Faculty of Arts and SciencesMathematics

Mathematics

Course Content

Old Curriculum

 

Analysis I (MAT 111)

Real Numbers; The Field of Real Numbers, Ordering and The Completeness Axioms, Interior Point,
Accumulation Point. The Concept of a Function; Types and Properties of Functions, The Concept of
Countabilitiy, Infinite and Countable Infinite Sets; The Concept of Supremum and Infimum. Sequences;
Convergence and Divergence of Sequences, Convergence Theorems. Elemanter Functions; Logaritmic and
Exponential Functions, Hyperbolic Functions. Series; Convergence of Series, Absolute Convergence,
Convergence Theorems. Power Series, Radius of Convergence. Trigonometric Functions, Limits of
Functions.

 

Analytic Geometry I (MAT 121)

Vector Space, Subspace and Spaning Space, Concepts of Linear Dependence, Bases and Dimension,
Vectors in Affine Spaces and Operations with Vectors, Barycentric Dependence. Operations on Vectors in
Euclidean Space. Line in a Plane and Basic Problems. Plane in a Three Dimensional Space and Basic
Problems. Parabola and Central Conics, Ellipse, Hyhperbola.

 

Linear Algebra I (MAT 131)

Definitions of Group, Ring and Field. Systems of Linear Equations. Matrices; Elemanter Row
Operations, Matrix Multiplication, Invertible Matrices. Vector Spaces; Subspaces, Basis, Dimension,
Coordinates. Linear Transformations; Algebra of Linear Transformations, Isomorphism, Matrix
Representations of Linear Transformations. Linear Functionals. Inverses of Linear Transformations.
Determinants; The Determinant Function, Properties of Determinant, Sarus’s Rule, Cramer’s Rule

 

Computer 1 (MAT 141 )

Basic Use of Computer; Ms Dos, Windows, Word.

 

Analysis II (MAT 112)

Continuous Functions, The Derivative. Rolle’s Theorem, The Mean Value Theorem, Cauchy Mean
Value Theorem. Applications of Derivatives, Taylor and Maclaurin Series. Power Series Expansion of
Functions . Integral; Definition and Properties, Integrable Functions. Techniques of Integration.

 

Analytic Geometry II (MAT 122)

Circle and Analytic Investigation of Circle, General Quadratic Equation , Line in Three Dimensional
Space and Basic Problems, Surfaces, Sphere, Cone and Cylinder, Surfaces of Revolution, Quadratic Surfaces
of Canonical Equations, Change of Variables in Three Dimensional Space and General Quadratic Equation.

 

Linear Algebra II (MAT 132)

Polynomials; Algebra of Polynomials, Divisibility in the Ring of Polynomials, Ideals. Eigenvalue
Equations; Eigenvalue Polynomials of Similar Matrices, Diagonilazations, Dimension of Eigenvalue Space,
Minimal Polynomial, Canonical Forms. Invariant. Inner Product Spaces; Standard Inner Product, Norm.
Quadratic Form, Orthogonality, Orthogonal Set, Orthonormal Set, Orthogonal Basis, Orthonormal Basis,
Orthogonal Projection. Bessel’s Inequality.

 

Computer 2 (MAT 142)

Excel, Powerpoint, Internet.

 

Analysis III (MAT 211)

Cartesian Spaces, Sequences in Rn and Convergence, Uniform Convergence, Uniform Convergence of
Sequences and Series of Functions, Fourier Series of a Functions with respect to Orthonormal Systems,

Fourier Series, Improper Integrals.

 

Algebra I (MAT 221)

Concept of a Set, Construction of Number Sets. Definition of Congruence and Basic Properties.
Complete and Reduced Systems, Euler’s ϕ–Function. Polynomial Congruences Two variables Linear
Congruences, Quadratic Congruences, Order of an Integer with respect to Modulo-m, Primitive Roots,
Index, Quadratic Reciprocity Theorem, Multivariables Linear Congruence Systems.

 

Differential Equations I (MAT 231)

Basic Definitions. Existence and Uniqueness Theorems of Solutions of Differential Equations,
First Order Equations and Methods of Solutions, Higher Order Differential Equations.

 

Differential Geometry I (MAT 331)

Euclidean Spaces, Tangent Vectors, Directional Derivatives, Curves in E3, Differential Forms, Theory
of Curves, Frénet Formulas, Covariant Derivatives, Field of Frames, Connection Forms. Structure Equations.

 

Matrix Theory (MAT 224)

Gauss Elimination and Inverse Substitution. Nonsingular Systems of Initial Basic Submatrices.
Methods of Factorizations. Lower, Upper Envelops and Band Matrices, Matrix Norms, Iterative Methods.
Inverses of Matrices and Determinants, Determination of Eigenvalues and Eigenvectors.

 

Computer 3 (MAT 241)

Pascal Programming Language.

 

Analysis IV (MAT 212)

Limit and Continuity of Functions of Two Variables. Partial Derivatives, Chain Rule, Differential,
Exact Differential, Directional Derivatives. Maxima and Minima of Functions of Two Variables, Lagrange
Multipliers (Constrained Extremum). Implicit Functions, Implicit Mapping Theorem, Inverse Functions.
Curves in Plane and Space, Line Integrals. Multiple Integrals and Applications.

 

Algebra II (MAT 222)

Group Theory, Permutation Groups, Subgroups, Cyclic Groups. Complexes of a Group and Calculus with Complexes,

Group Homomorphisms and Isomorphisms.

 

Differential Equations II (MAT 232)

Series Solutions of Differential Equations, Systems of Equations, Laplace Transforms.

 

Differential Geometry II (MAT 332)

Surfaces in E3, Differential Forms on Surfaces, Shape Operator, Normal Curvature, Gaussian
Curvature, Special Curves of a Surface, Fundamental Equations, Forms.

 

Computer 4 (MAT 242)

Pascal Programming Language.

 

Theory of Complex Functions I ( MAT 311)

Complex Numbers, Analytic Functions, Elemanter Functions, Complex Integration, Local Properties
of Analytic Functions. Residue Theorem and Applications.

 

Algebra III (MAT 321)

Rings, Integral Domain, Ideals and Quotient Rings. Homomorphism of Rings, Polynomial Rings,
Divisibility in an Integral Domain, Euclidean Domains and Field Extensions.

 

Partial Differential Equations (MAT 361)

First Order Homogeneous Linear Differential Equations, First Order Nonhomogeneous Linear
Differential Equations,, Pfaff’s Forms, Methods of Solutions of Nonlinear Partial Differential Equations,
Second Order Partial Differential Equations and Methods of Solutions.

 

Numerical Analysis I (MAT 415)

Numerical Error Sources, Error Analysis for Linear Systems, Classifications of Numbers, Methods for
Findings Fixed Points, Methods for Findings the Roots of Functions of One Variable, Order of Convergence
and Methods for Accelerating Convergence, Methods of Solutions for Nonlinear Systems.

 

Computer 5 (MAT 341)

Java Programming Language.

 

Numerical Analysis ( MAT 318)

Numerical Integration and Differentiation. Initial Value Problems for Ordinary Differenrial Equations.
Boundary Value Problems for Ordinary Differenrial Equations.

 

Theory of Complex Functions II (MAT 312)

Representation Theorems, Partial Fractions, Mittag-Leffler Theorem, Infinite Products, Canonical
Representation, Weierstrass Theorem. Special Functions; Gamma, Beta and Gauss Functions. Mappings;
Conformality. Fractional Linear Mappings, Cross Ratio and Symmetry. Basic Mapping Problems. Mapping
of a Polygon, Schwarz - Christoffel Formula, Elliptic Integrals, Complex Fourier Series.

 

Numerical Analysis II (MAT 416)

Weierstrass Theorem, Techniques of Polynomial Interpolation, Techniques of Other Interpolation The
Least Squares Method, Interpolation for Systems of Two Variables.

 

Probability (MAT 362 )

Probability. Sample Space, Sample Point and Events, Counting Rules of Sample Points. Permutations,
Combinations. Binomial Theorem. Probability of an Event, Probability Axioms, Some Probability Rules,
Geometric Probability, Conditional Probability, Independent Events, Bayes’s Theorem. Random Variables;
Discrete and Continuous Random Variables, Two Dimensional Random Variables, Expected Value,
Variance and Properties. Moments. Chebysev’s Inequality. Some Special Discrete Distributions; Bernoulli,
Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson and Uniform Distributions.

 

Computer 6 (MAT 342)

Java Programming Language.

 

Topology I ( MAT 413)

Sets, Operations on Sets, Indexed Sets, Relations, Equivalence Relations. Functions; Definition of a
Function, Inverse Functions, Inverse Images, Composition of Functions. Topological Spaces; Definition of
Topology Closed Sets, Topologies Defined by Functions, Interior, Exterior and Boundary of a Set
Accumulation Points, Bases, Subbases and Products; Bases, Finite Products of Topological Spaces,
Subbases, Genaral Product Spaces. Continuous Functions; Definition of a Continuous Function, Open
Functions and Homeomorphisms. Identification Topology, Quotient Spaces. Compactness, Compactness in
Rn .

 

Functional Analysis (MAT 411)

Classical Inequalities, Metric Spaces, Normed Linear Spaces, Banach Spaces Bounded Linear
Operators, Linear Functionals and Hahn-Banach Theorem, Baire Category Theorem and Consequences;
Uniform Boundedness Principle, Open Mapping Theorem, Inverse Mapping Theorem and Closed Graph
Theorem.

 

Statistics (MAT 451 )

Normal Distribution, Standard Normal Distribution, Normal Approximation to Binomial Distribution.

Moments Exerted Functions of Normal Distribution. Uniform, Exponential, Gamma and Beta Distributions.

Relations Betwen Distribution. Concept of Sample, Sample Selection. Organization of Data; Frequency
Distribution, Graphical Representations, Measures of Central Tendency, Measures of Variability. Sampling
Mean and Properties of Variance, Point Estimation, Interval Estimation. Test of Hypothesis for Mass
Parameters.

 

Applied Mathematics I (MAT 445)

Selected Topics in Applied Mathematics

 

Computer 7 (MAT 441)

Mathematica Programming Language.

 

Real Analysis (MAT 412)

Algebras of Sets, Functions of a Real Variable, Lebesque Measure, Lebesque Integral, Classical
Banach Spaces.

 

Topology II ( MAT 414)

Separation and Countability Axioms; Separation Axioms; Hausdorff Spaces, Regular and Normal
Spaces, The First Countability Axiom, The Second Countability Axiom. Convergence; Sequences,
Convergence in the First Countable Spaces, Definitions of Net and Filter. Connected and Compact Spaces;
Connected Spaces and Properties, Components and Locally Connected Spaces, Compactness and the
Properties of Compact Spaces, Compactness in Rn , Varieties of Compactness.

 

Mathematical Statistics (MAT 452)

Goodness of Fit, Chi - Square Test, Goodness of Fit with Binomial Distribution, Goodness of Fit with
Poisson Distribution, Tests of Independence, Regression Analysis, Model and Estimation of Parameters,
Confidence Intervals and Testing of Hypothesis, Mutivariables Linear Regression, Test of Linearity of
Regression, Correlations, Variance Analysis.

 

Applied Mathematics II (MAT 446)

Fredholm and Volterra Integral Equations. Relations of Integral Equations to Initial Value and
Boundary Value Problems and Green’s Function

 

Computer 8 (MAT 442)

Mathematica Programming Language.

 

Calculus I (MMAT 151)

Functions, Transcendental Functions, Limit and Continuity, Derivative, Applications of Derivative,
Integration, Techniques of Integration.

 

General Mathematics (BMAT 151)

Numbers, Functions, Graphs of Trigonometric and Exponential Functions. Permutation, Combination,
Binomial Formula and Probability Vectors, Vectors, Determinants and Systems of Linear Equation.

 

Calculus II (MMAT 152)

Applications of Integration, Improper Integrals, Conic Sections, Polar Coordinates, Vectors and
Analytic Geometry in Space, Functions of Several Variables and Partial Derivatives, Multiple Integrals.

 

Biostatistics (BMAT 152)

Statistics and Graphs, Frequency Distributions, Means, Variances, Probability, Distribution Theory,

 

New Curriculum

Analysis I (MAT1011)

Real Numbers and properties of real numbers. Definition of Neighborhood and Mathematical induction. Definition of function, finite, countable infinity and uncountable sets. Real Valued Functions: Properties of functions. Sequences of Real Numbers, convergent sequences. Monotone sequences, subsequences and convergence theorems. Cauchy sequences, limit inferior and limit superior. Elementary functions; logarithm and exponential function. Hyperbolic functions. Infinite Series; convergence and absolute convergence. Power series. Definiton of limit of a function and properties of limit. Left sided and right sided limits.

 

Analytic Geometry I (MAT  1021)

Cartesian coordinate systems in the plane and space.Vectors in the plane and space. Lines in the plane. Lines and planes in space. Conics: Circle, Ellipse, Hyperbola, Parabola.  

 

 

Linear Algebra I  (MAT  1037)

Vectors, norm of a vector, systems of linear equations, matrix and matrix operations, systems of linear equations and matrix, vector spaces, subspaces, linear independence, basis and dimension.

 

 

Computer Applications I (BSP2041)

What is Mathematica? Introduction Graphs, limit, and Continuity of Fucntions in Mathematica. Differentiation in Mathematica Integration in Mathematica. Applications of the Integral           

 

Analysis II (MAT  1012)

Continuous Functions. Propeties of function defined on an interval. Uniform continuity. Definiton of derivative. Mean value theorems and their applications, Taylor and Maclaurin series, Power series expansion of a function, definition of an integral, properties of integrals, Integrable functions, Methods of integration: Change of variable, integration by parts , integration of rational functions, Binomial integrals, integration of trigonometric functions, applications of integral.           

 

Analytic Geometry II (MAT  1022)

Circle and Analytic Invetigation of Circle,General Quadratic Equation,Lines in Three Dimensional Space,The Basic Problems,Surface and Spheres,The Basic Problems,Cones and Cylinders,The Basic Problems.Surface of Revolution,The Basic Problems,Quadratic Surfaces of Canonical Equations,The Basic Problems,Change of Variables in Three Dimensional Space and General Quadratic Equation,The Basic Problems.

 

 

Linear Algebra II (MAT  1038)

Inner product, orthogonality in inner product, Gram-Schmidt process, determinants, cramer rule, eigenvalues and eigenvectors, diagonalization and matrix operations, linear transformation, change of basis.

 

 

Computer Applications II (BSP 2042)

Introduction to Differential equations in Mathematica Infinite series in Mathematica Calculus of vector valued functions in Mathematica Differentiation in several variables in Mathematica Multiple Integration in Mathematica Line and surface integrals in Mathematica Fundamental Theorems of vector analysis in Mathematica

 

 

History of Atatürk’s Principles and Reforms I (ATA 121)

General condition of the Ottoman Empire; General appearances of main European states before World War I; Relationship with Turkey and Europe, East Question, wars in 1911-1913; World War I, the position of the Ottoman Empire in World War I, fronts; Fronts, Dardanells Wars and its effects, partition plans on Empire during the World War I; Brest-Litowsk Treaty, principles of Wilson, other treaties with Bulgaria, Ottoman Empire, Germany and Austurian-Hungary states; Peace Summit in Paris, end of the World War I, economical condition of Ottoman Empire and laborer movements Mondros Armistice, minorities, the state of Ottoman army, cabinets, occupation of Smyrna; The beginning of the new period and Mustafa Kemal Ataturk, congresses, national assembly in Ankara; Fronts in independency wars, economical resources; Abrogation of regency, Lousanne Treaty and its importance, National Economic Congress, the foundation of parties, the announcement of Republic; The acceptance of secular law, social and cultural reforms, economical improvements, secular education and science; Principles of Ataturk and Turkish Republic, its content and concept.

 

 

Turkish Language I (TRD121)

Perspectives on reality: the mechanist and universalist view of reality Development of Philosophical Ideas since Descartes Classical Physics: The Newtonian conception of the world Determinism, the logical structure of Newtonian mechanics Copenhagen interpretation of quantum theory Modern Physics: space, time and motion, Relativity Language and Reality in Modern Physics The Role of Modern Physics in the Present Development of Human Thinking; general evaluation of the course 

 

 

 

Foreign Language I (English) (YDZI121)

Verb to be, possessive adjectives,guestions and negatives, present simple social expressions informal letter, there is , there are , how many , how much , this , that, directions, prepositions of place , some,any,these,those,linking words, can, can't,could, couldn't, formal letter, past simple regular verbs, irregular verbs, silent letters, special occasions take part in the content of subject.

 

 

History of Atatürk’s Principles and Reforms II (ATA 122)

Turkish revolution and basic characteristics of Turkish revolution; The other revolutions that effected Turkish revolution; The aim of Turkish revolution: Democratic Law State; Establishment of secular Turkish secular law system; Establishment of Turkish secular education system Reconstruction of Turkish economy, national economic and globalization; Novelties that made the Turkish society contemporary General quality of Kemalist principles and republicanism; Nationalism; Etatism and Populism; Secularism; Revolutionism; Criticisms against Kemalist ideology and answers to them

 

 

Turkish Language II (TRD122)

Types of oral expression, kind of written expression.science research methods. How a book is to occur.

 

 

Foreign Language II (English) (YDZI122)

Past simple tense, count and uncount nouns, comparatives and superlatives, present continuous tense, going to, question forms, present perfect tense, ever and never, just and yet, present perfect and simple past tense 

 

 

Physic I (FZK1001)

Vectors; motion in one and  two dimensions; Newton’s first law and inertial frames; Newton’s second and third law; circular motion and other applications of Newton’s laws; work and energy; potential energy and conservation of energy; linear momentum and collisions; kinematics of a rigid body; rolling motion, angular momentum and torque; static equilibrium and elasticity.

 

 

Physic II (FZK1002)

Electric fields; electric potential; capacitance and dielectrics; current and resistance; direct current circuits; magnetic fields; sources of the magnetic fields; faradays's law; inductance; alternating current circuits; RLC circuits; electromagnetic waves. 

 

Analysis III (MAT  2011)

Sequences and series of functions, Pointwise and Uniform Convergence, Power Series, Taylor Series, Fourier Series, Improper Integrals

 

Introduction to Number Theory (MAT2021)

Integers, divisibility, prime numbers, modular aritmetic, linear congruences, polynomial congruences, primitive roots, quadratic residues, quadratic equation, arithmetic function

 

 

Differantial Equations I  (MAT  2031)

Introduction to Ordinary Differential Equations. Methods of Solutions of First Order Equations. Graphical Solution. Exact differential Equations. Equations Made Exact by a Suitable Integrating Factor. Linear Equations of the First Order. Bernoulli and Riccati Differential Equations. Second Order Equations Solvable by First Order Methods. Linear Differential Equations. Linear Homogen Equations. Solution of Linear Homogeneous Differential Equations of Second Order with Constant Coefficients. Reduction of Order. Linear Nonhomogeneous Equations. Methods of Solutions of Linear Nonhomogeneous Equations. Solution of Cauchy - Euler Equations.

 

Differential Geometry I (MAT  3033)

Euclidean Space, Tangent Vectors, Directional Derivatives, Curves in Euclidean Space,1-Forms, Differential Forms, Mappings, Dot Product, Curves, The Frenet Formulas, The Frenet Formulas, Arbitrary Speed Curves, Covariant Derivatives, Frame Fields, Special Curves.

 

 

Matrix Theory (MAT  3024)

Gauss Elimination and Inverse Substitution. Nonsingular Systems of Initial Basic Submatrices. Methods of Factorizations. Lower, Upper Envelops and Band Matrices, Matrix Norms, Iterative Methods. Inverses of Matrices and Determinants, Determination of Eigenvalues and Eigenvectors.

 

 

Analysis IV (MAT  2012)

Functions of Several Variables, Limit, Continuity, Partial Derivatives , Chain Rule, maximum and Minimum Values of Functions of Two Variables, Differential, Exact Differential, Directional Derivatives, Lagrange Multipliers, Implicit Functions and Implicit Functions Theorem, Inverse Functions and Inverse Function Theorem, Curves, Multiple Integrals, Fubini's Theorem, Area and Volumes, Line Integrals, Green's Theorem

 

 

 

Abstract Algebra I (MAT  3021)

Groups, Symmetric groups, Subgroups, Cyclic Groups, remaining Class and Lagrange's Theorem, Normal Subgroups, Quotient Groups, Homomorphisms and isomorfhisms, Isomorphism theorems and conjugate Element, Direct Products, Cauchy's Theorem and p-groups

 

 

Differential Equations II (MAT  2032)

Series Solution of Differential Equations. Power Series. Analytic Coefficients Linear Equations.Singular points. Solutions in Singular point. Real and different exponents.Real and equal exponents. Bessel differential equations. Infinitiy point.Properties of Bessel functions. Systems of differential equations First order equation systems. Eleminasyon Method. Matrix Differential Equation Systems. Equations with constant coefficients. Equations with variable coefficients. Higer Order Equation Systems. Laplace transformation. Properties. Inverse transformation. Convolution Theorem. Solution of differantiel equation by Laplace transformation.

 

 

 

Differential Geometry II (MAT  3034)

Covariant Derivatives,Connection Forms,The Structural Equations,Surfaces on Euclidean Space,Patch Computations,Differentiable Functions and Tangent Vectors,Differential Forms on a Surface,The Shape Operator of Surface,Normal Curvature,Gaussian Curvature,Computational Techniques,Special Curves in a Surface,Ruled surface,Surfaces of Revolution.

 

 

Complex Function Theory I ( MAT  3013)

Complex Numbers, Complex Functions, Limit and Continuity, Complex Derivative, Cauchy-Riemann Equations, Analytic Functions, Harmonic Functions, Elementary Functions, Cauchy's Integral and Derivative Formula, Liouville's Theorem, The Fundamental Theorem of Algebra, Morera's Theorem, Maximum and Minimum Modulus Principle, Zeros and Singular Points of Analytic Functions, The Residue Theorem and Applications

 

 

 

Abstract Algebra II (MAT  3022)

Rings, Subrings, Ideals, Homomorphisms, Isomorphisms, Theorems of Isomorphism, Field of fractions, Polynomial rings, Arithmetic in Rings, Unique factorization rings, Prime ideals, Maximal ideals, Primary ideals

 

 

Partial Differantial Equations (MAT  4061)

General definitions. Surfaces and Curves in three dimensions. One Parameter and Two Parameter Systems of Surfaces. Methods of Solutions of dx/P=dy/Q=dz/R Orthogonal Trajectories of a System of Curves on a Surface. Pfaffian Differantial Forms and Equations. Partial Differantial Equations of The First Order. Cauchy's Method of Caracteristics , Lagrange and Charpit's Method. Special Types of First Order Equations. Solutions Satisfying Given Conditions. Partial Differantial Equations of The Second Order. Reduce the Two Dimensional Equation to Canonical Form. Hyperbolic, Parabolic and Elliptic Equations. Fourier's Solutions. Wawe Equation and Diffision Equation.           

 

 

Introduction to Numerical Analysis (MAT  3016)

Numerical Error Sources, Error Analysis for Linear Systems, Classifications of Numbers, Methods for Findings Fixed Points, Methods for Findings the Roots of Functions of One Variable, Order of Convergence and Methods for Accelerating Convergence, Methods of Solutions for Nonlinear Systems.

 

 

Complex Function Theory II (MAT  3014)

Complex Series, Complex Power Series, Taylor Series, Laurent Series, Infinite Product, Weierstrass's Theorems, Mittag-Leffler's Theorem, Special Functions; Complex Gamma, Beta and Riemann-Zeta Functions, Conformal Mappings, Mobiüs Mappings, Automorphisms of Disc and the Plane

 

 

Numerical Analysis  (MAT  3016)

Numerical Integration and Differentiation. Initial Value Problems for Ordinary Differenrial Equations. Boundary Value Problems for Ordinary Differenrial Equations. 

 

 

Probability (MAT 2052)

Set Theory, Permutation-Combination-Binomial, Probability Axioms, Intermittent and Continuous Random Variables, Distributions, Moment and Moment Derivative Functions 

 

 

Topology I ( MAT  4013)

Basic Notions Concerning Sets. Basic Set Operations, Indexed Sets. Relations, Equivalence Relations. Defining A function, Inverse Functions and Inverse Images. Finite and Infinite Sets, Countable Sets. Topological Spaces. Way of Generating A Topology. Closed Sets, Topologies Induced by Functions. The interior, Exterior and Boundary of A set, Cluster Points. Subspaces. Bases and Subspaces. Continuous Functions. Open Functions and Homeomorphisms. Topological and Hereditary Properties. Identification Topology. Separation Axioms.

 

 

Functional Analysis (MAT  4011)

Classic Inequalities, Metric Spaces, Normed Linear Spaces, Bounded Linear Operators, Linear Functionals and The Hahn-Banach Theorem, Baire Category Theorem and Its Consequences; Uniform Boundedness Principle, Open Mapping heorem, Inverse Function Theorem, Closed Graph Theorem

 

 

Statistics (MAT  4051)

It is an introductory course that assumes no prior knowledge of statistics. Basic statistical concepts and methods are presented in a manner that emphasizes understanding the principles of data collection and analysis rather than theory. Much of the course will be devoted to discussions of how statistics is commonly used in the real world.There are two major parts to this course: 1. Data – which includes graphical and numerical summaries to describe the distribution of a variable. 2. Probability and Inference – using the language of probability and the properties of numerical summaries computed from a random samples we learn to draw conclusions about the population of interest, based on our random sample, and attach a measure of reliability to them. 

 

 

Real Analysis (MAT  4012)

Open and closed sets of real numbers. Continuous functions, Borel sets. Lebesgue Measure: Introduction. Outer measure. Measurable sets and Lebesgue measure. Measurable functions. Littlewood's three principles. The Lebesgue Integral: The Riemann integral. The Lebesgue integral of a bounded function over a set of finite measure. The linear spaces. The integral of a nonnegative function: The general Lebesgue integral. Differentiation: Differentiation of monotone functions. The classical Banach spaces: The Lp and lp spaces. The Hölder and Minkowski inequalities. Convergence and completeness. Bounded linear functionals on the Lp spaces.

 

 

Topology II ( MAT  4014)

First axiom of Countability. Second axiom of Countability. Separable spaces. Compact spaces. Properties of compact spaces. Disconnected Spaces. Connected Spaces. More poperties of Connected Spaces. Finite Product Spaces. Base for a product space. Base for a product space. Finite product spaces and Second countability. Finite Product spaces and separability. Infinite product spaces. Hereditary and Topological proıperties in product spaces.

 

 

Mathematical Statistics (MAT  4052)

Classical probability theory; discrete and continuous random variables; distribution functions; expectation; law of large numbers; central limit theorem; other applications; random sampling; estimation of parameters; hypothesis testing.

 

 

Tensor Calculus (MAT  4070)

n-dimensional space. Transformation of coordinates. Covariant and contravariant vectors. Tensors of second order. Algebra of tensors. Symmetric and skew-symmetric tensors. Outer multiplication and contraction. Inner multiplication. Riemannian metric. Christoffel symbols and their properties. Covariant differentiation of tensors.

 

 

Insurance Mathematics (MAT  4057)

Insurance economics,Interest accounts, Life insurance: the survival distributions and life tables,Life insurance and life annotes, Net premiums, Net premium equivalents, Capital insurance: damage tables, Net premium of various capital insurances.

 

 

Projective Geometry (MAT  3035)

Euclidean Geometry and Other Geometry, Geometry; Euclidean geometry Various geometrical constructions, Primitive concepts, Affine planes, Projective planes Relationships between Afine and Projective planes and Lower planes, Other Geometrical constructions, Dezarg, Pappus and Fano planes, Dezarg planes, Papus planes, Projective planes on partition rings, Fano axiom: Projective planes that provide and maintain this axiom, Transformations in projective planes, Isomorphism, One Dimensional Transformations in Projective Planes, Perspectivity and Projections.

 

 

Mathematics and Nature (MAT  3092)

Zenon's paradoxes, Philosophical questions such as "Is there mathematics in nature, mathematical concepts being creation or discovery", Probability theory, Games, Geometry, Combinatorial calculations, Number theory, Arithmetic.

 

Foundation of Business (MAT  4067)

It is based on giving basic information, based on examples from the relevant literature and practice, on concepts related to modern management and business used in an enterprise.

 

 

History of Science (BSB 1015)

Science in old Age Evaluation of the science from the near - east cvilizations to untill now Civilization of Helen-İyon Science in period of Roma Science in Middle Age World of Christianity Science in Periods of İslamic and Turkish ( Period of the World of eastern İslamic-Türk ) Science in Periods of İslamic and Turkish ( Period of the World of west ern İslam-Türk )İ Entrance of Turkısh people to Islamism and Scientific activities in that period Science in near Age The Renaissance and Science Scientific Revoluation and enlightenment Age Science in Ottomans ( Period of modernist and traditionalist ) Study of Science in near Age and western İn period of Turkısh Republic , science in Turkey

 

 

Introduction to Career (IK 4065)

To determine self-knowledge, values, vision and mission, brain work, career strategy development

 

 

Career (IK 4066)

To determine self-knowledge, values, vision and mission, brain work, career strategy development

 

 

Set Theory (MAT 3023)

Set Operations,Examples on set Operations,Continuation of Examples, Algebra of Sets, Boolean Algebra,Ordered Couples,Relations,Functions, Equivalence Relations,Equipotent sets, Cantor's Theorem,Characteristic              function, simple function,Family of Sets,Lower and Upper limit sets, Continuation of Lower and Upper limit sets, Sequence of sets with couple indices, Examples

 

Introduction to Optimization (MAT 4063)

Vector Spaces an Matrices, Transformation, Unconstrained Optimization, Linear programming

 

Optimization (MAT 4064)

Vector Spaces an Matrices, Transformation, Unconstrained Optimization, Linear programming

 

 

Riemannian Geometry (MAT 4071)

Coordinate transformations, covariant and contravariant tensors, metric tensor, Riemannian metric , Riemannian spaces, Christoffel symbols, covariant derivative, Levi-Civita connection, curvature of any curve, geodesics, parallel shifting, geodesic and Riemannian coordinates, the Riemannian curvature tensor, Ricci tensor, some special Riemannian surfaces (Einstein, symmetric, recurrent spaces, ...), hypersurface, second fundamental form, Gauss and Mainardi-Codazzi equations.

 

 

Integral Equations (MAT 4046)

Introduction for integral equations, classification of integral equations. Linear and non linear integral equations, Fredholm and Voltera integral equations. Method of successive aproximations. Applications to ordinary differential equations.

 

Community Service Practices (THU 100)

Pre-instruction for Developing Projects Determinig the Issue of Project and Planning Developing Projects Performing Projects Presentation of Projects Evaluation of Projects

 

 

History of Mathematics (MAT 3038)

Early number systems and symbols.Mathematics in early civilizations, Egyptian mathematics. Mathematics in early civilizations, Babylonian mathematics. Mathematics in early civilizations, Babylonian mathematics. Beginnings of Greek Mathematics. Alexandrian School: Euclid. Euclid and the elements. Euclid's number Theory. Eratosthenes. Archimedes. Estimating the value of pi. Apollonius of Perga:The Conics

 

Introduction to Special Functions (MAT 4047)

Special functions related with the Gamma function. Laguerre equation and its solution. Generating function. Orthogonality properties of Laguerre polynomials. Recurrence relations between Laguerre polynomials and their derivatives. Hermite equation and its solution. Generating function. Orthogonality properties of Hermite polynomials. Recurrence relations between Hermite polynomials and their derivatives. Chebyshev differential equation and Chebyshev polynomials. Gegenbauer and Jacobi polynomials. definition of Hypergometric function and relation between hypergeometric function and other special functions.

 

Special Functions (MAT 4048)

Special functions related with the Gamma function. Laguerre equation and its solution. Generating function. Orthogonality properties of Laguerre polynomials. Recurrence relations between Laguerre polynomials and their derivatives. Hermite equation and its solution. Generating function. Orthogonality properties of Hermite polynomials. Recurrence relations between Hermite polynomials and their derivatives. Chebyshev differential equation and Chebyshev polynomials. Gegenbauer and Jacobi polynomials. definition of Hypergometric function and relation between hypergeometric function and other special functions.

 

This page updated by Mathematics on 27.03.2018 15:50:05