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
The Aim of the Course on Atatürk’s Principles and the History of the Turkish Revolution; The Concepts of Revolution and Related Terms; The Collapse of the Ottoman Empire; Reform Movements in the Ottoman Empire in the 19th Century; Ideological Movements Aimed at Saving the Ottoman Empire in Its Final Period; The Situation of the Ottoman Empire in the Early 20th Century; The Situation of the Country Following the Armistice of Mudros; The Preparatory Period for the National Struggle; The Establishment and Activities of the Grand National Assembly of Türkiye; Political and Military Developments Following the Opening of the Grand National Assembly of Türkiye; The Treaty of Lausanne: Its Significance and Consequences.
Compulsory ENF1021 BASIC COMPUTER 2 2 3
Introduction to Computers and Computer Hardware; Operating Systems and Application Software; Windows Operating System; Microsoft Word; Microsoft Excel; Microsoft PowerPoint; Internet Usage; Information and Communication Technologies (ICT).
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
Groups, Rings, and Fields; Vector Spaces; Standard Vector Spaces Defined over R and C; Direct Sums of Vector Spaces; Subspaces; Inner Product Spaces; Orthonormal Vector Systems; Properties of Bases of Vector Spaces; Properties of the Underlying Vector Space; Dimensions of Subspaces; Direct Sums in Inner Product Spaces; Classification of Linear Transformations on Vector Spaces; Linear Transformations on Vector Spaces; The Concept of a Matrix; Equality and Addition of Matrices.
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 2 1 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
Language and Languages; The Relationship Between Language and Nation; The Relationship Between Language and Culture; Languages of the World and the Place of the Turkish Language among the World’s Languages; Language Families in Terms of Their Origins; The Historical Development of Written Turkish: Old Turkic, Middle Turkic, Dīwān Lughāt al-Turk, Atabetü’l-Hakayık, Khwarezmian Turkic, Old Turkish of Türkiye (Old Anatolian Turkish), the New Turkish Period, the Modern Turkish Period, Western (Southwestern) Turkic, Türkiye Turkish, Eastern (Northeastern) Turkic, and Karatay Turkish; Phonetics: Sounds and Sound Production, Major and Minor Vowel Harmony, Major Sound Changes in Turkish, Phonetic Characteristics of Turkish, Syllable Structure in Turkish, and Sentence Stress; Morphology: Words in Terms of Structure, Roots, Stems, Affixes (Derivational and Inflectional Affixes), Words in Terms of Meaning and Function, Nouns, Adjectives, Pronouns, Verbs, Verb Conjugation, Morphological and Tense Suffixes, Verbals, Postpositions, Words Derived from Verbs and Nouns; Semantics: Meaning in Words and the Semantic Scope of Words.
Compulsory YDL1013 FOREIGN LANGUAGE I 3 0 3
The course covers basic topics (verb to be, Simple Present, can/can’t, a/an, some/any, object pronouns, there is/are, have got, past tense of to be, Simple Past, etc.) to enable students to understand and use frequently used everyday expressions and simple sentences related to basic personal needs, introduce themselves and others, ask and answer questions about personal information, and communicate in familiar everyday situations.
2. SEMESTER COURSES
Ders Tipi Ders Teorik Pratik AKTS
Compulsory ATA1016 ATATÜRK PRINCIPLES AND THE HISTORY OF REVOLUTION II 2 0 2
Turkish Revolutionary Reforms; Turkish Foreign Policy During the Atatürk Era; Fundamental Principles of the Turkish Revolution (Atatürk’s Principles); Complementary Principles of Atatürk’s Principles; Atatürk’s Illness and Death; The Election of İsmet İnönü as President and the İsmet İnönü Era (1938–1950); World War II; The Democratic Party in Power and the Adnan Menderes Era (1950–1960); Military Coups and the Republic of Türkiye (1960–1980); The Coup of 12 September 1980 and Its Aftermath in 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
Matrices; Matrix Multiplication and Its Properties; Inverse Matrices; Matrices over the Complex Numbers; Modules; Linear Transformations; Linear Transformation Matrices; Rank of a Linear Transformation; Change of Basis; Properties of Matrices; Basis and Dimension in Matrix Spaces; Properties and Theorems Concerning Bases and Dimensions of Matrix Spaces; Change of Basis; Change of Basis and Properties of Matrices; Elementary Operations; Permutations; Functions; The Determinant Function.
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 2 1 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
Word Groups; Literal, Connotative, and Figurative Meanings of Words; Idioms; Reduplications; Technical Terms; Common Language Errors; Sentence Structure in Turkish; Sentence Elements; Sentence Analysis; Written Genres such as Novels, Articles, Essays, and Poetry; Examples of Presentations, Reports, and Minutes; Writing Petitions, Business Letters, and Résumés (CVs); Oral Expression Techniques, Including Dialogue and Discussion.
Compulsory YDL1014 FOREIGN LANGUAGE II 3 0 3
The course builds upon the topics covered in Foreign Language I and includes further grammar structures (Present Continuous, adverbs of manner, comparative and superlative adjectives, prefer + noun/-ing form, will, Present Perfect, have to/don’t have to, wh- questions, be going to for intentions and plans, infinitives of purpose, verbs followed by infinitives or -ing forms, etc.). It aims to enable students to understand sentences and frequently used expressions related to everyday life, including information about themselves, their families, work, immediate surroundings, and shopping; communicate directly and clearly in familiar situations; and describe themselves, their education, their immediate environment, and situations involving their basic needs using simple language.
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 ENTREPRENEURSHIP I 2 0 4
Detailed information is provided on topics such as the concepts of entrepreneurs and entrepreneurship, levels of entrepreneurship, stages of the entrepreneurial process, and the role of entrepreneurs in a free-market economy.
Elective MAT2015 KRIPTOLOJY I 2 0 4
Block Ciphers, DES (Data Encryption Standard), and Rijndael (AES – Advanced Encryption Standard).
Elective MAT2017 ECONOMIC MATHEMATICS I 2 0 4
Algebraic Calculations; Functions and Their Graphs; Lines, Parabolas, and Systems of Equations; Exponential and Logarithmic Functions; Introduction to Financial Mathematics; Interest Calculations; Present Value Calculations; Applications of Compound Interest; Loan Amortization and Its Applications; Basic Matrix Algebra; Leontief Input–Output Analysis and Its Applications.
Elective MAT2019 CURRICULUM AND GUIDANCE I 2 0 4
Primary Education Curricula, Their Reference Points and Vision; The Components and Content of the Curriculum; The Foundations of Curriculum Development: Social, Individual, Economic, Historical, and Cultural Foundations; Introduction to the Core Skills Included in the Curriculum: Critical Thinking, Creative Thinking, Communication, Research and Inquiry, Problem-Solving, Information Technology Skills, Entrepreneurship, and the Ability to Use Turkish Correctly and Effectively.
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 ENTREPRENEURSHIP II 2 0 4
The course provides detailed information on the concepts of entrepreneurs and entrepreneurship, levels and stages of entrepreneurship, and the role of entrepreneurs in a free-market economy.
Elective MAT2016 KRIPTOLOGY II 2 0 4
Stream Ciphers; Number Theory; Public-Key Cryptosystems; Cryptanalysis.
Elective MAT2018 ECONOMIC MATHEMATICS II 2 0 4
Limits; Continuity; Applications of Derivatives; Differentiation of Various Functions Using the Rules of Differentiation; Elasticity of Demand; Curve Sketching Using Derivatives; Maximum and Minimum Problems; Quantitative Analysis in Economic Systems; Population Growth Over Time; Integration and Techniques of Integration; Applications of Integration; Producer and Consumer Surplus; Market Price Determination; Methods of Integration and Their Applications in Business and Economics.
Elective MAT2020 CURRICULUM AND GUIDANCE II 2 0 4
The Foundations of the Curriculum: Social, Individual, Economic, Historical, and Cultural Foundations; Common Skills in the Curriculum: Critical Thinking, Creative Thinking, Communication, Research and Inquiry, Problem-Solving, Information Technology Skills, Entrepreneurship, and the Ability to Use Turkish Correctly and Effectively; Review and Reinforcement of Competencies; Assessment and Evaluation of Products and Learning; The Roles of Students, Teachers, and Parents in the Curriculum; Examination of Sample Unit-Based Annual Plans for Mathematics Courses in Grades 6, 7, and 8 of Primary Education.
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 USD3078 FIGHTING ADDICTION AND ADDICTION 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
To develop students’ research skills by assigning various research topics and helping them acquire the skills necessary to conduct research, write research reports, and present their findings.
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 AFFINE 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 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
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 THEORY II 3 0 5
Convolition Multiplication of Aritmetic Functions , Congruance Systems ,Quadric Congruences,Primitive Roots and Indexes ,Arithmetic Functions.
Elective MAT4036 AFFINE DIFFERENTIAL GEOMETRY 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 USD4070 CREATING PERSONAL STYLE IN CLOTHING 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