| MAT 500 Seminar
in Mathematics Education |
Credit 3. |
| Contemporary
issues and practical aspects in mathematics teaching, literature survey,
heuristics for problem solving and problem posing. Prerequisite: Approval
of the department. |
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| MAT 504 Advanced
Linear Algebra |
Lec. 3 Credit
3. |
| Linear Transformations,
isomorphisms, linear functionals, dual spaces, ideal thory in polynomial
rings, eigenvalues and eigenvectors, diagonalizable transformations, Jordan
canonical form, normal and unitary opeartors, bilinear forms. Prerequisite:
MAT 320 |
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| |
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| MAT 505 Introduction
to Topology |
Lec. 3 Credit
3. |
| Metric spaces,
point set topology, open and closed sets, closure, continuity, connectedness,
compactness, separability properties, Cauxhy sequences and completeness,
product spaces. Prerequisite: MAT 416 |
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| |
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| MAT 506 Numerical
Analysis I |
Lec. 3 Credit
3. |
| Finite precision
arithmetic, interpolation, spline approximation, numerical integration,
numerical solution of linear and nonlinear systmes of equations, optimization
in finite dimensional spaces Prerequisites: MAT 208, MAT 251 |
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| |
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| MAT 507 Numerical
Analysis II |
Lec. 3 Credit
3. |
| Numerical methods
for initial value problems and boundary value problmes of ODE's, stability
analysis, numerical eigenvalue problems, approximation theory, numerical
methods for PDE's. Prerequisite: MAT 506 |
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| |
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| MAT 511 Advanced
Ordinary Differential Equations |
Lec 3. Credit
3. |
| Series solutions
of differential equations, special functions, systems of linear differential
equations, eigenvalues and fundamental matrices, 2-dimensional autonomous
systems, Liapunov stability theory, boundary value problems, Sturm-Liouville
problems, Prerequisite: MAT 260 |
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| |
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| MAT 512 Elements
of Mathematics Modeling |
Lec 3. Credit
3. |
| Mathematical
modeling of problems arising in different practical areas of every day
life, including population dynamics, traffic flow, singularity analysis.
Prerequisite: MAT 260 |
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| |
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| MAT 513 Elements
of Real Analysis |
Lec 3. Credit
3. |
| Sequences and
their limits, series, topology of the real line, metric spaces, limits
and continuity, differentiability and integrability of functions, sequences
and series of functions. Prerequisite: MAT 416 |
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| |
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| MAT 514 Introduction
to Modern Analysis |
Lec 3. Credit
3. |
| Metric spaces,
normed linear spaces, linear operators, linear functional and dual spaces,
strong and weak convergence, Introduction to integration theory, LP spaces,
Hilbert spaces. Prerequisites: MAT 416, MAT 208 |
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| |
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| MAT 515 Functions
of a Complex Variable |
Lec 3. Credit
3. |
| Complex numbers,
analytic functions, Cauchy-Riemann equations, Cauchy theorem, Cauchy integral
formula and its applications, Liouville's theorem, Taylor and Laurent
series, residues and poles, conformal mappings. Prerequisite: MAT 416 |
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| |
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| MAT 520 Mathematics
for Elementary School Teachers I |
Lec 3. Credit
3. |
| Systematic development
of the number systems: natural numbers, integers, rational numbers and
real numbers, anaysis of basic algorithmic proceses of arithmetic operations,
metric systems, topics from geometry. Prerequisite: Approval of the
department. |
|
| |
|
| MAT 521 Mathematics
for Elementary School Teachers II |
Lec 3. Credit
3. |
| Elementary topics
from number theory, probability, data analysis, appropiate techniques
of teaching mathematics in elementary schools. Prerequisites: MAT 520 |
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| |
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| MAT 522 Mathematics
for Exceptional Children within Regular School Program (A/S) |
Lec 3. Credit
3. |
| Current trends
and techniques for individualizing mathematics in the regular classroom
of K-8 for exceptional children (both gifted adn those with minor learning
disabilities and/or handicap), non-clinical diagnostic prescriptive approach
using appropriate sequences of instructional emphasis on the classroom
environment. Prerequisite: Approval of the department. |
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| |
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| MAT 605 Algebraic
Structures |
Lec 3. Credit
3. |
| Group Theory,
homomorphism theorems, Sylow theorems, elementary ring theory, field theory,
field extensions. Prerequisite: MAT 320 |
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| |
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| MAT 606 Probability
Theory |
Lec 3. Credit
3. |
| Mathematical
foundations of probability, probability spaces, random variables, distribution
functions, sampling distributions expectation and conditional expectation,
laws of large numbers. Prerequisite: MAT 513 |
|
| |
|
| MAT 607 Mathematical
Statistics |
Lec 3. Credit
3. |
| Parametric point
estimation, Bayes estimators, parametric interval estimation, theory of
hypothesis testing, linear models, nonparametric statistics. Prerequisites:
MAT 606 |
|
| |
|
| MAT 608 Partial
Differential Equations I |
Lec 3. Credits
3. |
| Classification
of PDE's linear and quasi-linear wave equations, separation of variables,
Sturm-Liouville problems, non-homogeneous equations, Green's functions
for time independent problems, generalized Fourier series. Prerequisite:
MAT 511 |
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