Matematik Lisans Programı
Ders Planı
| Ders Kodu | Ders Adi |
( Teorik - Pratik ) Kredi |
|
1.Yıl - Güz Dönemi |
|||
| SE1001 | Intro. to Programming (Java) | ( 2 - 2 ) 3 | |
| GEP1005 | History of Civilization I | ( 3 - 0 ) 3 | |
| PHYS1001 | Physics I | ( 3 - 2 ) 4 | |
| MATH1055 | Abstract Mathematics I | ( 3 - 0 ) 3 | |
| MATH1001 | Analysis I | ( 4 - 2 ) 5 | |
| ENG1003 | Communications Skills & Academic Writing I | ( 3 - 0 ) 3 | |
1.Yıl - Bahar Dönemi |
|||
| ENG1004 | Communication Skills & Academic Reporting II | ( 3 - 0 ) 3 | |
| MATH1002 | Analysis II | ( 4 - 2 ) 5 | |
| PHYS1002 | Physics II | ( 3 - 2 ) 4 | |
| SE1002 | Object Oriented Programming (Java) | ( 2 - 2 ) 3 | |
| MATH1056 | Abstract Mathematics II | ( 3 - 0 ) 3 | |
| GEP1006 | History of Civilization II | ( 3 - 0 ) 3 | |
2.Yıl - Güz Dönemi |
|||
| MATH2007 | Analysis III | ( 3 - 2 ) 4 | |
| TLL2021 | Turkish Language & Literature I | ( 2 - 0 ) 2 | |
| MATH2013 | Linear Algebra I | ( 3 - 2 ) 4 | |
| MATH2033 | Discrete Mathematics | ( 3 - 0 ) 3 | |
| SE2211 | Data Structures and Algorithms I | ( 2 - 2 ) 3 | |
| GE Elective | ( 3 - 0 ) 3 | ||
2.Yıl Bahar Dönemi |
|||
| MATH2016 | Introduction to Topology | ( 3 - 0 ) 3 | |
| MATH2008 | Analysis IV | ( 3 - 2 ) 4 | |
| MATH2062 | Differential Equations | ( 3 - 0 ) 3 | |
| MATH2014 | Linear Algebra II | ( 3 - 2 ) 4 | |
| TLL2022 | Turkish Language & Literature II | ( 2 - 0 ) 2 | |
| SE2212 | Data Structures & Algorithms II | ( 2 - 2 ) 3 | |
3.Yıl - Güz Dönemi |
|||
| MATH3071 | Differential Geometry I | ( 3 - 0 ) 3 | |
| Departmental Elective | ( 3 - 0 ) 3 | ||
| MATH3061 | Algebra I | ( 3 - 0 ) 3 | |
| HIST3051 | Atatürk's Principles and History of Turkish Republic I | ( 2 - 0 ) 2 | |
| MATH4013 | Real Analysis I | ( 3 - 0 ) 3 | |
| MATH3015 | Real Analysis I | ( 3 - 0 ) 3 | |
| GE Elective | ( 3 - 0 ) 3 | ||
3.Yıl Bahar Dönemi |
|||
| GE Elective | ( 3 - 0 ) 3 | ||
| MATH3062 | Algebra II | ( 3 - 0 ) 3 | |
| MATH3072 | Differential Geometry II | ( 3 - 0 ) 3 | |
| MATH4016 | Real Analysis II | ( 3 - 0 ) 3 | |
| HIST3052 | Atatürk's Principles and History of Turkish Republic II | ( 2 - 0 ) 2 | |
| MATH3024 | Probability | ( 3 - 0 ) 3 | |
| MATH3022 | Complex Analysis | ( 3 - 0 ) 3 | |
4.Yıl - Güz Dönemi |
|||
| GE Elective | ( 3 - 0 ) 3 | ||
| MATH4053 | Partial Differential Equations I | ( 3 - 0 ) 3 | |
| MATH4031 | Functional Analysis I | ( 3 - 0 ) 3 | |
| MATH4001 | Graduation Project I | ( 0 - 4 ) 2 | |
| Departmental Elective | ( 3 - 0 ) 3 | ||
4.Yıl Bahar Dönemi |
|||
| MATH3012 | Numerical Analysis | ( 2 - 2 ) 3 | |
| MATH3014 | Number Theory | ( 3 - 0 ) 3 | |
| Departmental Elective | ( 3 - 0 ) 3 | ||
| GE Elective | ( 3 - 0 ) 3 | ||
| MATH4002 | Graduation Project II | ( 0 - 4 ) 2 | |
Ders Listesi
MATH1001
Analysis I
4 2 5
MATH1002
Analysis II
4 2 5
MATH1051
Calculus I
3 2 4
MATH1052
Calculus II
3 2 4
MATH1055
Abstract Mathematics I
3 0 3
MATH1056
Abstract Mathematics II
3 0 3
MATH2003
Calculus III
3 2 4
MATH2004
Analytic Geometry
2 2 3
MATH2005
Probability
3 0 3
MATH2006
Calculus IV
3 2 4
MATH2007
Analysis III
3 2 4
MATH2008
Analysis IV
3 2 4
MATH2013
Linear Algebra I
3 2 4
MATH2014
Linear Algebra II
3 2 4
MATH2016
Introduction to Topology
3 0 3
MATH2031
Discrete Comput. Structures
3 0 3
MATH2033
Discrete Mathematics
3 0 3
MATH2062
Differential Equations
3 0 3
MATH3012
Numerical Analysis
2 2 3
MATH3014
Number Theory
3 0 3
MATH3015
Real Analysis I
3 0 3
MATH3022
Complex Analysis
3 0 3
MATH3024
Probability
3 0 3
MATH3061
Algebra I
3 0 3
MATH3062
Algebra II
3 0 3
MATH3071
Differential Geometry I
3 0 3
MATH3072
Differential Geometry II
3 0 3
MATH3075
Statistics
3 0 3
MATH3082
Probability and Statistics
3 0 3
MATH4001
Graduation Project I
0 4 2
MATH4002
Graduation Project II
0 4 2
MATH4004
Selected Topics in Mathematics II
3 0 3
MATH4013
Real Analysis I
3 0 3
MATH4014
Number Theory
3 0 3
MATH4016
Real Analysis II
3 0 3
MATH4021
Advance Complex Analysis
3 0 3
MATH4031
Functional Analysis I
3 0 3
MATH4032
Functional Analysis II
3 0 3
MATH4052
Topology
3 0 3
MATH4053
Partial Differential Equations I
3 0 3
MATH4054
Partial Differential Equations II
3 0 3
MATH4063
Geometry
3 0 3
MATH4070
Mathematical Finance
3 0 3
MATH4071
Coding Theory
3 0 3
MATH4072
Cryptography
3 0 3
MATH4081
Introduction to Fluid Dynamics
3 0 3
MATH4082
Numerical Solution ofPartial DifferentialEquations
3 0 3
MATH4085
Commutative Algebra
3 0 3
MATH4086
Galois Theory
3 0 3
MATH4087
Graph Theory
3 0 3
MATH4088
Game Theory
3 0 3
MATH4089
Mathematics for Finance and Management
3 0 3
MATH4090
Fuzzy Mathematics
3 0 3
MATH4091
Kinematics
3 0 3
MATH4092
Dual Number Theory and Quatermions
3 0 3
MATH4093
Measure and Integration Theory
3 0 3
MATH4094
Selected Topics in Analysis
3 0 3
Ders Tanımları
MATH1001
Analysis I
Introduction, Real numbers, relation and functions, special functions (functions derived from equality), equations of line, circle, parabolas, hyperbolas, applications of linear and nonlinear curves to management and economics. Limits, continuity, derivation, change rate and marginal analysis, derivation rules.
MATH1002
Analysis II
MATH1051
Calculus I
Functions limits and continuity, derivatives of functions of one variable. Application of the derivative: related rates, maximum and minimum values, the mean value theorem. The integral: indefinite integrals and integration rules. Inverse functions, exponential and logarithmic functions, inverse trigonometric functions, hyperbolic functions, L’Hospital’s rule.
MATH1052
Calculus II
Application and techniques of integration: integration by substitution, integration by parts and integration by partial fractions. Application of integration: arc length, area of a surface of revolution. Parametric equations and polar coordinates. Series: test for series, power series and manipulating power series.
MATH1055
Abstract Mathematics I
The language of mathematics, theorems, theory of logics, quantifiers, statements and proofs, mathematical induction, sets and set operations, Cartesian products and relations, equivalence relations and partitions, functions, correspondences, composition of functions, image and pre-image functions, counting, finite and infinite sets, denumerable and countable sets, uncountable sets, cardinal numbers, ordering, partially ordered sets, least upper bound and greatest lower bound, axiom of choice and ordinal numbers.
MATH1056
Abstract Mathematics II
Binary operations, system of whole and natural numbers, system Z of integers, system Q of rational numbers, other aspects of order, real number system, complex numbers, introduction to group theory, rings and fields.
MATH2003
Calculus III
Vector functions: continuity, derivatives, and integrals . Parametric curves and surfaces, polar coordinates . Functions of several variables: continuity and partial derivatives, gradient, directional derivatives . The chain rule . Double and triple integrals . Iterated integrals . Integration using polar, cylindrical, and spherical coordinates . Change of variables . Line and surface integrals (including surface area) . Curl and divergence . The integral theorems of Green, Stokes and Gauss
MATH2004
Analytic Geometry
Euclidean Geometry to include conruence,similarity,measurement,coordinate geometry,symmetry,and isometries,in both two and three dimensions.Lines,planes,conics,and quadrics ,curves and surfaces in the three dimensional Euclidean Space.
MATH2005
Probability
Introduction to probability, operations on sets, counting problems, definition of probability, conditional probability, Bayes' theorem, one- and two-dimensional random variables, mathematical expectation and variance, basic discrete and continuous probability distributions, moment generating functions, law of large numbers, central limit theorem.
MATH2006
Calculus IV
Curvilinear coordinates, Improper integrals, Integrals depending on parameters, Leibnitz rule, Gamma ve Beta functions, Work and line integrals, Green’s theorem, Surface area, Surface integrals, Flux through a surface, Stokes’ theorem, Divergence theorem, Elliptic integrals.
MATH2007
Analysis III
MATH2008
Analysis IV
MATH2013
Linear Algebra I
Basic Properties of Matrices and Determinants: Vector Spaces, Linear Transformations Eigen Values, Eigenvectors and Jordan Normal Form. Introduction to Writing Proofs(Bu ders Proğramdan kaldırılan MATH 2011 Linear Algebra (303) ile eşdeğerdir).
MATH2014
Linear Algebra II
Change of basis and linear mappings, multi-linear functions, determinants, determinant functions, determinant of a linear transformation, dual determinant functions, characteristic polynomial, trace of a linear mapping, oriented vector spaces. Inner product spaces, duality in an inner product space, normed vector spaces, linear mappings of inner product spaces, adjoint mapping, self-adjoint, orthogonal projections, skew mappings, isometric mappings, rotations of the plane and of 3-space, symmetric bilinear functions, bilinear and quadratic functions, decomposition of E, pairs of symmetric bilinear functions, pseudo-Euclidean spaces, linear mappings of pseudo-Euclidean spaces, quadrics, affine spaces, quadrics in the affine space, affine equivalence of quadrics, quadrics in the Euclidean space, unitary spaces, Hermitian functions, unitary spaces, linear mappings of unitary spaces.
MATH2016
Introduction to Topology
MATH2031
Discrete Comput. Structures
Ayrık matematiksel yapıların teori ve uygulaması ve bunların bilgisayar bilimleri ile ilişkileri. Kümeler,bağıntılar, fonksiyonlar, permutasyon, kombinasyon, graf teori, ağaçlar, boolean cebri, rekurans bağıntıları, grup teori ve otomata teorisi.
MATH2033
Discrete Mathematics
Introduction to mathematical techniques fundamental to Computer Engineering and Computer Science. Topics: mathematical logic, induction, set theory, relations, functions, recursion, recurrence relations, introduction to asymptotic analysis, algebraic structures, graphs, machine computation
MATH2062
Differential Equations
Introduction to traditional course in ordinary differential equations includes 1st and 2nd order linear differential equation with numerous applications: Laplace transforms, power series solutions, numerical methods, Linear systems.
MATH3012
Numerical Analysis
Machine arithmetic, approximation and interpolation, numerical differentiation and integration, nonlinear equations, linear systems, differential equations, error analysis. Selected algorithms will be programmed for solution on computers. Matlab and other useful numerical analysis tools will be used.
MATH3014
Number Theory
MATH3015
Real Analysis I
MATH3022
Complex Analysis
Complex numbers and functions: contour integration, power series, Cauchy-Riemann equations, residues, poles, conformal mapping and applications.
MATH3024
Probability
MATH3061
Algebra I
Groups, basics, subgroups, cyclic subgroups, normal subgroups, homomorphism, permutation groups, direct product, Sylow theorems.
MATH3062
Algebra II
Integers and equivalence relations, polynomial rings and elementary ring theory, introduction to fields and splitting fields, elementary group theory and symmetry, homomorphism, normal subgroups, and ideals, quotient structures and solvability.
MATH3071
Differential Geometry I
Topological background, differentiable manifolds, topology of a manifold, properties of the induced topology, partitions of unity, differentiation on a manifold, tangent vectors, inverse function theorem, Leibniz's formula, submanifolds, immersions, quotient manifolds, vector fields, tangent bundle, orientable manifolds, f-related vector fields.
MATH3072
Differential Geometry II
Curves, parametrizations, arc length, curvatures, Frenet equations, global properties of curves in the plane. Some special curves: spherical curves, Inclined curves, evolute and involutes, Riemann manifolds, Intrinsic geometry of surfaces, frames and frame fields, covariant derivatives and connections, Riemannian metric, Gaussian curvature, fundamental forms, Meusnier?s theorem and the equations of Gauss and Codazzi-Mainardi, examples of hypersurfaces, surfaces of constant curvature, integration of forms (Stokes, Green and Gauss theorems), isometries and local isometries and congruent surfaces, Gauss-Bonnet formula.
MATH3075
Statistics
Methods of data analysis and data presentation, sampling distributions, point estimation and properties of estimators, Cramer Rao inequality, parameter estimation, maximum likelihood and moment matching, interval estimation, hypothesis testing, the Newman-Pearson lemma, likelihood ratio tests, goodness of fit tests, linear regression, analysis of variance, nonparametric tests.
MATH3082
Probability and Statistics
Introduction to probability, operations on sets, counting problems, definition of probability, conditional probability, Bayes' theorem, one and two dimensional random variables, mathematical expectation and variance, basic discrete and continuous probability distributions, moment generating functions, law of large numbers, limit theorem
MATH4001
Graduation Project I
Student will be required to complete an independent project. Topics are chosen in consultation with a faculty advisor and subject to departmental consent. A proposal for the graduation project in the form of a short report and a presentation will be required for the completion of this course.
MATH4002
Graduation Project II
Continuation of MATH 4001 (Graduation Project I). A short report and presentation will be required for the completion of this course.
MATH4004
Selected Topics in Mathematics II
Organised study of selected topics in Mathematics. Subjects may vary from term to term. Specific content defined depending upon available faculty resources and student needs.
MATH4013
Real Analysis I
Ordered sets, fields, real and complex fields, Euclidean spaces, finite, countable and uncountable sets, metric spaces, compact sets, perfect sets and connected sets. Convergence and divergence, some basic theorems, limits and continuity of functions, continuity and compactness, continuity and connectedness.
MATH4014
Number Theory
Divisibility, prime numbers, fundamental theorem of arithmetic, greatest common divisors, division algorithm, some arithmetical functions, congruence systems, polynomial congruences, quadratic residues, continued fractions.
MATH4016
Real Analysis II
Set theory and real number system, Lebesgue measure, Lebesgue integral, convergence theorems, differentiation and integration, classical Banach spaces.
MATH4021
Advance Complex Analysis
Rigorous introduction to the theory of function of a complex variable: analytic continuation, Riemann surfaces, entire and meromorphic functions and selected topics.
MATH4031
Functional Analysis I
Normed spaces, definition and examples of normed and Banach spaces. Hilbert spaces, linear mappings, bounded linear mappings and functionals, normed spaces of bounded linear mappings, the dual of a normed space.
MATH4032
Functional Analysis II
Linear mappings, the Hahn-Banach theorem, examples of dual spaces, category theorems, the Banach-Steinhaus theorem, finite-dimensional spaces, special properties of finite dimensional spaces
MATH4052
Topology
Topological spaces, compactness and connectedness, continuous functions, Tychonoff’s Theorem, seperation axioms, Urysohn and Tietze theorems, homotopy, fundamental group, covering spaces.
MATH4053
Partial Differential Equations I
First and second order partial differential equations, the Cauchy problem, method of separation of variables, eigen value problem, boundary value problem, Green’s functions and maximum principle.
MATH4054
Partial Differential Equations II
The Cauchy-Kovalevski theorem, the Lewy example, the heat operator, the wave operator, Sobolev space, local regularity of elliptic boundary value problems.
MATH4063
Geometry
Fundamental Principle of Analytic Geometry, Affine spaces and Affine coordinate systems, Euclidean space and Euclidean coordinate systems in plane and space, Lines in the plane, review of trigonometry and polar coordinates, cylindrical and spherical coordinates, lines and planes in 3-space, basics about conics, basic surface in space, cylinders, surface of revolutions, quadratic surfaces.
MATH4070
Mathematical Finance
Topics covered will include: an introduction to financial instruments and markets, fixed-income securities and rates of return, utility functions and optimal investment, simple models of random variation in prices, the fundamental concepts of arbitrage, replication, and completeness, and the use of arbitrage-free models for the valuation of securities and for the management of risk.
MATH4071
Coding Theory
Basic definitions, syndrome decoding, BCH and cyclic codes, quadratic residue codes, weight distributions, relati on to design theory.
MATH4072
Cryptography
Early crypto systems and simple systems, public key cryptography, primality and factoring, elliptic curve crypto systems.
MATH4081
Introduction to Fluid Dynamics
To provide an introduction to the theory of incompressible fluid dynamics, which describes the motion of liquids and gases at speeds small compared to the sound speed. Special attention is paid to a precise formulation of the various conservation laws that govern fluid dynamics, as this provides a convenient framework in which to study specific examples as well as extensions of the basic theory.
MATH4082
Numerical Solution ofPartial DifferentialEquations
This course is designed to the needs of the engineering curricula by providing an application oriented introduction to the finite difference method of solving partial differential equations arising from various physical phenomenon. The students will be asked to write codes and also be given an introduction on analytical solutions of PDE's. Elementary techniques including separation of variables, and the method of characteristics will be used to solve highly idealized problems
MATH4085
Commutative Algebra
Basic Notions, Unique Factorization Domains, Polynomial Rings on Unique Factorization Domains, Operations on Ideals, Prime and Primary Ideals, Primary Decomposition, Artinian Rings, Noetherian Rings, Zero Divisors on Noetherian Rings
MATH4086
Galois Theory
Structure of graph theory, Subgraph, Path, Tree, Connection matrix, the circuit-edge incidence matrix, cut-set matrix, graph extensions
MATH4087
Graph Theory
Structure of graph theory, Subgraph, Path, Tree, Connection matrix, the circuit-edge incidence matrix, cut-set matrix, graph extensions
MATH4088
Game Theory
Matrix games: Definition and basic concepts, The minimax theorem, 2*2 games, 2*n games, m*2 games, m*n games, Diagonal games, Symmetric games, Examples, Infinite antagonistic games: Equilibrium situations, Optimal strategies, Conditionally compact games, Continuous games on the unit square, convex games, Examples, Noncooperative games: Nash’s theorem, Prisoner’s dilemma, The battle of the sexes, Examples, Cooperative Games: Characteristic functions, Imputations, dominance of imputations,etc.
MATH4089
Mathematics for Finance and Management
Mathematics in Business Management: Income statement analysis, Simple interest and simple discount, bank discount and negotiable instruments, Mathematics in investment-basic topics: Compound Interest, annuities, Comparison methods for investment alternatives, Mathematics in investment – applications: Extinction of depts., Investment in Stocks and bonds, Depreciation and depletion, Perpetuity and capitalization, Life annuities, Life Insurance, Mathematical programming for capital Budgetment
MATH4090
Fuzzy Mathematics
Definition of a fuzzy set, Operations on fuzzy sets, Level sets, Fuzzy Subgroups, The relationship between fuzzy subgroup and subgroup of a group, Some basic theorem of fuzzy subgroups, Fuzzy Normal subgroups, Fuzzy Homomorphism, Isomorphism theorems.
MATH4091
Kinematics
One - Parameter Planar Motions, Velocities of The Orbit Curve, Closed Planar Motions, Steiner Area Formula, Holditch’s Theorem, The Area and Length of Enveloping Curve of Straight Lines,
MATH4092
Dual Number Theory and Quatermions
The Ring Of Dual Numbers , -Modul, The Inner Product and The Cross-Product of Dual Vectors, Dual Angle, Dual Unit Sphere, E. Study’s Map, Real Quaternions, Dual Quaternions
MATH4093
Measure and Integration Theory
Set theory and Real number system, Lebesgue measure, The Lebesgue Integral, Differentiation and Integration, Classical Banach Spaces
MATH4094
Selected Topics in Analysis
Ordered sets, fields, Real and Complex fields, Euclidean Spaces, finite, countable and uncountable sets, Metric Spaces, compact sets, perfect sets and connected sets. Convergence and divergence, some basic theorems, limits and continuity of functions, continuity and compactness, continuity and connectedness






