Niğde Ömer Halisdemir Üniversitesi Logo T.C. NIGDE UNIVERSITY
FACULTY OF SCIENCE - MATHEMATICS
COURSE DESCRIPTION
1. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory ATA1015 ATATURK PRINCIPLES AND THE HISTORY OF REVOLUTION I 2 0 2
Atatürk İlkeleri ve İnkılâp Tarihi Dersinin Amacı İnkılap ve İnkılapla Alakalı Kavramlar Osmanlı Devletinin Yıkılışı XIX. Yüzyılda Osmanlı Devletinde Yenilik Hareketleri Osmanlı Devletinin Son Döneminde Devleti Kurtarmaya Yönelik Fikir Akımları XX. Yüzyıl Başlarında Osmanlı Devletinin Durumu Mondros Ateşkes Antlaşması Sonrası Memleketin Durumu Milli Mücadeleye Hazırlık Dönemi Büyük Millet Meclisinin Açılması ve Çalışmaları Büyük Millet Meclisinin Açılışından Sonraki Siyasi ve Askeri Gelişmeler Lozan Barış Antlaşması, Önemi ve Sonuçları
Compulsory ENF1021 BASIC COMPUTER 2 2 3
Bilgisayara Giriş ve Donanım, İşletim Sistemleri ve Uygulama Yazılımları, Windows İşletim Sistemi, Microsoft Word, Microsoft Excel, Microsoft PowerPoint, İnternet Kullanımı, Bilişim Teknolojileri
Compulsory MAT1001 ANALYSIS I 4 2 7
Real Number,Inequalities, Consept of sequences, Convergence of sequences, Bounded sequences, Definition of functions,Some special functions, Limit of functions, Theorems of limit, Continuous functions and properties of continuous functions, Uniform continuity, The derivative, Derivatives of the some special functions, Derivative of the parametric and implicit functions, High degree derivatives, Geometrical meaning of the derivative, Fundamental theorems of derivative, Uncertain cases and LHospital Rule, Application of derivative, Maximum and Minimum, Linear approximation and differential, Generalized mean value theorem, Asymptots, Graph of a function.
Compulsory MAT1003 LINEAR ALGEBRA I 4 0 5
Compulsory MAT1005 ABSTRACT MATHEMATICS I 4 0 5
Propositions, Proof techniques, Sets, Family of sets, Product sets, Functions, Relations, Equivalance Relations, Partial and Complete Ordered Sets.
Compulsory MAT1007 GENERAL PHYSICS 3 0 3
Straight Line Motion, Motion in a Plane, Newton Laws, Applications of Newton Laws, Work and Kinetic Energy, Potential Energy and Conservation of Energy, Linear Momentum , Collisions, Center of Mass, Rotations of Rigid badies, Angler Momentum, Torque, Statics
Compulsory TDL1011 TURKISH LANGUAGE I 2 0 2
Dil ve Diller: Dil Millet İlişkisi, Dil Kültür İlişkisi Yeryüzündeki Diller ve Türk Dilinin Dünya Dilleri arasındaki Yeri; Kaynakları bakımından Dil AileleriTürk Yazı Dilinin tarihi gelişimi; Eski Türkçe, Orta Türkçe, Divanü Lügat-it Türk, Atabetü'l- Hakayık, Harezm Türkçesi, Eski Türkiye Türkçesi (Eski Anadolu Türkçesi) ; Yeni Türkçe Dönemi, Modern Türkçe Dönemi, Batı, Güney Batı Türkçesi) , Türkiye Türkçesi, Doğu ( Kuzey ) Doğu Türkçesi) , KaratayTürkçesi, Ses Bilgisi (FONETİK) , Ses ve sesin oluşumu, büyük ve küçük ünlü uyumu, Türkçedeki başlıca ses olayları; Türkçe'nin ses özellikleri, Türkçe'nin hece yapısı, cümle vurgusu. Şekil Bilgisi (MORFOLOJİ- BİÇİM BİLGİSİ) , şekil bakımından kelimeler, kökler, gövdeler, ekler (yapım ekleri, çekim ekleri) , anlatım ve vazifeleri bakımından kelimeler; isimler, sıfatlar, zamirler, fiiller, fiil çekimi, şekil ve zaman ekleri, fiilimsiler, edatlar, fiilden türeyenler ve isimden türeyenler, anlam bilimi; kelimede anlam, kelimenin anlam çerçevesi
Compulsory YDL1013 FOREIGN LANGUAGE I 3 0 3
Öğrencilerin, somut ihtiyaçları dile getiren günlük hayatta sık kullanılan ifadeleri ve basit cümleleri anlayabilmeleri ve bunlarla kendilerini ifade edebilmeleri, kendilerini ve başkalarını tanıtabilmeleri, başka insanların kişisel bilgilerine yönelik sorular sorabilmeleri ve bu tür sorulara yanıt verebilmeleri için gerekli temel konuları ( verb to be, Simple Present, can, can't, a/an, some, any, object pronouns, there is / are, have got, past of to be, Simple Past, etc.) içermektedir.
2. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory ATA1016 ATATÜRK PRINCIPLES AND THE HISTORY OF REVOLUTION II 2 0 2
Türk İnkılâp Hareketleri, Atatürk Dönemi Türk Dış Politikası, Türk İnkılâbının Temel İlkeleri (Atatürk İlkeleri), Bütünleyici İlkeler, Atatürk’ün Hastalığı ve Ölümü, İsmet İnönü’nün Cumhurbaşkanı Seçilmesi ve İsmet İnönü Dönemi (1938–1950), II. Dünya Savaşı, Demokrat Parti İktidarı ve Adnan Menderes Dönemi (1950–1960), Askeri Darbeler ve Türkiye Cumhuriyeti (1960–1980), 12 Eylül 1980 Darbesi ve Sonrasında Türkiye
Compulsory MAT1002 ANALYSIS II 4 2 8
Indefinite integral, Integration techniques, area under the curve and definite integral, Properties of Riemann integral, Fundamentel theorem of define integral, Applications of define integral, Calculation of area, Calculation of length of arc, Area of surface of revolution, Volume of a surface of revolution, Polar coordinates, Series, Positive term series, Pover Seriesi, Representation of functions by power Series, Taylor and Maclaurin series.
Compulsory MAT1004 LINEAR ALGEBRA II 4 0 6
Compulsory MAT1006 ABSTRACT MATHEMATICS II 4 0 6
Binary operations, Group Theory, Subgroups, Group homomorphisms, Ring Theory, Ideal and Maximal ideal, Numbers, Building integer numbers , Peano axioms, Building rational numbers, Real numbers, Factorization, Prime numbers.
Compulsory MAT1008 GENERAL PHYSICS II 3 0 3
Electric Charge, Electric Field, Cloump Law, Gauss Law, Electric Potential, Capacitors, Dielectrics, Currents in Materials, Direct Current Circuits, Magnetic Fields, Faradays Law, AC Currents.
Compulsory TDL1012 TURKISH LANGUAGE II 2 0 2
Kelime grupları, kelimelerin gerçek, yan ve mecaz anlamları, Deyimler, ikilemeler, terimler, dil yanlışları, Türkçenin cümle yapısı, cümle öğeleri, cümle çözümlemeleri, roman, makale, deneme, şiir gibi yazılı anlatım türleri, sunum, rapor ve tutanak örnekleri, dilekçe, iş mektubu ve Özgeçmiş (CV) yazma, karşılıklı konuşma ve tartışma gibi anlatım türleri
Compulsory YDL1014 FOREIGN LANGUAGE II 3 0 3
Öğrencilerin, güncel hayatla ilgili cümleleri ve sıkça kullanılan ifadeleri anlayabilmeleri (kendileri, aileleri, iş ve yakın çevreleri, alışveriş vb. ile ilgili bilgileri), gerekli durumlarda anlaşılır ve bildik konuların doğrudan aktarımını yapabilmeleri, temel seviyedeki anlatımlarla kendilerini, eğitimlerini, yakın çevrelerini ve doğrudan ihtiyaca yönelik durumlarını anlatabilmeleri için Yabancı Dil I dersini temel alan ve devamı olan konuları (Present Continuous, adverbs of manner, comparison of adjectives, superlative adjectives, prefer + noun/-ing form, will, Present Perfect, have to/ don’t have to, wh- questions, be going to for intentions and plans, infinitive of purpose, verbs + infinitive/-ing form etc.) içermektedir.
3. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory MAT2001 ANALYSIS III 4 2 6
Function sequences and function series, pointwise and uniform convergence, differantion and integration of power series, improper integrals, vector valued functions .
Compulsory MAT2003 ANALYTIC GEOMETRY I 4 0 6
Cartesian coordinates in the plane and in space,vectors in the plane,the equation of the plane,the plane equation in space,the line relationships with the plane,the vectors in space, linear dependence of vectors,independence,inner product,vector product,linear equations, the line equation in space, a line of a point projection,the distance,the distance between the two points,the equation of the plane,a line of a point projection,length,half plane,the plane in space,a plane projection of a point, distance,semi space,the angle between two planes, the general definition of conic curves,circles, tangent of the circle, according to the strength of a point in the circle, touching the chord,an ellipse,the ellipse equation,directions, Hyperbola,hyperbola equation,asymptotes, directions, parabola, parabola equation, the curve in space,some special curves
Compulsory MAT2005 DIFFERENTIAL EQUATIONS I 2 2 5
First order differential equations. The second and higher order linear homogeneous and nonhomogeneous differential equations with constant coefficients.
Compulsory MAT2007 PROBABILITY AND STATISTICS I 4 0 5
Giving brief information related set theory and the fundamentals of probability theory. Permutation and combination. Expected value and variance. Random variable. Discrete and continous distributions. Moments, the defintions of skewness and kurtosis, some special discrete distributions (Bernoulli, Binom, geometric). Normal distribution.
Elective MAT2009 VOCATIONAL FOREIGN LANGUAGE I 2 0 4
Simple Present tense , Simple progressie tense , Simple past tense, Past progressive tense , Simple future tense, Future progressive tense, Future perfect tense Future perfect progressive tense , Be going to formu, Present perfect tense, Present perfect progressive tense, Past perfect tense , Past perfect progressive tense, Modals , The passive voice, Repored speech ,The inversion construction, Sentences
Elective MAT2011 MATHEMATICAL SOFTWARES I 2 0 4
Basics of Mathematica, arithmetical operations, functions, algebraic expressions and equations, limit, differentiation, integral, finite sums and infinite series, vector operations, graphics.
Elective MAT2013 GIRISIMCILIK I 2 0 4
Elective MAT2015 KRIPTOLOJY I 2 0 4
YOK
Elective MAT2017 MATHEMATICS I 2 0 4
Elective MAT2019 CONTENTS AND MOTIVATION I 2 0 4
4. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory MAT2002 ANALYSIS IV 4 2 6
Extremums of several variabla functions , double and trible integrals , line and surface integrals.
Compulsory MAT2004 ANALYTIC GEOMETRY II 4 0 6
Quadratic equation in the plane, as indicated in geometrical conics, according to symmetry of a point in the plane , according to the symmetry of a point in space,according to symmetry of a line in the plane , according to symmetry of a line in space , the plane polar coordinates, the distance between two points, the line equation, curves in plane and in space , the surface of sphere, according to a sphere of a point force, the four point sphere equation, a sphere with a straight line in space, the intersection of two of the sphere bundle of the sphere, the parametric equation of the sphere, cylinder, cone, rotary surfaces, linear surfaces, quadric surfaces, the space coordinate systems.
Compulsory MAT2006 DIFFERENTIAL EQUATIONS II 2 2 5
Series solutions of second order linear equations, systems of first order differential equations and Laplace transform.
Compulsory MAT2008 PROBABILITY AND STATISTICS II 4 0 5
To ıntroduce some special continous distributions, giving the definitions of sample, introducing random sample, frequency distributions, the definitions of central tendency and disperision measure, point estimation, confidence intervals, hypothesis tests, chi-square indepence test, correlation, regression.
Elective MAT2010 VOCATIONAL FOREIGN LANGUAGE II 2 0 4
Different reading studies and examples form Reader at Work II between the passages number 1 with 28. Reading different mathematical texts with different level competency needs.
Elective MAT2012 MATHEMATICAL SOFTWARES II 2 0 4
Basics of MATLAB, windows, arithmetical operations, functions, sequences, matrices, M files, programming, graphics, mathematical applications.
Elective MAT2014 GIRISIMCILIK II 2 0 4
YOK
Elective MAT2016 KRIPTOLOGY II 2 0 4
YOK
Elective MAT2018 IKTISADI MATHEMATICS II 2 0 4
YOK
Elective MAT2020 CONTENTS AND MOTIVATION II 2 0 4
YOK
5. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory MAT3001 THEORY OF COMPLEX FUNCTIONS 4 0 5
Complex Numbers, Topology of Complex Plane,Complex Sequences and series, Functions of a Complex Variable and mappings, Stereographic Projection , Limits, continuity and uniform continuity of a Complex Function, Derivatives of Complex Function and Cauchy-Riemann Equations,Analytic and Harmonic Functions
Compulsory MAT3003 DIFFERENTIAL GEOMETRY I 4 0 5
Affine space, Euclidean space, topological space, metric space, topological manifolds, differentiable manifold, tangent space, vector space, cotangent space, directional derivatives, covariant derivatives, Jacobian matrix, differentiable functions, gradient functions, Divergence function, rotation functions, sub- manifolds, immersion and imbedding, the theory of curves, Frenet vector fields, osculating, normal and rectification planes, curvature of the curve, the circle of curvature, the sphere of curvature , the transformation of derivative, Involute, evolute, Bertrant curves and a curve of global indicators
Compulsory MAT3005 ALGEBRA AND NUMBER THEORY I 4 0 5
Set Theory, Functions, Numbers, Prime number, Group Theory, Group, condition of group, Subgroups, Cyclic groups, Lattices, Normal subgroups, Group homomorphisms, Isomorphims, Symmetric Groups, Sylow Groups
Compulsory MAT3007 COMPUTER PROGRAMMING I 3 0 5
Algorithm and flowcharts,Programming a Fortran Language,The input and output statements,control structures,subprograms.
Compulsory MAT3009 NUMERICAL ANALYSIS I 3 0 5
Error analysis in numerical calculation, Finete difference and construction of the table of finete difference, Forward opetaor, Shift operator, Problem of the interpolation and its application, Forward Newton-Gregory operator, Sub table problems, divided differences and the Newton divided difference equation, Lagrange interpolation equation, Centered difference, Extrapolasyon, Gauss and Stiriling equality, Curve fitting and least sqaure methods, Numerical solution of the linear equations by using the methods of Jacobi and Gauss-Siedel, Numerical solution of the eigen values and eigen vectors problem by using the pover, reverse iteration and QR factorization methods.
Compulsory MAT3011 GENERAL TOPOLOGY I 4 0 5
The first chapter, after giving the concept of topology, kapalılar, neighborhoods, clusters of a cluster derivative, defined, derived from a variety of features, the usual right and left of the numbers R reel are given.Resolved topological examples. The second section, the topology, the concepts of k spaces given point and everywhere continuous function, obtained with continuity.Example of The criteria are defined and two space is solved.Open and closed functions handled with homeomorfizm.Topolojical family relationship to be more coarse, arranged with supremum and infremum discussed. The third section, the initial topology and results topology have been obtained, are discussed in detail, as an example of the concept of product and quotient topologies are investigated. Moreover given sub space, all the concepts re examined the sub space topological spaces, topological and given to the concepts of inherited property, many of them are proved.
Elective USD3051 CURRENT BIOTECHNOLOGY 3 0 5
Elective USD3053 HISTORY OF ART 3 0 5
Elective USD3055 PROFESSIONAL ENGLISH 3 0 5
Elective USD3057 3 0 5
Elective USD3059 WEB DESIGN FOR EVERYONE 2 0 5
Elective USD3061 PROJECT PROCESSES AND MANAGEMENT 2 0 5
Elective USD3069 NEWS ANALYSIS 1 2 5
Elective USD3071 ARABIC RELIGIOUS AND LITERATURE MYTHS 2 0 5
Elective USD3073 METHODS OF MEMORYING THE QURAN 2 0 5
Elective USD3081 REPRODUCTIVE HEALTH FOR YOUTH 2 0 5
Elective USD3083 SELF KNOWLEDGE AND AWARENESS 2 0 5
Elective USD3085 HEALTHY LIFE AND PROTECTION FROM DISEASES 2 0 5
Elective USD3087 SCIENTIFIC PROJECT PREPARATION AND REPORTING 2 0 5
Elective USD3089 2 0 5
Elective USD3091 CRISIS COMMUNICATION 2 1 5
Elective USD3093 3 0 5
6. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory MAT3002 THEORY OF COMPLEX FUNCTIONS II 4 0 5
Cauchy Goursat Theorem and its applications, Cauchy s Integral Theorem and Cauchy s Integral Formulas,A Simply connected domain and a multiply connected domain, Sequences and Series of Analytic Functions, Taylor and Laurent Series. The Residue Theorem and its applications
Compulsory MAT3004 DIFFERENTIAL GEOMETRY II 4 0 5
The theory of surfaces, Surface orientation, Shape operator and the Gauss map, the basic forms, Gauss equation, the Gaussian curvature and mean curvature, Principal curvature, normal curvature, geodesical torsion, strip theory, lines of curvature, asymptotical curves, geodesical curves, surfaces of revolution on the relations, Ray surface differential geometry, the parallel surfaces, minimal surfaces, hypersurfaces, the surfaces smooth mapping, isometries.
Compulsory MAT3006 ALGEBRA AND NUMBER THEORY 4 0 5
Ring Theory, Subring, Integral domain, Ideal, Rings of Quotients, Polynomial rings, Aritmethic on ring, Homomorfisms, Isomorphism, Prime Factors, Fields.
Compulsory MAT3008 COMPUTER PROGRAMMING II 3 0 5
Short history of C++ programming language,basic rules of the writing program,statements,arrays,descriptives,decision,control structures,loops, categories,pointer structures,files.
Compulsory MAT3010 NUMERICAL ANALYSIS II 3 0 5
Numerical derivative, Numerical integrationl, Difference equation, Solution of the homegenous dififference equations with constant coefficients, Solution of the non homegenous dififference equations with constant coefficients, Solution of the ordinary differential equation by using the methods of power series, undetermined coefficients, Picard, Euler, Runge-Kutta, Kutta-Merson. Numerical solutions of the high degree ordinariy differential equations
Compulsory MAT3012 GENERAL TOPOLOGY II 4 0 5
The fourth section, the sequence, the nets and filters supremum and infimum found in the family and the help of these concepts, methods of setting up new ones added to the topological structure. The fifth section, the separation axioms are examined, given the criteria, compared with each other, plenty of examples are solved. sixth chapter, the compact and locally compact spaces are considered, compactness, sequential compactness and countable compactness are given to concepts, these concepts are compared between them, examples are solved.
Elective USD3050 RECENT DEVELOPMENTS IN PHYSICS 3 0 5
Elective USD3052 CIVILIZATION HISTORY 3 0 5
Elective USD3054 DECISION MAKING TECHNIQUES 3 0 5
Elective USD3056 CURRENT ISSUES IN FINANCE 3 0 5
Elective USD3060 NATURAL DISASTERS 2 0 5
Elective USD3066 SAIR AND ITS RESOURCES 2 0 5
Elective USD3068 MAIN SUBJECTS OF THE QUR'AN 2 0 5
Elective USD3070 CLOTHING HISTORY 2 0 5
Elective USD3080 CURRENT AND POPULAR MUSIC 2 0 5
7. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory MAT4000 GRADUTION THESIS 0 2 5
Compulsory MAT4003 FUNCTIONAL ANALYSIS I 3 0 5
Metric and normed spaces , banach spaces, kompaktness , linear operators and linear functionals , dual spaces.
Compulsory MAT4005 PARTIAL DIFFERENTIAL EQUATIONS I 3 0 5
The concept of Partial Differential Equation, first, second and higher order Partial differential equations, Modelling of Partial Differential Equations ( PDEs), Fourier serries expansion to used in solution of PDEs,Canonical forms of PDEs, Vibration of a string problem, Wave propagation in an elastic media, Heat Conduction problems and their related solutions.
Elective MAT4007 GEOMETRY I 3 0 5
Some remarks on topological concepts. Map and atlas on a set. Differentiable maps and atlases. Topological and Differentiable manifold. Manifold structure of the reduced topology. Real-valued function on a manifold and derivative and differentiation in a point .Partial derivatives of the function defined between two manifolds. tangent vector of a point of a manifold. Real-valued function defined on a manifold of a point, directional derivative and derivative of differentiation at a point defined functions between two manifolds. Inverse Function Theorem for functions between manifolds. Leibniz formula. Immersions . submanifolds. Submanifold types. Riemannian Manifold, metric and connection.
Elective MAT4009 ALGEBRA III 3 0 5
Semi groups, Monoids ve Groups, Homomorphisms and Subgroups, Cyclic groups, Kosts and Count, Normality, Symmetric Alternating and Dihedral groups, Free groups, Free products, Generators and Relations, Free abelian groups, The effect of a cluster of a group, Sylow theorems.
Elective MAT4011 CONNECTED SPACES 3 0 5
sets connected, connected space, component, local connected space, connected way, given the concepts of space, compared with these spaces, connectedness, R of real numbers, sub spaces connectedness, convexity and connectedness polygon is examined and examples are given.
Elective MAT4013 REAL ANALYSIS I 3 0 5
Sequences of sets, upper and lower limit and their convergence, ring and algebra, Measurable sets, measure and outher measure, of Lebesgue outher measure, Lebesgue measure, measurable functions, class of measurable functions.
Elective MAT4015 MATHEMATICAL MODELLING 3 0 5
Introduction to mathematical modeling, Compartmental models, single-population models, interaction population models.
Elective MAT4017 ALGEBRAIC TOPOLOGY I 3 0 5
topological equivalence, surfaces, routing and two multilateralism, connectedness, topological constants, Euler theorem on the very polyhedral, coloring maps, functions, equivalence relations, continuity on Euclidean planes, n-dimensional Euclidean space, metric spaces, continuity in metric spaces, open and closed sets in metric spaces, topological spaces, bases, relative topology, identification topology, topological product, topological groups, Hausdorff spaces, normal spaces, convergence, filters, lump spaces, connected spaces.
Elective MAT4019 TRANSFORMATIONS AND GEOMETRIES I 3 0 5
Affine Spaces, Affine Subspaces, Euclidean Spaces, Introduction To Transformations, Euclidean Plane Motions, Similarity Transformations.
Elective MAT4021 HISTORY OF MATHEMATICS I 3 0 5
The scientific research on the history of mathematics. Classifications based on scientific principles. Used in mathematics and comparative civilizations, and their chronology. On mathematics concepts. The development of mathematical concepts. Scientists in the history of mathematics.
Elective MAT4023 CATEGORY THEORY I 3 0 5
The definition of category and examples of category, several term used in categories, epic, monic, objects, morphisms, functors and its examples
Elective MAT4025 GROUP THEORY I 3 0 5
Group theory, Direct sums, Abelian groups, p- Groups and p-Subgroups, Supersolvable groups, Free groups and Free products.
Elective MAT4027 DIVERGENT SERIES I 3 0 5
Metric space, special sequene spaces, complete metric spaces, linear spaces, normed and paranormed spaces, linear transformations and Banach Steinhaus Theorem
Elective MAT4029 APPLIED MATHEMATICS I 3 0 5
Integral equations and their classifications, Fredholm integral equations, Volterra integral equations, Integro-differential equations, Singular integral equations, Solution methods for integral equations , Decomposion method, modified decomposion method, Direct mehod, Succesive approximations method, succcesive substitution ethod, Variaitonal principles and methods,weighted integrals, some mathematical concepts and formulas, boundary value, initial value and eigenvalue problems, foundations of variaitonal calculus euler equationnatural and basic boundary conditions, Hamilton principle, Variaitonal methods, Ritz method,Approximation functions, Weighted residuals method.
Elective MAT4031 SPECIAL TOPICS IN COMPLEX ANALYSIS I 3 0 5
Conformal Mappings and their basic properties, Analytic Continuation and uniqueness of Analytic Continuation , Schwarz reflection principle, Riemann surfaces multiple-valued functions and abstract Riemann surfaces
Elective MAT4033 NUMBER THEORY I 3 0 5
The aim of the lesson is to create numerical models , making hypothesis derived from observations as a mathematical method and to obtain concrete theorem , putting forward axioms that accept hypothesis models .
Elective MAT4035 AFFIN DIFFERENTIAL GEOMETRY I 3 0 5
Affine Spaces, Affine Connection, Nondejenere metrics, and the basic equations of affine immersions, Blaschke immersions, Cubic Forms, Affine Hypersurfaces, Affine Spheres, Ruled Affine spheres, Cayley surfaces.
Elective MAT4037 METRIC AND TOPOLOGICAL SPACES I 3 0 5
Metric space, normed space, and to teach the concepts of topological space is to consider the relationships between them. In addition, courses in functional analysis and general topology is to assist in understanding.
Elective MAT4039 MOTION GEOMETRY 3 0 5
D-Module, Dual vector space, E-Study transformation, dual-variable function theory, Theory of quaternions, The geometry of the lines.
Elective MAT4041 TOPOLOGICAL ANALYSIS 3 0 5
analyze the course and sets, the sequence, limit, continuity concepts are discussed and analyzed samples. later, more generally, these concepts are topological spaces. also limit and closing the concepts of the family of filters is discussed and topological structure was obtained with the family of filters and examples are given.
Elective MAT4043 NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS 3 0 5
Initial and boundary value problems of ordinary differantial equation, The single step methods for the numerical solution of ordinary differential equation, Taylor series method, Euler Method, Corrected Euler method, Runge-Kutta Methods, High degree Runge-Kutta methods, Multi step metods, Adams, Milne and Adams-Moulton methods, Stiff differential equation, Boundary value problems, shothing method, finite difference methods, numerical solution of the system of equations, Engineering applications.
Elective MAT4045 SIGN LANGUAGE 3 0 5
Elective MAT4047 CAREER PLANNING 3 0 5
Elective USD4053 HISTORY OF SCIENCE 3 0 5
Elective USD4055 CURRENT ISSUES IN BUSINESS 3 0 5
Elective USD4057 CURRENT ISSUES IN FINANCE 3 0 5
Elective USD4059 ROBOTIC CODING 2 0 5
Elective USD4061 CLIMATE CHANGE AND ITS IMPACTS 2 0 5
Elective USD4067 ISLAM, HUMAN RIGHTS AND DEMOCRACY 2 0 5
Elective USD4069 TODAY'S WORD PROBLEMS 2 0 5
Elective USD4071 HISTORY OF JEWELERY ART 2 0 5
Elective USD4073 EXPERIMENTAL ART 2 0 5
Elective USD4081 HEALTH TOURISM 3 0 5
Elective USD4083 HOME ACCIDENTS PREVENTION AND SAFETY IN CHILDREN 2 0 5
Elective USD4085 CINEMA AND ART 3 0 5
8. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Elective FRM4020 1 8 10
Compulsory MAT4004 FUNCTIONAL ANALYSIS II 3 0 5
Hahn- Banach theorem, Open Mapping Theorem, Closed graph Theorem, Uniform Boundedness Principle, Innerproduct spaces, hilbert space, Banach algebra, spectrum.
Compulsory MAT4006 PARTIAL DIFFERENTIAL EQUATIONS II 3 0 5
Separation of variables ( Fourier Method), heat conduction problen in an finite rod, Laplace equation, solution of LAplace equation on different domains, Wave equation with different conditions, Higher order partial differential equations, Drichlet problems on different domains, 3-D wave equation, heat conduction problem in 2-D and 3-D cartesin coordinates, Non-homogenous partial differential equations, some classical problems of partial differential equations,Laplace equation in polar coordinates.
Elective MAT4008 GEOMETRY II 3 0 5
Topological manifold, Differentiable manifold and dif.bilir transformations, vector fields on manifolds, integral curves, Lie shock, on the differentiable manifold forms, Riemannian manifold, Connection, LC Connection, the Riemann curvature, sectional curvature, Ricci curvature, induced connection on the submanifold, Gaussian equation
Elective MAT4010 ALGEBRA IV 3 0 5
Rings : Rings and Homomorphisms, Ideals, Polynomial rings, Extension Rings, Algebraic extensions, Finite Fields and Coding theory.
Elective MAT4012 METRIC SPACES 3 0 5
before, given normed space, Samples dissolved,then obtained from the metric space topology and metrics are discussed.supported by examples.
Elective MAT4014 REAL ANALYSIS II 3 0 5
Integral of simple and positive functions , integrable functions, Lebesgue convergence theorem and Lebesgue bounded convergence theorem, relation between Riemann and Lebesgue integral, Lp and L infinity spaces.
Elective MAT4016 MATHEMATICAL MODELLING II 3 0 5
Phase diagrams, Linearization analysis, some population models, heating and cooling.
Elective MAT4018 ALGEBRAIC TOPOLOGY II 3 0 5
The concept of homotopy, homotopy type, curves, the main group, homotopy groups, linear subspaces of Euclidean space, simplex, simplex orientation, simplicial complexes, touching, triangulation, finite viviparous Abelian groups, chains, borders, cycle, homology groups, Betti numbers, cohomology groups, the calculation of homology groups.
Elective MAT4020 TRANSFORMATIONS AND GEOMETRIES II 3 0 5
Affine transformations, Projections, Projective Transformations, Topological Transformations.
Elective MAT4022 HISTORY OF MATHEMATICS II 3 0 5
Obtained as a result of many years of scientific research, information and documents are classified according to scientific principles. The resulting of this information, the date of the places in comparative civilizations, and describes a chronological manner. In mathematics, numbers, counting, shapes, definitions, theorems, such as topics, to date the beginning of the development of scientific thought and exhibited in a chronological framework. To date, scientists have found in history are examined in chronological committed.
Elective MAT4024 CATEGORY THEORY II 3 0 5
Teaching new concepts used in Category theory and giving these concepts with their application to student in detail. Structuring the Morphism Sets, Functors, Equivalent Categories and Adjoint Functors.
Elective MAT4026 GROUP THEORY II 3 0 5
Permutation groups, Simetric and Alternating groups, Representation, Products of subgroups, The multiplicative group of a division ring, Infinite groups.
Elective MAT4028 DIVERGENT SERIES II 3 0 5
Sequence to sequence, serie to sequence and erie to serie matrix trasformations, particular limitation methods, consistency, absolute equivalence and tanslativity.
Elective MAT4030 APPLIED MATHEMATICS II 3 0 5
Emergence of boundary value problems and Sturm-Liouville problems, singular sturm-Liouville boundary value problems, Vectoral differential calculations, speed, acceleration, curvature, gradient field, Divergence, curl, line integral, Green theorem, path independence, potential theory, surface integrals and applications of surface integrals, Gauss, stokes theorems , Tensors and tensoral calculations, Einstein summation rule, basic rules for tensoral calculations, General tensors and some operations on them, Metric tensor.
Elective MAT4032 SPECIAL TOPICS IN COMPLEX ANALYSIS II 3 0 5
The Basic Spaces, upper half-plane model,The Group of Möbius Transformations, Classification of Möbius Transformations, Matrix Representation, Preserving of upper half-plane, Topological groups, Topological transformation groups, The group PSL(2,IR) and its discrete subgroups, Hyperbolic distance and hyperbolic length in upper half-plane, Gauss-Bonnet Formula, Fuchsian groups and its properties.
Elective MAT4034 NUMBER THAORY II 3 0 5
Convolition Multiplication of Aritmetic Functions , Congruance Systems ,Quadric Congruences,Primitive Roots and Indexes ,Arithmetic Functions.
Elective MAT4036 AFFIN DIFFERENTIAL EQUATIONS II 3 0 5
Affine convexity, Ovaloid and ellipsoid, Minkowski integral formula and applications, Affine minimal hypersurfaces, affine paraboloids, from R ^ n to R ^ n +1 affine immersions, Cartan-Norden theorem, locally symmetric affine hypersurfaces, projective structures and projective immersions.
Elective MAT4038 METRIC AND TOPOLOGICAL SPACES II 3 0 5
Convergence of sequences in metric spaces, continuity of functions in metric spaces, normed spaces, convergence and continuity. complete metric spaces, compact metric spaces, connectedness, continuity in connected metric spaces, connected metric spaces with path, topological spaces, a set of topological spaces, a cluster interior, exterior, boundary, accumulation points, continuity in topological spaces, convergence in topological spaces,neighborhoods in topological spaces are given. the bases in topological spaces are given.
Elective MAT4040 COVERING SPACES 3 0 5
curves, manifolds and some important properties of manifolds, tor surface, Möbius strip, smooth manifolds, simple connectedness, homotopy, back to the transforms, deformations, curves are not simply connected, simpleksel complexes, high-dimension circle and tor, Klein bottle, projective space, sphere.
Elective MAT4042 KINEMATICS 3 0 5
Kinematics of a particle, Lagrange Formulas, Kinematics of Rigid Bodies, Relative motion, Plane motions
Elective MAT4044 NUMERICAL SOLUTIONS OF PARTIAL DIFF EQUATIONS 3 0 5
Classifications of partial differential equations, finite difference method, Taylor Series expansion and formulas of finite different, Converting differential eauation to finite differece equation, Numerical solution of the types of Parabolic, Hyperbolic and Eliptic equations by using the finite differece, Explicite and implicite solution methods, Method of differential quadrature, method of generalized differential quadrature, method of two dimensional generalized differential quadrature, Cranck-Nicholson method, numerical solution of Laplace, heat and wave equations by using the finite difference method, Engineering applications.
Elective USD4052 POLITICS AND CULTURE 3 0 5
Elective USD4056 GAME PROGRAMMING 2 0 5
Elective USD4066 THE HISTORY OF THE SPREAD OF ISLAM 2 0 5
Elective USD4068 CHARACTER AND VALUES EDUCATION 2 0 5
Elective USD4072 EXHIBITION MAKING 2 0 5
Elective USD4078 COMMUNITY SERVICE PRACTICES 2 0 5
Elective USD4080 REPRODUCTIVE HEALTH IN RISKY GROUPS 2 0 5
Elective USD4082 3 0 5
Elective USD4084 2 0 5