificial neural networks (ANN) are very advantageous in most systems, especially in the systems which has very complex mathematical structures. In this course, the aim is to teach the fundamental ANN subjects.

Textbook and Supplementary readings1 Foundations of Neural Networks, T. Khana2 Fuzzy and Neural Approaches in Engineering, L. H. Tsoukalas, R. E. Uhrig3 Neural Networks for Control, W.T Miller,. R.S Sutton,.and P.J. Werbos4


1 Introduction

2 Fundamentals of Artificial Neural Networks (ANN)

3 Multilayered Feedforward Neural Nets

4 Back Propagation Algorithms

5 Competitive Learning and Other Special Neural Networks

6 Self- Organizing Systems

7 Radial Basis Function

8 Generalized Regression Neural Networks

9 Dynamic Systems and Recurrent Neural Networks

10 ANNs in System Identification

11 Adaptive Processors and Neural Networks

12 Neural networks for Control; Applications: Modelling, Neural networks in Spectral Analysis and Time-Series Prediction




Course Title Mathematical Methods of Physics IIDepartment Mathematics Division in the Dept. Analysis and Function Theory



MAT 582 Spring MS Elective Turkish 3 0 3 10



Name of Instructors

Assist. Prof. Dr. İnci Ege


Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 AYDIN, [email protected]


This course gives the fundamental concepts of generalized functions

Textbook and Supplementary readings1 Generalized Functions, Vol. I, I. M. Gelfand and Shilov, Academic Press, 1964

2 Distributions, Ultradistributions and Other Generalized Functions, R. Hoskins and J.S. Pinto, Ellis

Horward, Chichester, 1994


1 Canonical functions

2 Taylor’s and Laurent Series for ve

3 Taylor’s series for ,

4 Convolutions of generalized functions

5 Convolutions of generalized functions

6 Elementary solutions of differential equations with constant coefficents

7 Fourier transforms of test functions

8 EXAM

9 Fourier transforms of test functions

10 Fourier transforms of generalized functions . A single Variable

11 Fourier transforms of generalized functions . A single Variable

12 Fourier transforms of generalized functions .Several Variable

13 Fourier transforms of generalized functions . Several Variable

14 Fourier transforms and differential equations



Course Title Data CompressionDepartment MathematicsDivision in the Dept. Applied Mathematics





Name of Instructors Assist. Prof. Dr. Rıfat Aşlıyan, Assist. Prof. Dr. Korhan Günel


Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 21284 98 - 2116 [email protected], [email protected]


In this course, the fundamental data compression subjects will be presented .

Textbook and Supplementary readings1 Introduction to Data Compression, K.Sayood, Morgan Kauffman, 19962 Data Compression, D.Salomon, 199834


1 Introduction to data compression and source coding

2 Block coding

3 Arithmetic coding

4 Huffman coding

5 Huffman coding

6 Dictionary based coding

7 Dictionary based coding

8 Scalar quantization

9 Vector quantization

10 Predictive coding

11 Transform, subband and wavelet based coding

12 In class presentations of image, audio, video and computer graphics compression methods

13 In class presentations of image, audio, video and computer graphics compression methods



Course Title Function theory of real variableDepartment MathematicsDivision in the Dept. Analysis and Function Theory


Lecture Lab. Credit ECTS CreditMAT601 Fall PhD Elective Turkish 3 0 3 10Course Prerequisites None






This course aims to acquaint students with the fundamental notions of function theory of real variable including measures, construction of measures, measure and topology,continuous linear functionals, duality, bounded operators, Banach algebras, Hilbert spaces, integral representations, unbounded operators.

Textbook and Supplementary readings1 Introduction to Modern Analysis, Shmuel Kantorovitz


1 Measures

2 Construction of measures

3 Measure and topology

4 Continuous linear functionals

5 Duality

6 Bounded operators

7 Bounded operators

8 Banach algebras

9 Banach algebras

10 Hilbert spaces

11 Hilbert spaces

12 Integral representations

13 Unbounded operators

14 Final Exam


Course Title Algebra Department Mathematics Division in the Dept. Algebra and Number Theory



MAT603 Spring Ph. D. Obligatory Turkish 3 0 3 10Course Prerequisites None

Name of Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma


Instructors Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz


[email protected], [email protected], [email protected], [email protected], [email protected]


Introduction to advanced algebra

Textbook and Supplementary readings1 Algebra, Thomas W. Hungerford2 Algebra, S. Lang34


1 Structure of groups

2 Free groups

3 Free groups

4 Finitely generated groups



7 Fields and Galois theory

8 Cyclic extension

9 Structure of fieldsExam

10 Structure of fields

11 Structure of rings

12 Structure of rings

13 Simple and Primitive rings

14 Jacopson radical



Course Title Advanced TopologyDepartment MathematicsDivision in the Dept. Topology


Lecture Credit ECTS creditMAT 605 Fall Ph. D. Obligatory Turkish 3 3 10Course Prerequisites None

Name of Assist. Prof. Dr. Adnan MELEKOĞLU





Instructors




The aim of this course is to present General Topology subjects at advanced level.

Textbook and Supplementary Readings1 Willard S. (1970) General Topology, Addison-Wesley Publishing Company2 Munkres, J.R. (1999) Topology, Prentice Hall


1 Convergence

2 Countability and separation axioms

3 Countability and separation axioms

4 Compactness and connectedness

5 Tychonoff theorem

6 Compactifications

7 Metrization theorems

8 Midterm Exam

9 Paracompactness

10 Paracompactness

11 Complete metric spaces and function spaces

12 Complete metric spaces and function spaces

13 Uniform spaces

14 Baire spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Group Theory IDepartment MathematicsDivision in the Dept. Algebra and Number Theory


MAT607 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None

Name of Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma

Instructors Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected]


To prepare the students to current resarch in group theory and study some special groups

Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson

2 An introduction to theory of the groups Rotman J.J.


1 Abelian groups

2 Torsion, divisible, torsion-free groups

3 Pure groups

4 Finitely generated abelian groups

5 Soluble groups

6 Nilpotent groups

7 Hall Pi-groups

8 Permutation groups

9 Representations

10 Fixed-point-free automorphisms

11 Locally nilpotent groups

12 Locally soluble groups

13 Finiteness properties

14 Infinite soluble groupsCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Module Theory IDepartment Mathematics Division in the Dept. Algebra and Number Theory



MAT609 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Algebra I-II

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya






İnceboz Günaydın




Working in Advance Modüle Theory


2 Lectures on Modules, T.Y. Lam, Graduate Texts in Mathematics, Springer 1998


1 Introduction to Module Theory

2 Cartesian Products and Direct Sums of Modules

3 Homomorphisms

4 Split Exact Sequences

5 Projective and Injective Modules

6 Length of a Module

7 Artinian and Noetherian Modules

8Artinian and Noetherian Rings

9 Simple and Semisimple Modules-EXAM

10 Simple and Semisimple Rings

11 Radicals of Modules and rings

12 Finitely Generated Modules

13 Von Neumann Regular Rings

14 The Group Ring


FACULTY OF ART AND SCIENCES

Course Title Differantial and Inregral EquationsDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 615 Fall Ph. D. Elective Turkish 3 0 3 10

Course Prerequisites Theory of Integral Equations

Name of Instructors

Assist. Prof. Ali IŞIK, Asist. Prof. Ali FİLİZ

Instructor Adnan Menderes Üniversity, Faculty of arts and science 09100 Aydın







Information Tel:256 2128498 [email protected], [email protected]


This course aims to acquaint students with the advanced knowledge of integral equations. Students will be familiar with classification of equations Volterra and singular Volterra method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.

Textbook and Supplementary readings1 V.S.VLADIMIROV (1971)Equations of Mathemetical Physics , Marcel Dekker, NewYork2 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London3 Ram P. KANWAL (1971) Linear integral equations, Academic Pres, New York and London


1 Basic Equations of Mathematical Physics

2 Classification of Linear (Second Order ) Differential Equations

3 Formulation of Boundary value Problems for Linear Second Order Differential Equations

4 Fundamental Solutions of Linear Differantial Equations,

5 The Cauchy Problem for the Wave Equations

6 The Cauchy Problem for the Equation of Heat Conduction,

7 The Method of Successive Approximation,

8 Fredholm’s Theorems

9 The Sturm-Liouville Problem,

10 Spherical Functinos

11 Sobolev Methods for Solving Wave Equations,





Course Title Tauberian TheoryDepartment MathematicsDivision in the Dept. Analysis and Functions Theory


Lecture Lab. Credit ECTS CreditMAT617 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors

Assoc. Prof. Dr. İbrahim Çanak






This course aims to acquaint students with the fundamental notions of Tauberian theory including the Hardy-Littleweood theorems, Wiener’s theory, complex Tauberian theory, Karamata’s Heritage: Regular variation, Borel summability and general circle methods and Tauberian remainder theory.

Textbook and Supplementary readings1 Tauberian theory, Jacob Korevaar


1 Hardy-Littleweood theorems

2 Hardy-Littleweood theorems

3 Wiener’s theory

4 Wiener’s theory

5 complex Tauberian theory

6 Complex Tauberian theory

7 Karamata’s Heritage: Regular variation

8 Karamata’s Heritage: Regular variation

9 Borel summability and general circle methods

10 Borel summability and general circle methods

11 Tauberian remainder theory



14 Final Exam


Course Title Gödel’s TheoremsDepartment MathematicsDivision in the Dept. Foundations of Mathematics and Mathematical Logic



MAT 619 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors Assist. Prof. Dr. Ali Filiz

Instructor Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN


Information Tel: 256 2128498 [email protected] Objective and Brief Description

To introduce the student to Gödel’s two incompleteness theorems and to their most important corollaries.

Textbook and Supplementary Readings1 H.B. Enderton, A Mathematical Introduction to Logic, (especially chapter 3). Academic Press.2 J.R. Shoenfield, Mathematical Logic, (chapters 4 and 6). Addison-Wesley, 1967.3 G.T. Kneebone, Mathematical Logic and the Foundations of Mathematics. Van Nostrand, 1963.4 Hao Wang, From Mathematics to Philosophy. RKP, 1974


1 The completeness theorem for the predicate calculus: a review

2 First order theories

3 Recursive functions and relations. Basic properties.

4 Basic properties. Primitive recursion

5 Closure under bounded quantification

6 Gödel’s Coding of finite sequences

7 . Recursively enumerable sets and the arithmetic hierarchy

8 Midterm exam

9 Church’s Thesis

10 Gödel numbering and the arithmetization of logic. The recursiveness of the proof predicate. Gödel’s first

11 . Tarski’s undefinability theorem

12Applications of the incompleteness theorem to show the undecidability of the predicate calculus and other axiom systems. Examples of decidable theories: Presburger arithmetic

13 Gödel’s second incompleteness theorem. The philosophical impact of Gödel’s work. The limitations of the axiomatic method

14 Final exam


Course Title Conformal MappingDepartment MathematicsDivision in the Dept. Analysis and Functions Theory


Lecture Lab. Credit ECTS CreditMAT621 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None







This course aims to acquaint students with the fundamental notions of conformal mapping including harmonic funtions, analytic functions, the complex integral calculus, families of analytic functions, conformal mapping of simply-connected domains, mapping properties of special functions and conformal mapping of multiple-connected domains.

Textbook and Supplementary readings1 Conformal Mapping, Zeev Nehari.


1 harmonic funtions

2 harmonic funtions

3 analytic functions

4 analytic functions

5 complex integral calculus

6 complex integral calculus

7 families of analytic functions

8 families of analytic functions

9 conformal mapping of simply-connected domains

10 conformal mapping of simply-connected domains

11 mapping properties of special functions

12 conformal mapping of multiple-connected domains

13 conformal mapping of multiple-connected domains

14 Final Exam


Course Title Category Theory IDepartment Mathematics Division in the Dept. Algebra and Number Theory




Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Erdal Özyurt. Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın






[email protected], [email protected], [email protected] Objective and brief Description

Introduction to Theory of Category

Textbook and Supplementary readings1 Theory of Categories, Barry Mitchell, Academic Pres, New York and London, 1965

2 Categories fort he Working Mathematics, S. Mac Lane, Graduate Texs in Mathematics 53


1 Introduction to Category Theory

2 Duality, Special Morphisms, Equalizers

3 Pullbacks and Pushouts, Intersections, Unions

4 Images, Kernals, Normality

5 Exact Categories, The 9 lemma, Producs

6 Variety of Categories

7 Diagrams, Limits, Functors

8 Preservation Properties of Functors

9 Limit Preserving Functors, Faithful Functors-EXAM

10 Natural Transformations, Equivalence of Categories

11 Diagrams as Functors

12 Categories of Additive Functors, Modules

13 Projectives, Injectives

14 Generaters, Small Objects



Course Title Homological Algebra IDepartment Mathematics Division in the Dept. Algebra and Number Theory



MAT625 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites It is necessary to know module theory

Name of Instructors




Course Objective Introduction to Homological Algebra and some fundamental properties









and brief Description

Textbook and Supplementary readings1 Basic Homological Algebra, M. Scott Osborne, Springer Verlag

2 Homology, Saunders Mac lane, Springer Verlag3 Introduction to Homological Algebra, Rotman, J.J.

4 Relative Homological Algebra, Edgar E. Enochs, Overtoun M. G. Jenda


1 Categories

2 Modules (Generalities, Tensor Products, Exactness of Functors)

3 Modules (Projectives, Injectives and Flats)

4 Ext and Tors ( Complexes and Projective Resolutions )

5 Long Exact Sequences

6 Flat Resolutions and Injective Resolutions,

7 Consequences

8 Dimension Theory

9 Dimension Theory-EXAM

10 Change of Rings (Computational Considirations,

11 Change of Rings (Matrix Rings, Polynomials, Quotients and Localization)

12 Additive Functors

13 Derived Functors

14 Long Exact Sequences ( Existence)



Course Title Riemannian ManifoldsDepartment MathematicsDivision in the Dept. Topology


Lecture Credit ECTS creditMAT 627 Fall Ph. D. Elective Turkish 3 3 10Course Prerequisites None





The aim of this course is to introduce Riemannian Manifolds


Textbook and Supplementary Readings1 Lee J.M. (1997) Riemannian Manifolds, Sringer2 Gallot S., Hulin D., Lafontaine J. (1990) Riemannian Geometry, Sringer


1 Manifolds

2 Vector bundles

3 Riemannian metrics

4 Model spaces of Riemannian geometry

5 Connections

6 Vector fields

7 Riemannian geodesics

8 Midterm Exam

9 Geodesics of the model spaces

10 Lengths and distances on Riemannian manifolds

11 Lengths and distances on Riemannian manifolds

12 Completeness

13 Curvature

14 Manifolds of constant curvature Course assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Graph TheoryDepartment MathematicsDivision in the Dept. Algebra and Number Theory


Lecture Credit ETSC credit

MAT 629 Fall Graduate Elective Turkish 3 3 10Course Prerequisites None

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Asst. Prof. Dr. Semra Doğruöz, Asst. Prof. Dr. Erdal Özyurt


Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected], [email protected], [email protected] , [email protected]


The aim of this course is to give some properties for graph theory.

Textbook and Supplementary Readings1 Graph Theory , Reinhard Diestel


1 Graph Theory

2 Graph Theory

3 Path Theory4 Algebraic and Topological methods

5 Algebraic and Topological methods

6 Nets7 Graph Algorithma8 Midterm Exam

9 Hamilton and Euler Graphs

10 Hamilton and Euler Graphs

11 Extremal Graph Theory

12 Extremal Graph Theory

13 Random Graphs

14 Random GraphsCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on

instructor’s preference, assessment may be written examination, oral examination or homework.






Course Title Differential and Riemannian Manifolds IDepartment MathematicsDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT631 Fall Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None



Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AydınTel:02562128498 [email protected]


The main goal is this course to provide a working knowledge of Riemanniann manifolds, tensors and differential forms.

Textbook and Supplementary readings1 Lang S. Differential and Riemannian Manifolds,Springer-Verlag 1995.


1 Basic Properties

2 Define Manifold

3 Submanifold and İmmersions

4 Tangent Bundle

5 Operations on Vector Bundles

6 Operations on Vector Fields


8 Lie Derivative

9 Killing Vector Fields

10 Covariant Derivatives

11 Metrics

12 The Metric Derivative



.

tel:02562128498


Course Title Semi- Riemannian GeometryDepartment MathematicDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT 633 Fall Ph.D. Elective Turkish 3 0 3 10






The main goal is this course to provide a working knowledge of Semi-Riemannian Geometry.

Textbook and Supplementary readings1 O’Neill,B., Semi-Riemannian Geometry with Application to Relativity Academic Press.Inc.New York

1983COURSE CALANDER / SCHEDULE

Week Lecture topics Practice/Lab/Field1 Symmetric bilinear form and scalar producrs

2 Isometry

3 The Levi-Civita connections4 Geodesics

5 Exponential maps

6 Curvature


8 Semi-Riemannian surfaces

9 Metric contraction

10 Tensor derivation

11 Differential operator

12 Ricci and scalar curvature



tel:02562128498


Course Title Discrete GeometryDepartment MathematicsDivision in the Dept. Geometry


Lecture Lab Cre

dit ECTS credit

MAT 635 Fall Graduate Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors Asst. Prof. Adnan MELEKOĞLU


Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected]


The aim of this course is to introduce Discrete Geometry at the graduate level.

Textbook and Supplementary Readings1 Matousek, J. (2002) Lectures on Discrete Geometry, Springer. 2 Pach J. and Agarwal P.K. (1995) Combinatorial Geometry, John Wiley & Sons, Inc.


1 Convex sets

2 Minkowski’s Theorem

3 General lattices

4 Convex independent subsets

5 Polytopes

6 Convex polytopes

7 Intersection patterns of convex sets

8 Midterm Exam

9 Geometric selection theorems

10 Transversals

11 Epsilon nets

12 High dimensional polytopes

13 Volumes in high dimension

14 Embedding finite metric spaces into normed spacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


http://www.amazon.com/s/ref=rdr_ext_aut?_encoding=UTF8&index=books&field-author=Jiri%20Matousek

Course Title Advanced Neural NetworksDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 637 Fall Ph. D. Elective Turkish 3 0 3 8






Nowadays the methods of artificial intelligence are widely used in computer science. Artificial neural networks (ANN) are very advantageous in most systems, especially in the systems which has very complex mathematical structures. In this course, the aim is to teach the fundamental ANN subjects.

Textbook and Supplementary readings1 Foundations of Neural Networks, T. Khana2 Fuzzy and Neural Approaches in Engineering, L. H. Tsoukalas, R. E. Uhrig3 Neural Networks for Control, W.T Miller,. R.S Sutton,.and P.J. Werbos4


1 Introduction

2 Fundamentals of Artificial Neural Networks (ANN)

3 Multilayered Feedforward Neural Nets

4 Back Propagation Algorithms

5 Competitive Learning and Other Special Neural Networks

6 Self- Organizing Systems

7 Radial Basis Function

8 Generalized Regression Neural Networks

9 Dynamic Systems and Recurrent Neural Networks

10 ANNs in System Identification

11 Adaptive Processors and Neural Networks






Course Title Automatic Speech Recognition and Synthesis Department MathematicsDivision in the Dept. Applied Mathematics




Name of Instructors Asst. Prof. Dr. Rıfat AŞLIYAN




This course introduces students to the rapidly developing field of automatic speech recognition and synthesis. The content is divided into two parts. Part I deals with background material in the acoustic theory of speech production, acoustic-phonetics, and signal representation. Part II describes algorithmic aspects of speech recognition systems including pattern classification, search algorithms, stochastic modelling, and language modelling techniques.

Textbook and Supplementary readings1 Rabiner and Juang, “Fundamentals of Speech Recognition,” Prentice-Hall, 1993.2 Thierry Dutoit, “An Introduction to Text-to-Speech Synthesis”, Kluwer Academic Publishers, Dordrecht

Hardbound, ISBN 0-7923-4498-7,1997.34


1 Acoustic Theory of Speech Production, Human hearing, acoustics, and phonetics

2 Signal Representation, Vector Quantization

3 Speech spectrum analysis (Fourier analysis, cepstral analysis, spectrogram reading)

4 Fundamental frequency analysis (F0 estimation, prosody models)

5 Speech synthesis

6 Linear Prediction (all-pole model, LPC, PARCOR, LSP analysis)

7 Learning algorithms and application (Viterbi algorithm, Bayes’ Theorem)

8 Speech coding (waveform coding, PCM, LPC)

9 Dynamic time warping and acoustic modeling

10 Hidden Markov Modeling, expectation-maximization, and search

11 Language Modeling

12 Graphical Models

13 Segment-Based ASR, Finite State Transducers

14 Final Exam




Course Title Expert Systems Department MathematicsDivision in the Dept. Applied Mathematics








In this courses fundamental concepts of expert systems, some techniques and their application will be introduced to students. Also, some tools for developing expert systems will be explained.

Textbook and Supplementary readings1 P. Jackson, "Introduction to Expert System", Addison-Wesley Publishing Company, ISBN 0201876868,

1998. 2 J. P.Egnizo, "Introduction to Expert System", ISBN 0-079-09785-5, McGraw Hill, 1990.34


1 Overview of Artificial Intelligence. What are Expert Systems?

2 Knowledge Representation

3 Rule-Based Systems

4 Associative Nets and Frame Systems

5 Logic Programming

6 Representing Uncertainty

7 Knowledge Acquisition

8 Heuristic Classification

9 Constructive Problem Solving

10 Tools for Building Expert Systems

11 Machine Learning

12 Belief Networks

13 Case-based reasoning

14 Final Exam




Course Title Radical TheoryDepartment MathematicsDivision in the Dept. Algebra



MAT 643 Fall Ph. D. Elective Turkish 3 0 3 10


Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assoc. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın, Assist. Prof. Dr. Erdal Özyurt


Adnan Menderes University, Faculty of Art and Sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]


In this course, it is aimed to present fundamental subjects of radical theory.

Textbook and Supplementary readings1 Rings and Radicals, N. J. Divinsky2 A Radical Approach to Algebra, M. Gray3


1 Construction of a Radical Property, Ordinal Numbers

2 Construction of a Second Radical Property, Partitions of the Simple Rings

3 Nil and Nilpotent, The Descending Chain Condition

4 Ideals in Nil Semisimple Rings with Descending Chain Condition

5 Direct Sums, Central Idempotent Elements

6 First Structure Theorem, Idempotent Elements, Second Structure Theorem: Simple Rings

7 Generalizations: Radical Properties that Coincide with Nil on Rings with Descending Chain Condition

8 Arasınav

9 Relationship Between Ascending Chain Condition and Descending Chain Condition

10 The Baer Lower Radical, Prime Rings, Prime Ideals

11 Subdirect Sums, Prime and Semiprime Rings with Ascending Chain Condition

12 Jacobson Radical

13 Brown-McCoy Radical, Levitzki Nil Radical

14 Final ExamCourse assessment will be weighted 40 % for mid-term exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.


Course Title Gamma Rings






Department MathematicsDivision in the Dept. Algebra



MAT 645 Fall Ph. D. Elective Turkish 3 0 3 10


Name of Instructors


Instuctor Information

Adnan Menderes University, Faculty of Art and Sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]


In this course, it is aimed to present fundamental gamma ring subjects

Textbook and Supplementary readings1 Gamma Rings, S. Kyuno2 Structureof Rings, N. Jacobson3 Theory of Rings, N. McCoy


1 Definitions and Examples of Gamma Rings,

2 Operator Rings, Ideals, Homomorphisms and Residue Class Gamma Rings

3 Prime, Primitive and Simple Gamma Rings

4 Density Theorem

5 Semi-Prime Gamma Rings with Min-r Condition

6 Simple Gamma Rings with Min-r Condition, Gamma Rings with Min-r and Min-l Conditions

7 Prime Radical, Levitzki Nil Radical, Jacobson Radical

8 Arasınav

9 Relation Among Radicals of R, of L and of M

10 Relations Among the Various Radicals

11 Relations Between Gamma Rings and Other Algebraic Systems

12 Morita Pairs and Morita Equivalences

13 Subdirect Sums of Gamma Rings, Commutative Gamma Rings

14 Final ExamCourse assessment will be weighted 40 % for mid-term exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.







Course Title Function Theory of one Complex VariableDepartment MathematicsDivision in the Dept. Analysis and Functions Theory


Lecture Lab. Credit ECTS CreditMAT602 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None





This course aims to acquaint students with the fundamental notions of function theory of one complex variable including fundamental concepts, complex line integrals, applications of Cauchy integral, meromorphic functions and residues, the zeros of holomorphic function, holomorphic functions as geometric mappings, harmonic functions, infinite series and product, applications of infinite sums and products, analytic continuation, rational approximation theory, special classes of holomorphic functions, special functions.

Textbook and Supplementary readings1 Function Theory of One Complex Variable, Robert E. Grene, Steven G. Krantz.


1 Complex line integrals

2 Applications of Cauchy integral

3 Meromorphic functions and residues

4 The zeros of holomorphic function

5 Holomorphic functions as geometric mappings


7 Infinite series and product

8 Applications of infinite sums and products

9 Analytic continuation

10 Rational approximation theory

11 Special classes of holomorphic functions

12 Special classes of holomorphic functions

13 Special functions

14 Final Exam


Course Title Commutative AlgebraDepartment Mathematics Division in the Dept. Algebra and Number Theory




MAT604 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Algebra I

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın




To give necessary fundameltal properties of commutative algebra for algebraic geometry.

Textbook and Supplementary readings1 Introduction to Commutative Algebra, M.F. Atiyah ve I.G. MacDonald

2 Değişmeli Cebire Giriş, A. Harmancı, M.Akgül, H.I. Tutalar, K.Taş (Çeviri)


1 Modules

2 Exact Sequences

3 Tensor Product of Modules

4 Algebras

5 Rings and Modules of Fractions

6 Localizations

7 Primary Decomposition

8Integral Dependence and Valuations

9 Chain Conditions- EXAM

10 Noetherian and Artinian Rings

11 Dedekind Domains

12 Completions

13 Dimension Theory

14 Non Algebraic Dimensions



Course Title Algebraic Geometry







Department Mathematics Division in the Dept. Algebra and Number Theory, and Geometry



MAT606 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Commutative Algebra

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok

Instructor Information [email protected]


Algebraic geometry is the study of Geometry coming from Algebra and Rings. Algebra, polynomials rings and geomety are roots of polynomials. In the last centurary, it is discovered that Algebraic Geometry can be applied to Commutative Rings with unity. As a result of this , Algebraic Geometry can be applied into many areas, a specially Number Theory. For example, Andrew Wiles used Algebraic Geometry tools to prove the Fermat Last Theorem. This course’s aim is to teach the fundamental concepts of Algebraic Geometry

Textbook and Supplementary readings1 Algebraic Geometry, Hartshorne2 Using Algebraic Geometry, Cox, Little, O’Shea


1 Affine varieties

2 Affine varieties

3 Projective varieties

4 Projective varieties

5 Morphisms, Rational maps

6 Nonsingular varieties

7 Divisors, Projective Morphism. Curves; Riemann-Roch Teorem, Hurwitz’s Theorem

8 Divisors, Projective Morphism. Curves; Riemann-Roch Teorem, Hurwitz’s Theorem

9 Clasification of Curves in 3- dimentional Projective SpaceExam

10 Clasification of Curves in 3- dimentional Projective Space

11 Clasification of Curves in 3- dimentional Projective Space

12 Surfaces; Geometry on a Surface, Ruled Surfaces, Cubic Surfaces in 3-dimensional Projective Space

13 Surfaces; Geometry on a Surface, Ruled Surfaces, Cubic Surfaces in 3-dimensional Projective Space

14 Clasification of Surfaces



Course Title Group Theory II


Department MathematicsDivision in the Dept. Algebra and Number Theory

Code Term Level Type Language Credit hours/WeekLecture Lab. Credit ECTS

CreditMAT608 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected], [email protected], [email protected], [email protected]


To prepare the students to current resarch in group theory and study some special groups

Textbook and Supplementary readings1 A course in the theory of the groups, Derek R. J. Robinson

2 Group Theory I-II Michio Suzuki


1 Locally finite groups

2 Maximal and minimal conditions

3 Cernikov groups and automorphisms of Cernikov groups

4 Direct limit of groups

5 Inverse limit of groups

6 Linear groups

7 Classical simple groups

8 Locally finite simple groups

9 Hall universal group MIDTERM

10 Finite simple groups

11 Lie types of simple groups

12 Centralizers of elements in simple locally finite groups





Course Title Module Theory II





Department Mathematics Division in the Dept. Algebra and Number Theory



MAT610 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Module Theory I

Name of Instructors





Working in Advance Modüle Theory

Textbook and Supplementary readings1 Lectures on Modules, T.Y. Lam, Graduate Texts in Mathematics, Springer 1998

2 Rings and Categories of Modules, F.W. Anderson-K.R. Fuller, Springer Verlag 1974


1 Free Modules( Invariant Basis Number, The Rank Conditions)



4 Injective Modules

5 Injective Modules

6 Injective Modules

7 Flat Modules

8 Faitfully Flat Modules

9 Homological Dimensions-EXAM

10 Injective Dimensions

11 Global Dimensions of Semiprimary Rings

12 Global Dimensions of Local Rings

13 Uniform Dimensions

14 CS-Modules









Course Title Functional AnalysisDepartment MathematicsDivision in the Dept. Analysis and Functions Theory


Lecture Lab. Credit ECTS CreditMAT612 Spring Ph. D. Obligatory Turkish 3 0 3 10Course Prerequisites None





This course aims to acquaint students with the fundamental notions of Functional Analysis including Differentiation, Lebesgue Integral, Stieltjes Integral and its generalizations, Integral Equations and Linear transformations, Hilbert and Banach spaces, Completely contınuous symmetric transformations of Hilbert space, Bounded symmetric, Unitary, and normal transformations of Hilbert space, Unbounded linear transformations of Hilbert space.

Textbook and Supplementary readings1 Functional Analysis, Frigyes Riesz, Bela Sz. –Nagy, 1990.


1 Differentiation

2 Lebesgue Integral

3 Stieltjes Integral and its generalizations

4 Stieltjes Integral and its generalizations

5 Integral Equations and Linear transformations

6 Integral Equations and Linear transformations

7 Hilbert and Banach spaces

8 Hilbert and Banach spaces

9 Completely contınuous symmetric transformations of Hilbert space

10 Completely contınuous symmetric transformations of Hilbert space

11 Bounded symmetric, Unitary, and normal transformations of Hilbert space

12 Bounded symmetric, Unitary, and normal transformations of Hilbert space

13 Unbounded linear transformations of Hilbert space

14 Final Exam



Course Title Special FuctionsDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit EC TSCreditMAT 614 Spring Ph. D. Elective Turkish 3 0 3 10


Name of Instructors

Assist. Prof. Ali IŞIK, Assist. Prof. Ali Filiz


Adnan Menderes Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, 09010 AYDIN Tel: 256 2128498 [email protected], [email protected]


The aim of this course is to introduce special functions of mathematics.

Textbook and Supplementary readings1 W. W. Bell, Special Functions for Scienlisls and Enginccrs, Dover I ublications, 2004.

Larry C. Andrevvs, Ronold L. Phillips, Mathematical Techniques for Engineers and Scientists, Spie Press,2003.

2 Larry C. Andrews, Special Functions of Mathematics for Engineers, Spie Press, 1998.3 lan N. Sneddon, Fourier Transforms, Dover Pub., 1995.


1 Series solutions of ordinary differential equations,

2 Intergral Functions: Gamma function.

3 Beta function., Error function..

4 Exponential integrals, Elliptic integrals;

5 Special functions: Bessel function.

6 Legendre, Hermite, Laguerre

7 Chebyshev,

8 Gegenbauer,

9 Jacobi polinomials,

10 Hipergcometric functions

11 Integral transforms: Fourier

12 Laplace, Mellin, Hankel,

13 Kontorovich-Lebedev, Mehler-Fock transforms.



Course Title Numerical Solution of Differential and Integral EquationsDepartment MathematicsDivision in the Dept. Foundations of Mathematics and Mathematical Logic





MAT 616 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites MAT527

Name of Instructors Assist. Prof. Dr. Ali FİLİZ




To provide a unified account of numerical methods for solving integral, differential and partial differantial equations.

Textbook and Supplementary Readings1 E Hairer, S P Norsett and G Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, (2nd edition),

1993, Springer-Verlag.2 E Hairer and G Wanner, Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems, (2nd

edition), 1996, Springer-Verlag.3 A Iserles, Numerical Analysis of Differential Equations, 1996, Cambridge University Press.4 K W Morton and D F Mayers, Numerical Solution of Partial Differential Equations, 1994, Cambridge University

Press.


1 Discrete methods for solving ODEs: Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order

2 Review of Runge-Kutta methods, linear multistep methods (Adams) convergence and order.

3A number of practical ODE/PDE problems from different areas of applications will be introduced. They will be used and solved to illustrate ideas throughout the course. Implicit Runge-Kutta methods.

4 Stability regions, A-stability and other stability concepts. The BDF methods. Finite difference methods for linear equations and for more general problems.

5 The BDF methods. Finite difference methods for linear equations and for more general problems.

6 Implicit Runge-Kutta methods, deferred correction. Numerical solution of integral equations using different numerical methods.

7 The comparasion LaTeX and Word

8 Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula

9 Finite difference methods for heat equation, wave equation and Poisson's equation: The 5-point Formula

10 Existence and order of convergence for the grid-solution. Curved boundaries and derivative boundary conditions.

11 Existence and order of convergence for the grid-solution. Curved boundaries and derivative boundary conditions.

12 Numerical solution of parabolic Volterra integral equations using Finite difference methods

13 Numerical solution of parabolic Volterra integral equations using Finite difference methods

14 Final exam


Course Title Tauberian Theory and its ApplicationsDepartment Mathematics

Division in the Dept. Analysis and Functions Theory


Lecture Lab. Credit ECTS CreditMAT618 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None





This course aims to acquaint students with the fundamental notions of Tauberian theory and its applications including the Laplace-Stieltjes transform, convergence and absolute convergence of the Laplace-Stieltjes transform, uniform convergence of the Laplace-Stieltjes transform, Abelian theorems for power series, Abelian theorems for the Laplace-Stieltjes transforms, Tauber’s theorem, the remainder term in Tauber’s theorem, Littlewood’s theorem, the theorem of Hardy and Littlewood, Fatou’s theorem, Korevaar’s proof of Fatou’s theorem, the Haryd-Littlewood theorem in the complex domain and Ikehara’s theorem.

Textbook and Supplementary readings1 Tauberian theory and its applications, A. G. Postnikov


1 Laplace-Stieltjes transform

2 convergence and absolute convergence of the Laplace-Stieltjes transform

3 uniform convergence of the Laplace-Stieltjes transform

4 Abelian theorems for power series

5 Abelian theorems for the Laplace-Stieltjes transforms

6 Tauber’s theorem

7 the remainder term in Tauber’s theorem

8 Littlewood’s theorem

9 the theorem of Hardy and Littlewood

10 Fatou’s theorem

11 proof of Fatou’s theorem

12 the Haryd-Littlewood theorem in the complex domain

13 Ikehara’s theorem

14 Final Exam


Course Title Algebraic Curves


Department MathematicsDivision in the Dept. Topology


Lecture Credit ECTS creditMAT 620 Spring Ph. D. Elective Turkish 3 3 10Course Prerequisites None





The aim of this course is to introduce Algebraic Curves

Textbook and Supplementary Readings1 Kirwan F. (1992) Complex Algebraic Curves, Cambridge University Press2 Fulton W. (1989) Algebraic Curves, Addison-Wesley


1 Real algebraic curves

2 Complex algebraic curves in

3 Complex algebraic curves in

4 Complex projective spaces

5 Complex projective curves in

6 Affine and projective curves

7 Bézout’s theorem

8 Midterm Exam

9 Degree-genus Formula

10 Weierstrass P-function

11 Riemann surfaces

12 Riemann surfaces

13 Abel’s theorem

14 Riemann-Roch theoremCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


Course Title Lie AlgebraDepartment MathematicsDivision in the Dept. Algebra and Number Theory



Name of Instructors

Prof. Dr. Hatice Kandamar , Prof. Dr. Gonca Güngöroğlu ,Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Erdal Özyurt, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz


ADÜ Fen Edebiyat Fak. Matematik Bl. Aydın [email protected], [email protected],[email protected],, [email protected], [email protected]


This course is to introduce the students to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0. Besides being useful in many parts of mathematics an Phiysics, the theory of semisimple lie algebras inherently attractive.

Textbook and Supplementary readings1 Introduction to Lie Algebras and Representation Theory

2


1 Basic concepts: Definitions and first examples

2 Ideals and homomorphisms,

3 Soluble and nilpotent Lie algebras

4 Semisimple Lie Algebras: Theorems of Lie and Cartan

5 Killing form

6 Complete reducibility of representation

7 Representation of SL(2,F)

8 Root space and decompositons MIDTERM

9 Root systems: Axiomatics

10 Simple roots and Weyl group

11 Classification

12 Construction of root systems and automorphisms

13 Abstract theory of weights

14 Borel subalgebraCourse assessment will be weighted 40 % for one quiz and 60 % for the final exam. Depending on instructor’s preference, assessment may be by written or/and oral examination, homework, lab assay, projects, group presentation, or a combination of these.







Course Title Category Theory IIDepartment Mathematics Division in the Dept. Algebra and Number Theory



MAT624 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites Category Theory I

Name of Instructors





Advance Category and Aplications

Textbook and Supplementary readings1 Theory of Categories, Barry Mitchell, Academic Press, New York and London, 1965

2 Categories fort he Working Mathematics, S. Mac Lane, Graduate Texs in Mathematics 5


1 Complete Categories (C_i Categories, Injective Envelopes)

2 Existence of Injectives

3 Adjoint Functors (Generalities)

4 Existence of Adjoints

5 Functor Categories

6 Reflections

7 Projective Classes

8 Application to Limits

9 Tensor Product-EXAM

10 Full Imbedding Theorem

11 Ext^1, Ext^n

12 The Relation

13 The Exact Sequences

14 Global Dimension








Course Title Homological Algebra IIDepartment Mathematics Division in the Dept. Algebra and Number Theory



MAT626 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites It is necessary to know module theory and take Homological Algebra I before

Name of Instructors

Prof. Dr. Hatice Kandamar, Prof. Dr. Gonca Güngöroğlu, Assist. Prof. Erdal Özyurt, Assist. Prof. Dr. Selma Altınok, Assist. Prof. Dr. Semra Doğruöz, Assist. Prof. Dr. Hülya İnceboz Günaydın




Advance Homological Algebra

Textbook and Supplementary readings1 Basic Homological Algebra, M. Scott Osborne, Springer Verlag

2 Homology, Saunders Mac lane, Springer Verlag3 Introduction to Homological Algebra, Rotman, J.J.

4 Relative Homological Algebra, Edgar E. Enochs, Overtoun M. G. Jenda


1 Abstract Homological Algebra ( Living without Elements)

2 Additive Categories

3 Kernels and Cokernels

4 Cheating with Projectives

5 Arrow Categories

6 Homology in Abelian Category

7 Long Exact Sequences

8 An alternative for Unbalanced Categories

9 Limits and Colimits-EXAM

10 Adjoint Functors

11 Directed Colimits Tensor product and Tor

12 Lazard’s Theorem

13 Weak Dimension Revisited

14 Injective Envelops








Course Title Compact Riemann SurfacesDepartment MathematicsDivision in the Dept. Topology


Lecture Credit ECTS creditMAT 628 Fall Ph. D. Elective Turkish 3 3 10Course Prerequisites None





The aim of this course is to introduce compact Riemann surfaces

Textbook and Supplementary Readings1 Jost J. (1997) Compact Riemann Surfaces, Springer2 Jones G.A. and Singerman D. (1987) Complex Functions, Cambridge University pres


1 Manifolds

2 Riemann surfaces of analytic functions

3 Riemann surfaces of analytic functions

4 Topological classification of compact Riemann surfaces

5 Topological classification of compact Riemann surfaces

6 The theorems of Gauss-Bonnet and Riemann-Hurwitz

7 The theorems of Gauss-Bonnet and Riemann-Hurwitz

8 Midterm Exam

9 Harmonic maps

10 Metrics and conformal structures

11 Teichmüller spaces

12 Teichmüller spaces

13 Hyperelliptic Riemann surfaces

14 Geometric structures on Riemann surfacesCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.



Course Title Differential and Riemannian Manifolds IIDepartment MathematicsDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT632 Spring Ph. D. Elective Turkish 3 0 3 10Course Prerequisites None



Adnan Menderes Üniversitesi Fen Edebiyat Fakültesi Matematik Bölümü 09010-AydınTel:02562128498 [email protected]


The main goal is this course to provide a working knowledge of Riemanniann manifolds, tensors and differential forms.

Textbook and Supplementary readings1 Lang S. Differential and Riemannian Manifolds, Springer-Verlag 1995.


1 Basic Properties

2 The Riemannian Distance

3 The Riemannian Tensor

4 The Second Variation Formula

5 The Riemannian Volume Form

6 Covariant Derivatives


8 The Jacobıan Determinant of the Exponential Map

9 Orientation

10 Stoke’s Theorem on a Manifold

11 The Divergence Theorem

12 Cauch’y Theorem



.


tel:02562128498


Course Title Tensor AlgebraDepartment MathematicDivision in the Dept. Geometry


Lecture Lab Credit ECTS CreditMAT 634 Spring Ph.D. Elective Turkish 3 0 3 10






The main goal is this course to provide a working knowledge of Tensor Algebra

Textbook and Supplementary readings1 Greub,W.H. Multilinear algebra, Springer-Verlag New York 1967


1 Multilinear mappins

2 Tensor Product

3 Linear mappins4 Dual spaces

5 Tensors

6 Tensor algebra


8 Mixed tensors

9 Symmetry in the tensor algebra

10 Exterior algebra

11 The Poincare isomorphism

12 Symmetric tensor algebra




tel:02562128498

Course Title Digital Geometry Department MathematicsDivision in the Dept. Geometry


Lecture Lab

Credit ECTS credit

MAT 636 Spring PhD Elective Turkish 3 0 3 10Course Prerequisites None



Department of Mathematics, Faculty of Arts and Sciences, Adnan Menderes University, 09010 AYDIN, Tel: 256 2128498, E-mail: [email protected]


The aim of this course is to introduce Digital Geometry at the graduate level.

Textbook and Supplementary Readings1 Klette, R. and Rosenfeld, A. (2004) Digital Geometry: Geometric Methods for Digital Picture Analysis,

Elsevier. 2 Herman G.T. (1998) Geometry of Digital Spaces, Birkhauser.


1 Grids

2 Digitization

3 Metrics

4 Adjacency Graphs

5 Digital Topology

6 Combinatorial Topology

7 Topology of curves and surfaces

8 Midterm Exam

9 Geometry of curves and surfaces

10 Digital arc length

11 Digital curvature

12 Digital planes

13 Transformations

14 DeformationsCourse assessment will be weighted 40 % for one midterm exam and 60 % for the final exam. Depending on instructor’s preference, assessment may be written examination, oral examination or homework.


http://www.amazon.com/s/ref=rdr_ext_aut?_encoding=UTF8&index=books&field-author=Jiri%20Matousek

Course Title Advance Artificial IntelligenceDepartment MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 638 Spring Ph. D. Elective Turkish 3 0 3 8






In this course, it is aimed to present fundamental artificial intelligence subjects

Textbook and Supplementary readings1 Artificial Intelligence: A Guide to Intelligent Systems, M. Negnevitsky2 Artificial Intelligence: A Modern Approach, S. J. J. Russell and P. Norvig34


1 Introduction to AI

2 Programming languages

3 Knowledge representation: Production rules, inclusion hierarchies, prepositional and predicate calculus

4 Knowledge representation: Rules of inference, frames, semantic networks, constraints and syntactic approaches.

5 Searching: Hypothesis and test, depth-first search, breadth-first search

6 Searching: Heuristic search, optimal search

7 Searching: Game trees and adversarial search: minimax search and alpha-beta pruning

8 Learning: Identification trees

9 Learning: Neural nets, perceptrons

10 Learning:Genetic algorithms

11 Expert systems, robotics, computer vision, natural language processing, speech recognition






Course Title Digital Signal Processing Department MathematicsDivision in the Dept. Applied Mathematics


Lecture Lab Credit ECTS CreditMAT 640 Spring Ph.D. Elective Turkish 3 0 3 8






This course will introduce the basic concepts and techniques for processing signals on a computer. By the end of the course, you be familiar with the most important methods in DSP, including digital filter design and transform-domain processing. The course emphasizes intuitive understanding and practical implementations of the theoretical concepts using the Matlab environment.

Textbook and Supplementary readings1 McClellan, J. H., et al. “Computer-Based Exercises for Signal Processing Using MATLAB® 5”, Upper

Saddle River, NJ: Prentice Hall, 1998. ISBN: 0137890095.2 Emmanuel C. Ifeachor, Barrie W. Jervis, 2002; “Digital Signal Processing, A practical Approach”. Second

Edition, Prentice Hall.3 Sanjit K. Mitra ,” Digital Signal Processing: A computer-based approach” (3rd ed.), McGraw-Hill, 2005

(ISBN 0-07-304837-2, international edition ISBN 007-124467-0)4


1 Introduction to digital signal processing and its applications

2 Analog/digital input/output interfaces for real time systems

3 Discrete transforms, Discrete Fourier transform

4 Fast Fourier transform, inverseFFT, and discrete transforms

5 Z-transorm and applications

6 Extracting correlation and convolution function

7 Training algorithms for digital signal processing and speech recognition

8 Digital filter design

9 Finite impulse response (FIR) digital filter design

10 Window-based FIR filter design

11 FIR filter design by frequency sampling

12 Recursive (IIR) digital filter design

13 Adaptive digital filters

14 Final Exam




Course Title Special RingsDepartment MathematicsDivision in the Dept. Algebra



MAT 642 Spring Ph. D. Elective Turkish 3 0 3 10


Name of Instructors



Adnan Menderes University, Faculty of art and sciences, Department of Mathematics-09010 Aydın Tel: 256 218 20 00, E-posta : [email protected], [email protected], [email protected], [email protected], [email protected]


In this course, it is aimed to introduce some special rings and to present fundamental ring strucrute

Textbook and Supplementary readings1 Noncommutative Rings, I. N. Herstein2 Algebra, T.W. Hungerford


1 Jacobson Radical, Artinian Rings

2 Semisimple Artinian Rings

3 Density Theorem

4 Semisimple Rings, Applications of Wedderburn’s Theorem

5 Wedderburn’s Theorem and Some Generalizations

6 Some Special Rings

7 The Brauer Group

8 Midterm Exam

9 Maximal Subfields

10 Representations of Finite Groups

11 A Theorem of Hurwitz, Applications to Group Theory

12 Polynomial Identities

13 Standart Identities, A Theorem of Kaplansky







Documents

· Web viewCode Term Level Type Language Credit hours/week Lecture Lab Credit ECTS Credit Mat 540 Spring MS Elective Turkish 3 0 3 10 Course Prerequisites None Name of Instructors