 |
 |
GRADUATE COURSES (M.S. and Ph.D. in Mathematics and Computer Science)
GRADUATE COURSES (M.S. in Information Systems)
Sets and set operations. Numbers. Polynomials, factorization, rationals and simplification. Systems of linear equations. Real axis. Absolute value. Cartesian coordinate system. Straight line. Quadratics. Functions, graphs. Triangles, trigonometry. Exponentiation and Logarithm. Vectors.
MATH 103 Mathematics for Business and Economics I
First degree-equations in one variable. Second degree-equations in one variable. Inequalities and their solutions. Absolute value relationship. Rectangular coordinate system. Linear equations; Graphical characteristics, slope-intercept form, determination of the equation of a straight line. Systems of linear equations; two-variable systems of linear equations, Gaussian elimination method, n-variable systems, selected applications of systems of linear equations. Functions; types of functions, graphical representation of functions. Linear functions and applications; Linear cost, revenue, profit, demand and supply functions. Break-even models. Quadratic functions and their characteristics; quadratic cost, revenue, profit, demand and supply functions. Polynomial functions. Exponential and logarithmic functions and their characteristics. Equations involving logarithmic and exponential expressions.
MATH 104 Mathematics for Business and Economics II
Matrices and determinants; Applications. Solution of systems of linear equations; Inverse matrix method, Cramer's rule. Rate of change. Derivatives. Higher order derivatives. Curve sketching. Optimization. Revenue, cost, profit applications. Cost-benefit analysis. Functions of several variables. Partial derivatives. Applications. Lagrange multipliers. Integrals. Definite Integrals. Areas, Applications.
Prerequisite: MATH 103
MATH 105 Elementary Mathematics
Cartesian coordinate system; Linear equations and lines, system of linear equations, quadratic equations, functions. Matrices, determinants, systems of linear equations and their solutions using Cramer's Rule. Selected application to economics and accounting. Set theory, counting theory, discrete probability. Descriptive statistics
Prerequisite: Math 100
MATH 106 Linear Algebra
Systems of linear equations: elementary row operations, echelon forms, Gaussian elimination method; Matrices: elementary matrices, invertible matrices, symmetric matrices, quadratic forms and Law of Inertia; Determinants: adjoint and inverse matrices, Cramer's rule. Vector spaces: linear independence, basis and dimensions, Euclidean spaces. Linear mappings: matrix representations, changes of bases; Inner product spaces: Cauchy-Schwarz inequality, Gram-Schmidt orthogonalization; Eigenvalues and eigenvectors: characteristic polynomials, Cayley-Hamilton Theorem, Diagonalizations, basic ideas of Jordan forms.
MATH 107 Elementary Mathematics
Some preliminaries: Solving first and second degree equations. Inequalities and their solutions. Absolute value relationships. Rectangular coordinate system. Linear equations: characteristics of linear equations, graphical characteristics, slope intercept form, determining the equation of a straight line, systems of linear equations and their solutions. Mathematical functions: definition of a function and types of functions, graphical representation of linear and quadratic functions. Selected applications. Matrix algebra: introduction, special types of matrices, matrix operations, the determinant. Introduction to probability theory: sets and set operations, permutations and combinations, basic probability concepts, statistical independence and dependence. Probability distributions: random variable and probability distributions, measure of central tendency and variation.
MATH 111 Basic Mathematics I
Numbers, Number systems, exponents, sets, set operations, intervals, absolute value. Equations and inequalities; solving first degree equations in one variable, solving second degree equations in one variable, quadratic formula, inequalities and their solutions, absolute value relationship. Trigonometry; trigonometric functions, trigonometric identities. Function, domain and range, types of functions; linear, quadratic, polynomial functions, graphs of linear and quadratic functions. Analytic geometry in 2-space and 3-space: operations on points in 2-space and 3-space. Mid-point formula, distance formula, lines and their properties; parallel and perpendicular lines, slope, angle between two lines. Matrix algebra: Operations on matrices; addition, subtraction, transpose of matrices, scalar multiplication, determinants, cofactors, cofactor matricex, adjoint matrix, inverse matrix, elimination method, Cramer's rule.
Prerequisite: Math 100
MATH 112 Basic Mathematics II
Exponential and logarithmic functions and their properties, exponenlial and logarithmic functions with base e. Differentiation: limits, limit properties, the derivative, rules of differentiation, first derivative test, increasing and decreasing functions, higher order derivatives, second derivative test, concavity, curve sketching. Applications: revenue, cost, profit applications, break - even analysis, supply - demand applications, equilibrium point. Functions of several variables: Bivariate functions, partial derivatives, extrema of functions, Lagrange multipliers. Integral calculus: rules of integration, substitution technique, definite integral, applications of definite integral.
Prerequisite: Math 111
MATH 131 Analytic Geometry
Cartesian coordinates in 2 and 3 dimensional spaces. Vectors. Equations of lines and planes. Conics. Cylindrical and spherical coordinates. Identifying and sketching some elementary curves and surfaces.
MATH 150 Calculus with Precalculus
Sets, set operations and numbers. Polynomials, factorization, equations and root finding. Real axis, labeling integers, rationals and some irrationals on the number axis. Cartesian coordinates. Lines. Graphs of equations and quadratic curves. Functions and graphs of functions. Limits and continuity. Derivatives. Rules of differentiation. Higher order derivatives. Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals. Fundamental Theorem. Techniques of integration. Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Infinite series. Geometric series. Power series. Taylor series and binomial series.
Prerequisite: Mathematics Proficiency Exam
MATH 151 Calculus I
Limits and continuity. Derivatives. Rules of differentiation. Higher order derivatives. Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals. Fundamental Theorem. Techniques of integration. Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Infinite series. Geometric series. Power series. Taylor series and binomial series.
Prerequisite: MATH 100
MATH 152 Calculus II
Vectors in R3. Lines and Planes. Functions of several variables. Limit and continuity. Partial differentiation. Chain rule. Tangent plane. Critical Points. Global and local extrema. Lagrange multipliers. Directional derivative. Gradient, Divergence and Curl. Multiple integrals with applications. Triple integrals with applications. Triple integral in cylindrical and spherical coordinates. Line, surface and volume integrals. Independence of path. Green's Theorem. Conservative vector fields. Divergence Theorem. Stokes' Theorem.
Prerequisite: MATH 150 or MATH 151
MATH 161 Mathematical Logic of Computers
Basic set theory; Terminology and notation, venn diagrams, truth tables and proof, functions and relations, partial orderings and equivalence relations, mathematical induction. Theory of counting; the multiplication rule, ordered samples and permutations, unordered samples without repetition; binomial coefficients, unordered samples with repetition, the principle of inclusion and exclusion. Graphs and algorithms; trees and spanning trees, minimal spanning trees, Prim's algorithm. Propositional calculus and boolean algebra; propositional calculus, basic boolean functions, logic gates, minterm and maxterm expansions. Discrete probability theory; discrete probability spaces, conditional probabilities.
MATH 163 Discrete Mathematics
Set theory, functions and relations; introduction to set theory, functions and relations, inductive proofs and recursive definitions. Combinatorics; basic counting rules, permutations, combinations, allocation problems, selection problems, the pigeonhole principle, the principle of inclusion and exclusion. Generating functions; ordinary generating functions and their applications. Recurrence relations; homogeneous recurrence relations, inhomogeneous recurrence relations, recurrence relations and generating functions, analysis of algorithms. Propositional calculus and boolean algebra; basic boolean functions, digital logic gates, minterm and maxterm expansions, the basic theorems of boolean algebra, simplifying boolean function with karnaugh maps. Graphs and trees; adjacency matrices, incidence matrices, eulerian graphs, hamiltonian graphs, colored graphs, planar graphs, spanning trees, minimal spanning trees, Prim's algorithm, shortest path problems, Dijkstra's algorithms .
MATH 191 Introductory Mathematics
Algebraic expressions, equations and inequalities. Relations and functions, Quadratic functions. Trigonometric functions, trigonometric identities and equations, applications of trigonometry. Vectors and their applications, polar equations. Matrices and determinants, solution of linear system of equations. Analytic geometry; parabolas, ellipses, hyperbolas, conic sections, quadratic surfaces.
MATH 201 Linear Algebra and Ordinary Differential Equations
Linear Algebra; Matrix algebra, special matrices and row operations, Gaussian elimination method, determinants, adjoint and inverse matrices, Cramer's rule, linear vector spaces, linear independence, basis and dimension. First order ordinary differential equations; definitions and general properties of solutions, separable, homogeneous and linear equations, exact equations and integration factors. Higher order equations with constant coefficients; Basic theory and the method of reduction of order, second order homogeneous equations with constant coefficients, nonhomogeneous equations, the method of undetermined coefficients, the method of variation of parameters, the Cauchy-Euler equations. Power series solutions; classification of points, ordinary and singular points, power series solutions about ordinary points, power series solutions about regular singular points, the method of frobenius. Systems of differential equations; general properties of constant coefficient systems, eigenvalues and eigenvectors, diagonalizable matrices, solutions of linear systems with constant coefficients. Boundary value problems.
MATH 203 Ordinary Differential Equations
Ordinary differential equations of the first order; separation of variables, exact equations, integrating factors, linear and homogeneous equations. Special first order equations; Bernoulli, Riccati, Clairaut equations. Homogeneous higher order equations with constant coefficients. Nonhomogeneous linear equations; variation of parameters, operator method. Power series solution of differential equations. Laplace transforms. Systems of linear differential equations.
Prerequisite: MATH 106 -MATH 151
MATH 204 Partial Differential Equations
Existence theorems. Canonical forms. First- and second-order partial differential equations; hyperbolic, elliptic and parabolic equations. Wave and heat equations. Fourier solution of partial differential equations. Dirichlet's problem. Green's functions. Laplace transform solutions.
Prerequisite: MATH 203
MATH 205 Complex Calculus
Complex numbers. Algebra of complex numbers. Polar representation. Complex functions. Limits and continuity. Analyticity. Analytic functions. Cauchy-Riemann equations. Mobius transformations. Conformal mapping. Line integrals. Cauchy integral formula. Isolated singularities. Residue theorem.
Prerequisite: MATH 152
MATH 206 Linear Algebra II
Vector spaces, subspaces, basis and dimension, coordinates, row equivalence. Linear transformations, representation by matrices, linear functionals, dual. Algebras, algebra and factorization of polynomials. Commutative rings, determinant function, permutations and properties of determinants. Characteristic values, the Cayley-Hamilton theorem, invariant subspaces, direct-sum decompositions, the primary decomposition theorem, cyclic decompositions and rational form, the jordan form, inner product spaces.
Prerequisite: MATH 106
MATH 207 Differential Equations
First-order differential equations. Higher order
homogeneous linear differential equations. Solution space. Linear
differential equations with constant coefficient. Non-homogeneous
linear equations; variation of parameters, operator methods. System of
linear differential equations with constant coefficients. Laplace
transforms. Power series solutions. Bessel and Legendre equations.
Orthogonal functions and Fourier expansions. Introduction to partial
differential equations. First- and second-order linear PDE's.
Separation of variables. Heat and wave equations.
Prerequisite: MATH 106 and MATH 151
MATH 211 Introduction to Statistics
Variables and Graphs; Statistic, population and
sample, inductive and descriptive statistics. Variables; Discrete and
continuous. Frequency Distributions; General rules of forming
frequency distributions. Histograms and frequency polygons. Measures
of central tendency; the arithmetic mean, the median and the mode.
Harmonic and geometric mean, root mean square, quartiles deciles and
percentiles. Measures of dispersion; the range, the mean deviation,
the semi-interquartile range, the 10-90 percentile range, the standard
deviation, the variance. Elementary probability theory; conditional
probability, probability distributions, expectation, relation between
population, sample, mean and variance. Some discrete probability
distributions; binomial and normal distributions, poisson
distribution, multinomial distribution. Elementary sampling theory.
Curve fitting and method of least squares.
MATH 251 Advanced Calculus
Elements of set theory, functions. Basic
topology of R", real number system, sequences. Limits of functions,
continuity and uniform continuity. Riemann integral, improper
integral. Convergence of infinite series, power series. Uniform
convergence. Transformations and their differentials.
Prerequisite: MATH 152
Math 252 Mathematical Methods for Engineering
Complex numbers. Algebra of complex numbers. Polar representation. Complex functions. Limit and continuity. Analyticity. Analytic functions. Cauchy-Riemann equations. Line integrals. Cauchy integral formula. Isolated singularities. Residue theorem. Numerical error. Solution of nonlinear equations. Convergence. Solution of linear system of equations: direct and iterative methods. Interpolation. Curve fitting. Numerical differentiation and integration.
Prerequisite: MATH 106 and MATH 152
MATH 253 Mathematical Analyis I
Sequences and series, continuity, uniform continuity, sequences and
series of functions, uniform convergence.
MATH 254 Mathematical Analyis II
Differentiation, inverse and implicit function theorems, L'Hopital's
rule, power series, the Riemann-Stieltjes integral.
MATH 255 Geometry
Hilbert's axioms for Euclidean geometry. Basic
properties of triangles and circles. Constructions with ruler and
compass. Transformations. Axioms leading to non Euclidean geometries.
Models for various geometries. Introduction to affine and projective
geometries.
MATH 261 Discrete Mathematics II
Set theory. Venn diagrams. Product sets.
Mathematical induction. Propositional calculus. Permutations and
combinations. Equivalence relations, partitions, partial ordering.
Introduction to graph theory. Paths and cycles. Shortest paths.
Eulerian and Hamiltonian paths. Trees. Lagrange's theorem. Boolean
algebra. Truth tables. Discrete probability.
MATH 305 Theory of Ordinary Differential
Equations
Existence, uniqueness and extensions of
solutions, basic theory of linear equations and systems of linear
equations, the Sturm theory, classification of critical points,
stability, limit cycles, periodic solutions.
MATH 322 Probability and Statistical Methods
Introduction to probability and statistics.
Operations on sets. Counting problems. Conditional probability and
total probability formula, Bayes' theorem. Introduction to random
variables, density and distribution functions. Expectation, variance
and covariance. Basic distributions. Joint density and distribution
function. Descriptive statistics. Estimation of parameters, maximum
likelihood estimator. Hypothesis testing.
Prerequisite: MATH 152
MATH 323 Probability Theory
Introduction to probability. Operations on sets.
Counting problems. Conditional probability, total probability formula,
Bayes' theorem. Random variables, density and distribution functions.
Expectation, variance and covariance. Moment generating function.
Basic distributions. Joint density and distribution function. Law of
large numbers. Central limit theorem.
Prerequisite: MATH 152
MATH 324 Statistics
Introduction to statistics. Basic methods of
working with observation data, histogram and ogive Descriptive
statistics. Estimation of parameters, maximum likelihood estimator.
Hypothesis testing. Linear regression.
Prerequisite: MATH 323
MATH 341 Measurement and Evaluation
Concepts of measurement and evaluation in
education. Construction and use of teacher-made and standardized tests
for mathematics and computer education. How to major outcome of the
teaching-learning process in mathematics and computer education. Basic
descriptive statistics, statistical analysis of tests scores and item
responses. Formative and summative evaluation. Interpretation of tests
results and grading systems.
Prerequisite: EDUC 101
MATH 342 Curriculum Development
What is curriculum. Principles and innovative
approaches to curriculum development. The relationship among
curriculum and outcomes of education. Basic concepts in educational
research. Aspects of developing and planning mathematics and computer
education curriculum for high schools.
Prerequisite: EDUC 101
MATH 343 Teaching Geometry and Trig. with
Discovery Approach
Introduction. Discovering angle relationships,
triangle sum conjecture, polygon sum conjecture. Discovering
properties of parallel lines, trapezoids, mid segments,
parallelograms. Coordinate geometry, slope of a line. Circles, area.
Pythagorean theorem. Volume. Similarity. Trigonometry - activities.
Geometric proofs - proofs without words. Lab experiments related to
geometry, geoboard activities, paper folding. Aids for informal
geometry. Class activities.
MATH 346 Teaching Secondary School Algebra
Introduction. Historical perspectives in the
development of algebra. A generalization perspective on the
introduction of algebra. A problem - solving perspective on the
introduction of algebra. Developing algebraic aspects of problem
solving within a spreadsheet environment. The transition from
arithmetic to algebra in problem solving. Creative enrichment units in
algebra.
MATH 353
Methods of Applied Mathematics
Calculus of variations. Euler-Lagrange
equations. Systems with constraints. Boundary-value problems.
Eigenvalues and eigenfunctions; orthogonality of eigenfunctions;
representation of arbitrary functions in terms of eigenfunctions.
Boundary-value problems involving inhomogeneous differential
equations. Fourier-Bessel series and Legendre series. Green's
functions; one dimensional examples. The Dirac delta function. General
Properties of Green's functions. Integral equations; general
introduction. Relation between differential and integral equations.
Fredholm type equations with separable kernels. Hilbert-Schmidt
theory. Iterative methods; the Neumann series. Fredholm theory.
Prerequisite: MATH 203
MATH 365 Combinatorial Mathematics
Number and counting; odometer principle,
principle of induction, order of magnitude, handshaking lemma, set
notation. Subsets, partitions, permutations; subset, subset of fixed
size, the binomial theorem, pascal's triangle, Lucas' theorem,
permutations, estimates for factorials, Cayley's theorem on trees,
Bell numbers, generating combinatorial objects. Recurrence relations
and generating functions; Fibonacci numbers, linear recurrence
relations with constant coefficients, derangements and involutions,
Catalan and Bell numbers. The principle of inclusion and exclusion;
PIE and its generalization, Stirling numbers and exponentials, even
add odd permutations. System of distinct representatives; Hall's
theorem. Extremal set theory; intersecting families, Erdos-Ko-Rado
theorem, Sperner's theorem, the de Brujin-Erdos theorem. Graphs; trees
and forests, Cayley's theorem, minimal spanning tree, Eulerian graphs,
Hamiltonian graphs, Ore's theorem, gray codes, the traveling salesman,
digraphs, networks, max-flow min-cut theorem , integrity theorem,
Menger's theorem, Könsg's theorem, Hall's theorem, diameter and girth.
Ramsey's theoremlthe pigeonhole principle, bounds for Ramsey's
theorem, Applications, infinite version.
MATH 373 Numerical Analysis for Engineers
Numerical error. Solution of nonlinear
equations, and linear systems of equations. Interpolation and
extrapolation. Curve fitting. Numerical differentiation and
integration. Numerical solution of ordinary differential equations.
Prerequisite: MATH 203 or MATH 207
MATH 378 Numerical Analysis I
Numerical error. Solution of nonlinear
equations. Convergence. Solution of linear systems of equations:
direct and iterative methods. Interpolation. Curve fitting. Numerical
differentiation and integration.
-Also available as a Service
Course
Prerequisite: MATH 106 -MATH 152
MATH 402 Graduation Project
A practical/theoretical training in mathematics
or in the use of computational techniques and/or computers. A short
report and presentation will be required for the completion of this
course.
MATH 412 Introduction to Algebra
Groups, subgroups, cyclic groups, homomorphisms
and isomorphisms, permutations and Cayley's Theorem, cosets and
Lagrange's Theorem, quotient groups and the isomorphism theorems,
Sylow's Theorem; Rings and fields, ideals and quotient rings, integral
domains, prime and maximal ideals, the field of quotients, properties
of integers; rings of polynomials, polynomials over C, R and Q, basic
ideas of field extensions.
MATH 431 Operational Research
Linear programming models. Primal simplex
method. Duality, dual simplex method, post-optimality analysis,
shortest path problems, CPM algorithm, integer programming models.
Branch and bound technique. Dynamic programming.
MATH 441 Methods of Teaching Mathematics and
Computers
A study of curriculum, methods and materials of
teaching high school mathematics and computer. Recent trends and
developments in teaching mathematics and computers. Selection and
application of appropriate methods for teaching mathematics and
computer. Design and development of computer assisted teaching.
MATH 442 Practice in Teaching Mathematics and
Computers
Observation of mathematics and computers
instruction in schools. Design of resource, unit and lesson plans,
experience in deductive and inductive teaching styles; supervised
student teaching in real settings.
Prerequisite: EDUC 102 -EDUC 201 -MATH
341 -MATH 342 -MATH 441
MATH 474 Numerical Analysis II
Finite difference calculus. Numerical solution
of ordinary and partial differential equations. Stability and
convergence of solution methods. Case studies.
Prerequisite: MATH 373 or MATH 378
MATH 476 Optimization Theory
Introduction to convex analysis. Convex
programming models. Lagrange function. Saddle point. Fenchel function.
Lagrange and Fenchel duality of convex programming. Algorithms for
convex programming problems. Special classes of convex programming (QP,
Geometric programming, lp-programming, entropy programming).
Nonlinear, nonconvex programming problems (HP, disjunctive programming
problem). Global optimization problems and solution techniques.
Prerequisite: MATH 251
MATH 481 Finite Element Method
An introduction to the basic concepts of the
Finite Element method. Solution of elliptic boundary value problems.
Solution of time-dependent problems. The Galerkin method. Case
studies.
Prerequisite: MATH 374
MATH 491 History of Mathematics
Mathematics in Egypt and Mesopotamia. Heroic
age. Mathematical works of Plato, Aristotle, Euclid, Archimedes,
Appolonius and Diophantus. Mathematics in China and India. Mathematics
of the Renaissance, Islamic contributions. Time of Fermat and
Descartes. Works of Newton, Leibniz, Euler, Gauss, Cauchy, Bolyai,
Lobachevsky and Galois. Aspects of the twentieth century
COMP 181 Introduction to Computer Science I
Organization of a digital computer. Number
systems. Algorithmic approach to problem solving. Flowcharting.
Concepts of structured programming.Programming in at least one of the
programming languages. Data types, constants and variable
declarations. Expressions. Input/output statements. Control
structures, loops, arrays.
COMP 182 Introduction to Computer Science II
Advanced programming concepts, strings and
string processing. Record structures. Modular programming. Procedures,
subroutines and functions. Communication between program modules.
Scopes of variables. Recursive programs. Introduction to file
processing. Applications in the programming languages.
Prerequisite: COMP 181
COMP 190 Computer Applications for Law
Introduction to the world of computers. Hardware
components: system unit, spectrum of input/output devices, memory
devices. Word processing and desktop publishing. Programming
languages.
COMP 191 Introduction to Computers
Organization of a computer, hardware and
software components. Disk operating system and file system. Text
editors and word processors. Introduction to structured programming.
Programming in one of the high-level programming languages.
COMP 194 Introduction to Computers -in Turkish
Organization of a computer, hardware and
software components. Disk operating system and file system. Text
editors and word processors. Introduction to structured programming.
Programming in one of the high-level programming languages.
COMP 275 Object Oriented Programming
Introduction to object technology; objects,
attributes, methods, classes, constructor. Basic C++ types and
programs; integer objects, and simple expressions, C++ input and
output, character objects, real number objects, string objects.
Describing and declaring classes; class description, declaring and
using objects, class declaration, function prototypes, with default
values. Selection statements; logical expressions, if statement,
nested selection statements. Loop structures. Developing your own
classes; implementing classes, organizing program source code, error
checking. Additional C++ control structures; multiple selection,
enumeration types, date class, for loop, advanced loop concepts,
argument passing. Arrays; array storage, initializing arrays, arrays
as arguments, arrays of objects, arrays of class data members, string
objects, multidimensional arrays
COMP 285 Design and Analysis of Algorithms
Complexity measure. Asymptotic notation.
Time-space trade-off. A study of fundamental strategies used in design
of algorithm classes including divide and concur, recursion, search
and traversal. Backtracking. Branch and bound techniques. Analysis
tools and techniques for algorithms. NP-complete problems.
Approximation algorithms. Introduction to parallel and fast
algorithms.
Prerequisite: COMP 182
COMP 286 Data Structures
Primitive data structures Linear data
structures: stacks, queues, deques and their application. Concept of
linking, linked lists. Non-linear data structures: trees, graphs.
Algorithmic implementation of data structures.
Prerequisite: COMP 182
COMP 332 Programming Languages
Preliminary concepts. Control structures.
Modular programming. Procedural and data abstraction. Top-down design
method. Imperative languages. Functional programming to
Object-oriented programming. Studies of existing programming
languages.
Prerequisite: COMP 182
COMP 361 File Organization and Processing
Basics of file structures. Tapes and disks.
Logical file organization techniques. Sequential files. Direct files:
deterministic and hashing transformations. Indexed files.
COMP 366 Java Programming Language
Classes of objects. Fields. Constructor.
Methods. Extending classes. Constructors in extended classes.
Overriding methods and hiding fields. Interfaces, single and multiple
inheritance. Tokens. Primitive types. Operations. Operator precedence.
Expressions and assignment statements. Arrays. Arrays of arrays. Type
conversion. Statements and blocks. If - else. Switch. While and do -
while statements. Labels, break, continue. Strings. String comparison.
String conversion. Threads. Creating threads. Synchronization. Wait
and notify. I/O package. Streams. Standard stream types.
COMP 373 Database Management Systems
Introduction to the evolution of database
concepts. Data abstraction. Entity relationship model. Relational
model. Relational algebra. Relational calculus. Integrity constraints.
File and system structure, mapping relational data to files.
Relational database design. Distributed databases. Database security.
Cryptography, encryption and decryption.
COMP 385 Parallel Algorithms
Parallel models and architecture: parallel
computers and models, performance measures, parallel complexity.
Arithmetic problems: analysis of parallel addition, multiplication and
division. Parallelism in arithmetic expressions. Matrix problems:
firstorder linear recurrences, linear tridiagonal, triangular,
block-two-diagonal systems. Parallel sorting. Parallel graph
algorithms. Searching a graph, connected components, shortest-path
algorithms, minimal spanning tree algorithms.
COMP 432 Programming
Languages
Overview of Programming Languages. Syntax and Semantics.
Names, Bindings and Scopes. Data Types. Expressions and Evaluation.
Subprograms. Abstract Data Types. Object Oriented Languages.
Concurrency.
Exception Handling.
COMP 483 Operating Systems
View and functions of operating systems.
Interprocess communication, process scheduling. Memory management,
multiprogramming, swapping, paging, virtual memory. File system, its
security and protection mechanisms. Deadlocks. Study of operating
systems introducing MS DOS, UNIX.
COMP 486 System Programming
Fundamental concepts of multiprogramming
language processors and operating systems. One-and two-pass
assemblers. Macro system tables. Syntax and semantic phases.
Optimization. Compilers. Parsing. Lexical and syntactic analysis. Code
generation and optimization. Studies of some compilers.
GRADUATE COURSE DESCRIPTIONS
MATH 500 M.S. Thesis
M.S. Thesis in pure/applied mathematics. A
presentations is required for the completion of the thesis.
MATH 501 Analysis I
Set theory. Construction of real numbers.
Convergence, continuous functions. Differentiation. Riemann integral.
Introduction to metric spaces. Spaces of continuous functions.
Lebesgue measure. Lebesgue integral.
MATH 502 Complex Analysis
Analytic functions. Singular points and
zeros. The argument principle. Conformal mappings. Riemann mapping
theorem. Mittag - Leffler theorem. Analytic continuation.
MATH 503 Commutative Algebra
Rings and ideals, modules, Notherian rings,
Dedekind domains, classical ideal theory, valuation theory, polynomial
and power series rings.
Prerequisite: MATH 508
MATH 504 Homological Algebra
Categories and functors, natural
transformations, chain complexes, Hom and tensor, derived functors,
projectives, group extensions, group homology and cohomology.
Math 505 Theory of Partial Differential Equations
Cawchy-Kowalevski Theorem. Linear and
quasilinear first order equations. Existence and uniqueness theorems
for second order Elliptic, Parabolic and Hyperbolic equations.
Correctly posed problems. Green's functions.
MATH 506 Theory of Ordinary Differential Equations
Existence and uniqueness of solutions of
initial value problems, continuation of solution, dependence on the
initial value, Wronskian identity, boundary value problems, eigenvalue
problems, zeros of solutions
MATH 507 Algebra I
Group theory, ring theory; polynomials,
modules. Fields and simple field extensions. Construction with ruler
and compass, the elements of Galois theory. Solvability by radicals.
Finite fields.
MATH 508 Algebra II
A brief review of group theory and ring
theory, polynomials, Notherian rings and modules. Algebraic field
extensions, Galois theory. Extension of rings, transcendental
extensions.
Prerequisite: MATH 507
MATH 509 Selected Topics in Algebra
Advanced topics in algebra selected by the
instructor.
MATH 516 Measure and Integration
Outer measure, measurable sets and the
Lebesque measure on R. Measurable functions, Borel measurability,
Lusin's and Egoroff's theorems. Generalizations to Rn. Lebesque
integral of nonnegative measurable functions, general Lebesque
integral, convergence in measure. Differentiation and integration,
absolute continuty, Lp spaces. Abstract measure spaces, measurable
functions, signed measures, the Radon-Nikodym theorem.
Lebesque-Stieltjes integral. The daniell approach, extension theorem.
Elements of measures in locally compact spaces.
Prerequisite: MATH 501
MATH 517 Lie Groups and Lie Algebras
Differential Manifolds. Lie Groups. Tangent
space. One-parameter subgroup. Rotation groups. Homogeneous spaces.
Lie Algebras. Adjoint representations. Complex extensions. Simple and
semi-simple algebras. Cartan's Criterion. Cartan-Weyl Normalization.
Representation of Lie Groups.
Math 518 Lie Algebras and Representation Theory
Lie algebras of derivations. Solvable and
nilpotent Lie algebras. Semi-simple Lie algebras. Killing form.
Complete reducibility of representations. Weyl's Theorem.
Classification of irreducible modules. Orthogonality properties.
Integrality properties. Rationality properties. Axiomatics. The Weyl
group. Coxeter graphs and Dynkin diagrams. Theory of weights.
Isomorphism Theorem. Cartan subalgebras. Representation Theory.
Weights and maximal vectors. Finite-dimensional modules. Multiplicity
formula. Characters. Formulas of Weyl, Kostant and Steinberg.
Math 520 Group Theory
Review of elementary group theory. Group
actions on sets. Finite p-groups and Sylow's theorem. Groups of small
orders. Composition series and Jordan-Hölder's theorem. Soluble groups
and nilpotent groups. The Frattini subgroups and Burnside's basis
theorem. Direct products, direct sums and the structure of finitely
generated abelian groups. Free groups and presentations.
MATH 521 Probability Theory
Classes of events, s-fields. Axioms of
probability, probability space. Various probability distributions.
Measurable mappings, random variables and vectors. Distribution
functions. Expectation as Lebesgue-Stieltjes integrals. Convergence of
random variables. Characteristic functions and their properties.
Conditional expectation and independence. Law of large numbers and
central limit theorem.
Prerequisite: MATH 501
MATH 522 Random Process
Definition and construction of a random
process. Classification of random processes. Markov chains. Continuous
time processes. Poisson process. Markov process. Birth and Death
processes. Second order processes. Stationary processes. Gaussian
processes. Wiener process and white noise.
Prerequisite: MATH 521
MATH 525 Algebraic Functions
Preliminaries from valuation theory.
Valuations and prime divisors. Valuation metric. Extensions and
projections of a valuation. Algebraic theory of algebraic functions.
Prime divisors of an algebraic field. Differentials. Hasse
differentials. Riemann-Roch theorem and its applications. Special
types of algebraic function fields.
Prerequisite: MATH 503
MATH 527 Algebraic Curves
Algebraic preliminaries. Projective spaces.
Plane algebraic curves. Formal power series. Transformation of a
curve. Linear series.
MATH 528 Elliptic Curves
Curves of genus 0. P-adic numbers. The
local-global principle for conics. Geometry of numbers. Cubic curves.
Nonsingular cubics. The group law. Elliptic curves. Canonical form.
The P-adic case. Global torsion. Finite basis cohomology. Construction
of the Jacobian Tate-Shafarevich group. Points over finite fields.
Factorization using elliptic curves.
Prerequisite: MATH 527
MATH 529 Linear Programming
Constructive proof of some fundamental
theorems of linear algebra (matrix rank theorem, orthogonality theorem
etc.) Linear alternative theorems (Rouche-Kronecker-Campelli lemma,
Farkas-Minty lemma, Farkas lemma and its variants,
Farkas-Minkowski-Weyl theorem, Motzkin theorem). Linear programming (criss-cross
algorithm, primaldual algorithm, constructive proof of the duality
theorem). Parametric linear programming problem and its solution
method. Interior point methods of linear programming.
MATH 530 Non-Linear Programming
Unconstrained optimization. Convex sets and
convex functions. Iterative methods for unconstrained optimization.
Convex programming. Karush-Kulin-Tucker condition. Penalty methods.
Optimization with equivality constraints.
Prerequisite: MATH 529
MATH 531 Selected Topics in Operational Research
Advanced topics in operational research
selected by the instructor.
MATH 534 Ring Theory
Construction of rings, rings of fractions
and embedding theorem, categorical aspects of module theory, homology
and cohomology, rings with polynomial identities, rings from
representation theory..
Prerequisite: MATH 507
MATH 535 Topology
Topological spaces, continuous functions;
Connectedness, countability, separation axioms, compactness and
Tchykonoff theorem; metric spaces and metrizability; topological
groups; Homotopy of maps, fundamental groups, covering spaces;
Simplicial complexes and singular complexes, homology groups.
MATH 536 Algebraic Topology
Elementary homotopy theory: loop spaces and
suspensions, homology groups, fibrations and cofibrations; Singular
homology: the homology functor, homotopy invariance, exactness,
excision and Mayer-Vietoris sequence, applications to spheres and
Euclidean spaces; Cellular homology: attaching cells, CW complexes,
Hurewicz theorem, Whitehead theorem; Axiomatic characterization:
Eilenberg-Steenrod axioms, universal coefficients, Eilenberg-Zilber
Theorem and Kunneth formula; Cohomology: cohomology groups, universal
coefficents, cup and cap products, the ring structure, topological
manifolds, Poincare duality.
Prerequisite: MATH 535
MATH 537 Differential Topology
Smooth manifolds and smooth maps, tangent
spaces, immersions and embeddings, submersions, transversality, Sard
Theorem, degrees, intersection numbers, the Euler characteristic,
vector fields, tubular neighbourhoods, cobordism, Thom construction,
isotopy and gluing manifolds.
Prerequisite: MATH 535
MATH 538 Differentiable Manifolds
Differential forms and integration in Rn.
Submanifolds of Rn, abstract manifolds. Differentiable maps. Vector
fields, the tangent bundle. Submanifolds, immersions, submersions,
imbeddings. Differential forms on a manifold, orientiation.
Integration of differential forms, Stokes' theorem.
MATH 540 Selected Topics in Random Process
Advanced topics in Random Processes selected
by the instructor.
MATH 541 Selected Topics in Probability Theory
Advanced topics in Probability Theory
selected by the instructor.
MATH 543 Selected Topics in Systems Theory
Advanced topics in Systems Theory selected
by the instructor.
MATH 544 Selected Topics in Optimal Control
Advanced topics in Optimal Control selected
by the instructor.
MATH 545 Selected Topics in Quantum Theory
Advanced topics in Quantum Theory selected
by the instructor
MATH 547 Selected Topics Algebraic Topology
Advanced topics in Algebraic Topology
selected by the instructor.
MATH 548 Selected Topics in Algebraic Geometry
Advanced topics in Algebraic Geometry
selected by the instructor.
MATH 549 Selected Topics in Differential Equations
Advanced topics in Differential Equations
selected by the instructor.
MATH 550 Selected Topics in Complex Analysis
Advanced topics in Complex Analysis selected
by the instructor.
MATH 551 Selected Topics in Analysis
Advanced topics in Analysis selected by the
instructor.
MATH 553 Selected Topics in Differential Topology
Advanced topics in Differential Topology
selected by the instructor.
MATH 555 Selected Topics in Differential Geometry
Advanced topics in Differential Geometry
selected by the instructor.
MATH 556 Selected Topics in Optimization
Advanced topics in Applied Mathematics
selected by the instructor.
MATH 558 Selected Topics in Applied Mathematics
Advanced topics in Applied Mathematics
selected by the instructor.
MATH 560 Selected Topics in Topology
Advanced topics in Topology selected by the
instructor.
MATH 561 Functional Analysis I
Set Theory, Zorn's lemma. Topological
spaces. Metric spaces. Linear spaces, Banach spaces, Hilbert spaces,
Dual space. Completeness, separability, compactness. Linear operators
and functionals, Riesz representation theorem. Hahn-Banach theorem.
Contraction mapping. Strong and weak convergences.
Prerequisite: MATH 501
MATH 562 Functional Analysis II
Bounded operators. Compact operators. Closed
operators. Self-adjoint, positive and nonnegative operators.
Hilbert-Schmidt operators, nuclear operators. Spectral theory.
Application to integral and differential equations.
Prerequisite: MATH 561
MATH 563 Selected Topics in Functional Analysis
Advanced topics in Functional Analysis
selected by the instructor.
MATH 566 Linear Algebra
Vector spaces, linear transformations,
invariant direct sum decompositions, the rational and Jordan forms.
MATH 567 Elements of Information Theory
Entropy, relative entropy and mutual
information. The asymptotic equipartition property. Entropy rates of a
stochastic process. Data compression. Channel capacity. Differential
entropy. The Gaussian channel. Information theory and statistics. Rate
distortion theory. Network information theory.
MATH 568 Introduction to Algebraic Geometry
General theory of planes, algebraic
varieties, absolute theory of varieties, products, projections and
correspondences, normal varieties, divisors and linear systems,
differential forms, theory of simple points, algebraic groups,
Riemann-Roch Theorem.
Prerequisite: MATH 503
MATH 569 Numerical Linear Algebra
Matrices, Norms and Eigenvalues, spectral
radius. Gresghorin theorems. Numerical methods for estimating the
Eigenvalues, special matrices. M-matrices, L, and Steltires matrices.
Solution of linear system. Review, splitting of a matrix, convergence
of methods based on splitting criteria, consistency of iterative
methods, conditioning system. Extrapolation methods and the
convengence (updated). Decomposition of matrices (the know how of the
decomposition). Preconditioning of iterative methods. Lanczos-type
method, conjugate-gradient method, convergence and reduction of the
error, basis of solutions generated from C.G. Precondition conjugate
gradient method and the rate of convergence.
MATH 571 Selected Topics in Numerical Analysis
Advanced topics in Numerical Analysis
selected by the instructor.
MATH 573 Numerical Solution of Elliptic Boundary Value Problem
Difference methods for the Poisson Equation.
The one-dimensional case. The five-point formula. M-matrices.
Properties of the matrix obtained in the five-point formula.
Convergence. Discretizations of higher order. The discretization of
the Neuman boundary value problem. Proof of the stability theorem.
Discretization in an Arbitrary Domain. Shortley-Weller Approximation.
Difference methods for the General Differential Equation of second
order. Dicretization of the Biharmonic Differential Equation.
Convergence. Finite elements. Linear elements. Bilinear elements.
Quadratic elements. Error estimates for finite element methods.
MATH 575 Numerical Solution of the Systems of Ordinary Diff. Eqn.
Difference equations for system ODE with
constant coefficients. Solution methods. Multi-step methods: Theory.
Convergence, consistency and errors (local and global). Stability.
Multi step methods: Applications. Bound for local and global error.
Stability, relative stability and Weak Stability for
predictor-corrector. Step control. Specific methods for first order
systems. Derivation of Runge-Kutta method of higher order and their
stability. Implicit Runge-Kutta methods. Extrapolation methods. Stiff
systems.
MATH 576 Optimal Control Theory
Calculus of variations. Minimum problems on
an abstract space. Elementary theory. Euler equation. Jacobi necessary
condition. Optimal control problem. Statement of Pontryagin's
principle. Linear quadratic control problem. Riccati equation.
Extremals for the LQ control problem. Existence and continuity
properties of optimal controls. The existence problem. Continuity
properties of optimal controls. Dynamic programming. LQ control
problem.
MATH 577 Computational Fluid Dynamcs
Governing equations. Finite difference
discretization of the momentum. Continuity equations. Boundary
condition applications. Linear equation solvers. Solution procedures
for the assembled system. Direct, segregated and implicit procedures.
State-of-the-art solvers. Case studies.
MATH 578 Theory of Finite Difference Schemes
Hyperbolic partial differential equations.
Introduction to finite difference schemes. Convergence and
consistency. Stability. The Courant-Friedricks-Lewiy Condition. Von
Neumann Analysis. The stability condition. Order of Accuracy of finite
difference schemes. Parabolic partial differential equations. Finite
difference schemes for parabolic equations. Convergence estimates for
initial value problems. The matrix method for analyzing stability.
Elliptic partial differential equations. Difference schemes for
Poisson's equation. The discrete maximum principle. Regularity
estimates for schemes.
MATH 579 Theory of Multigrid Methods
Finite difference and finite volume
discretization. Basic relaxation method. Incomplete point LU,
incomplete block LU. Non-symmetric matrices. Convergence analysis.
Multigrid methods for P.D.E. Two levels grid algorithm. Variation of
prolongation and restriction. Course grid approximation. Computation
of grid operator with Galerkin approximation. Multigrid algorithms.
Convergence analysis.
MATH 580 Block Method For Solving the Laplace Equation
A finite covering of a polygon by blocks of
three types. Carrier functions. Representation of the solution on
blocks. An algebraic problem. Theorem on the convergence of the block
method. Theorem on the solvability of an algebraic problem. The
stability and the labor content of computations required by the block
method. Verification of the criterion of solvability of an algebraic
problem. The solvability of Neumann's problem on a polygon.
Approximate solving of Neumann's problem by block method. The case of
arbitrary analytic mixed boundary conditions.
MATH 581 Stochastic Optimal Control and Estimates
.Review of random processes. Stochastic
integral. Linear stochastic differential equation. Linear filtering,
prediction and smoothing. Partially observed systems. Linear quadratic
optimal control of stochastic systems. Separation principle.
MATH 582 Introduction to Infinite Dimensional Linear Systems
Semigroups of bounded linear operators.
Infinite dimensional linear systems. Controllability and observability.
Linear regulator problem. White, colored and wide-band noise
processes. Partially observable systems. Linear estimation theory.
Duality principle. Seperation principle.
MATH 590 Nonlinear Differential Eqns. and Dynamical Systems
Exponentials of operators. Basic properties
of linear systems. Elementary and non-elementary critical points.
Stable and unstable manifold theorem. The Hartman-Grobman theorem.
Periodic solutions, limit cycles and seperatrix cycles. The
Pincare-Bendixon theory. The Poincare sphere and the behavior at
infinity. Index theory. Floquet theory. Characteristic exponents and
multipliers. Stability by linearization and by the direct method of
Lyapunov. Normalization. Centre manifolds. Topological equivalence of
dynamical systems. Introduction to bifurcation theory and chaos.
MATH 600 Ph.D Thesis
Ph.D. Thesis in pure/applied mathematics.
The thesis must conform to the regulations of the Institute of
Research and Graduate Studies.
COMP 500 M.S. Thesis
MS thesis in computer science. Presentation
is required for the completion of the thesis.
COMP 512 Theory of Algorithms
Analysis of efficiency of algorithms.
Analysis of complexity of algorithms. NP-completeness. The classes P
and NP. Deterministic and non deterministic algorithms.
COMP 521 Selected Topics in Computer Programming I
Advanced topics in Computer Programming
selected by the instructor.
COMP 522 Selected Topics in Computer Programming II
Advanced topics in Computer Programming
selected by the instructor.
COMP 525 Selected Topics in Theory Algorithms
Advanced topics in Theory of Algorithms
selected by the instructor.
COMP 531 Selected Topics in Computer Science I
Advanced topics in Computer Science selected
by the instructor.
COMP 532 Selected Topics in Computer Science II
Advanced topics in Computer Science selected
by the instructor.
COMP 549 Network Data Security
Network protocol and their loop holes.
Firewalls: concept and flows, net and API. Method of connectivity. The
purpose of data security. Protecting internet and intranet services.
Security policies- design and implementation. Security maintenance.
Prerequisite: COMP 550
COMP 550 Data Communication and Computer Networks
Introduction to computer networks. LANs:
special issues, types, protocols, performance. High-speed and bridged
LANs, high-speed LANs/MANs, bridges. WANs: PDNs packet and circuit
switching, integrated services. Internetworking: architectures,
issues, network layer structure, IPs and routing. Transport protocols:
user diagram, transmission control and OSI protocols
COMP 551 Combinatorics
Ubsets, partitions, permutations. Recurrence
relations and generating functions. Stirling numbers. Latin squares.
Extremal set theory. Steiner triple systems. Finite geometry. Posets,
lattices and matroids. Designs. Error-correcting codes.
COMP 552 Graph Theory
Graphs, trees, bipartite graphs. 0-1
matrices. Coloring Ramsey theorem. Extremal graphs, Turan's theorem.
Dilworh theorem. Algebraic methods of graph theory. Planarity,
duality, embeddings. Hypergraphs.
COMP 554 Selected Topics in Graph Theory
Advanced topics in Graph Theory selected by
the instructor.
COMP 557 Combinatorial Optimization
Complexity, Oracles and numerical
computations, Ellipsoid method, algorithms for convex bodies,
Diophantine approximation and basis reduction, Rational polyhedra,
Combinational optimization: some basic examples, Submodular functions.
Prerequisite: MATH 529
COMP 558 Parallel Processing
Introduction to parallel computers. Taxonomy
of parallel computers. Array of processors, pipelining,
multiprocessing. Systolic arrays. Complexity and efficiency of
parallel algerithms. Principles of optimal parallel algorithm design.
COMP 559 Software Development
Stages in problem resolving through computer
programming: mathematical model of the problem, database, modular
programming, debugging, algorithm analysis, verification,
documentation. Basic algorithm types: searching and sorting,
algorithms on files, algorithms on trees and graphs, algorithms.
COMP 571 Network Flows
Network representations, search techniques,
polynomial algorithms. Flow decomposition properties, Optimality
conditions, cycle free and spanning tree solutions, network
transformation. Shortest path problems, Dijkstra's algorithms, Dial's
algorithm, label correcting algorithms, all shortest path algorithm.
Maximum flow minimum cut theorem, shortest augmenting path algorithm,
preflow-push algorithm, excess-scaling algorithm. Minimum cost flow
problem, successive shortest path algorithms primal-dual algorithm,
out-of-kilter algorithm, network simplex algorithm, right-hand-scaling
algorithm, sensitivity analysis. Extensions to further problems of
combinatorial optimization.
COMP 585 Fast Algorithms
Introduction, history and applications of
fast algorithms. Fast sorting algorithms. Fast algorithms for matrix
problems. Fast algorithms for DFT. Application of FFT algorithms:
convolution of vectors, product of polynomials, Schonhage-Strassen
algorithm.
COMP 600 Ph.D. Thesis
Ph.D. Thesis in computer science. The thesis
must conform to the regulations of the Institute of Research and
Graduate Studies.
Courses of Information Systems
IS 501
Selected Topics in Information Systems
Advanced Topics in Information Systems selected by instructor.
IS 502
Selected
Topics in Information Systems II
Advanced Topics in
Information Systems selected by instructor.
IS 503 Selected Topics in Information Systems III
Advanced Topics in
Information Systems selected by instructor.
IS 504 Selected Topics in Information Systems IV
Advanced Topics in
Information Systems selected by instructor.
Graphs, trees,
bipartite graphs, 0-1 matrices. Data structures for graphs, running
time of an algorithm, searching techniques on graphs, connectivity,
spanning tree algorithms, shortest path algorithms, mathching
problems, planarity, embeddings.
Mathematical
models, unconstrained and constrained optimization problems, linear
programming, network programming. Computer packages (QSB, LINDO, GAMS)
for solving optimization problems.
IS 507 Parallel Models and Methods
Architecture of
parallel computers, taxonomy of parallel computers, array of
processors, pipelining, multiprocessing, systolic arrays. Complexity
and efficiency measures. Principles of optimal parallel algorithm
design.
Process management
and scheduling, interprocess communication. Device management, device
drivers. Interrupts, deadlocks. Memory management, swapping, virtual
memory, file system. Practical study introducing well-known operating
systems.
Introduction to
database concepts, the theory of relational database model. Semantic
database models. Extended relational data model, deductive databases,
distributed database, object-oriented database systems. Recent
database management systems.
IS 510 Artificial Intelligence
Basic expert system
structures and application areas. Propositional logic. Predicate logic.
Knowledge representation using predicate logic and production rules.
Inference and knowledge processing. Search strategies. Expert system
development process. Handling uncertainty. Survey of AI techniques of
knowledge representation, search, learning, and natural language
processing. Introduction to AI programming in LISP.
IS 511 Object-Oriented Programming
Object oriented
software development concepts. Teaching of a current object oriented
programming language: Data abstraction, classes and objects,
polymorphism, inheritance and software reuse. Object oriented design
and modelling techniques. Introduction to GUI programming
Introduction to
multimedia systems. Hardware requirements for multimedia applications.
Creating and processing images and sounds by computer. HTML language.
Structure of HTML file. Colors, fonts, background. Basic elements:
lists, rules, comments, tables. Links, anchors. Images, aligning.
Advanced HTML elements: forms, buttons, frames. HTML style of writing.
Introducing editors for creating HTML documents.
VRML. A language to
create 3D world on web. Key concepts. Events, routes, shapes,
redefined shapes - boxes, cones, cylinders, spheres. Groups. Text
shapes. Positioning shapes. Translation, rotation, scaling. Animating
position, orientation and scale. Sensing viewer actions. Material,
textures, shading, sound, anchors. Study of VRML browsers and crating 3D
interactive moves introducing various software packages such as VRML
browser and macromedia Director.
Basic notions.
Raster graphics: 2D primitives drawing algorithms. Filling, clipping,
antialiasing. Geometrical transformations (2D and 3D translation,
rotation and scaling). Curves and surfaces representation. Solid
modeling. Projection. Removal of hidden lines and surfaces.
Illumination, shading. Interactive graphics. Animation.
Introduction to
privacy, data security, communication security in computers and
computer networks. Trusted computer systems, issues in authentication
and verification.
IS 516 Data Communication and Computer Networks
Introduction to
computer networks. LANs: special issues, types, protocols,
performance. High-speed LANs/MANs,
bridges. WANs: PDNs. Packet and circuit switching, integrated services.
Internetworking: architectures, issues, network layer structure, IPs
and routing. Transport layer protocols: user datagram protocol, transmission control
protocol
and OSI protocols.
Group Project is a
one-term project which contributes 3 credits to the students’ account.
A project subject must be proposed and supervised by a doctoral
instructor. A group of at least 4 students with CGPA 3.00 or above can
be assigned group project starting 3rd
semester of
study. The expected letter grade is in the range F though A. Output of
the Group Project is a software-implemented and application-oriented
solution of a certain problem that can be practically used in the
university or other organization.
Term Project is a
non-credit course proposed and supervised by a doctoral instructor.
Any student with CGPA 3.00 or above can register to Term Project
starting 3rd
semester of
study. Term Project is individual work of a student that should be
defended in front of a jury. Output of the Term Project is a
software-implemented and application-oriented solution of certain
problem that can be practically used in the university or other
organizations. Jury grades the student’s work either ‘S’ or ‘U’. A
student failed from Term Project must repeat it successive semester.
Project development
and organization, risk analysis, project appraisal, contracting and
negotiating, planning and scheduling, network analysis techniques,
monitoring and control methods, project budgeting and financial
control, conflict resolution and team building,
problem
solving in project environment, project termination, application of
computers in project management.
IS 520 Decision Making and Forecasting
Introduction to decision making, decision making process, decision trees, utility theory, group decision making, data warehousing and data mining, decision making under uncertainty, Dempster rule, fuzzy decision making, discrete event and Monte Carlo model, risk theory, decision making under risk, linear regression model and correlation, multiple regression model, exponential smoothing and time series, forecast accuracy.
Last Modified:
15-09-2004