Bahçeşehir Üniversitesi | Bölüm Sayfaları

İletişim

Ulaşım

2009-2010 Katalog

Öğrenci El Kitabı

DUYURU ve HABERLER

Projeler

Yayınlar

Matematik Lisans Programı

Ders Planı

Ders Kodu	Ders Adi	( Teorik - Pratik ) Kredi
1.Yıl - Güz Dönemi
MATH1055	Abstract Mathematics I	( 3 - 0 ) 3
GEP1005	History of Civilization I	( 3 - 0 ) 3
SE1001	Intro. to Programming (Java)	( 2 - 2 ) 3
PHYS1001	Physics I	( 3 - 2 ) 4
MATH1051	Calculus I	( 3 - 2 ) 4
ENG1003	Communications Skills & Academic Writing I	( 2 - 2 ) 3
1.Yıl - Bahar Dönemi
MATH1052	Calculus II	( 3 - 2 ) 4
SE1002	Object Oriented Programming (Java)	( 2 - 2 ) 3
MATH1056	Abstract Mathematics II	( 3 - 0 ) 3
ENG1004	Communication Skills & Academic Reporting II	( 2 - 2 ) 3
GEP1006	History of Civilization II	( 3 - 0 ) 3
PHYS1002	Physics II	( 3 - 2 ) 4
2.Yıl - Güz Dönemi
MATH2005	Probability	( 3 - 0 ) 3
TLL2021	Turkish Language & Literature I	( 2 - 0 ) 2
MATH2003	Calculus III	( 3 - 2 ) 4
MATH2013	Linear Algebra I	( 3 - 2 ) 4
MATH2033	Discrete Mathematics	( 3 - 0 ) 3
SE2211	Data Structures and Algorithms I	( 2 - 2 ) 3

Ders Listesi

Ders Tanımları

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.

MATH2008

General Topology

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.

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.

MATH3022

Complex Analysis

Complex numbers and functions: contour integration, power series, Cauchy-Riemann equations, residues, poles, conformal mapping and applications.

MATH3061

Algebra I

Groups, basics, subgroups, cyclic subgroups, normal subgroups, homomorphism, permutation groups, direct product, Sylow theorems.

MATH3062

Algebra

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