# Descriptions of Mathmatics

**MATH 441
Introduction to
Numerical Analysis. [3]
**Topics of this course include:

numerical linear algebra , interpolation,

numerical differentiation

and integration, solution of

non -linear equations, acceleration

of convergence and numerical

treatment of differential

equations . Prerequisites: MATH

225, 251, 301 and CMSC 201,

or permission of instructor.

**MATH 452
Introduction to
Stochastic Processes. [3]
**This is a non-measure theoretic

course. Topics include general

Markov chains (branching

process, queuing processes,

birth and death processes, and

Poisson processes), secondorder

processes (Gaussian

processes and Wiener

processes) and an introduction

to stochastic differential equations .

Prerequisite: STAT 451

or 355.

**MATH 456
Mathematical Methods for
Science and Engineering. [3]
**Vector analysis and tensors,

Sturm-Liouville problems and

Fourier series, complex analysis ,

integral transforms and

variational calculus. Prerequisites:

MATH 221, 225 and 251.

**MATH 465
Introduction to
Artificial Neural Networks.
**This course gives a systematic

introduction to artificial neural

networks, which represent a

rather new and fundamentally

different approach to computing

and information processing.

Providing parsimonious universal

approximators for static and

dynamic mappings, synthetic

methodologies for building models

and/or solutions, abilities to

learn from and adapt to environments,

and massively parallel

computation paradigms, the

artificial neural networks have

formed a powerful approach to

solving non -linear or complex

problems in a broad spectrum

of areas including signal

speech/image processing, system

control, pattern recognition,

robotics, financial management,

digital communication , etc. This

course will cover multi-layer perceptrons,

recurrent neural nets,

global minimization for training,

adaptive and robust neural

nets, neural filtering, identification

and control, support vector

machines, self-organizing maps,

etc. Prerequisites: MATH 221,

251, 301 and STAT 451, or permission

of instructor.

**MATH 470
Introduction to Actuarial
Mathematics. [2]
**This course is intended to prepare

students for Society of

Actuaries Exam Course I Mathematical

Foundations of Actuarial

Science. Prerequisites: MATH

251 and STAT 451.

** MATH 475
Combinatorics
and Graph Theory . [3]
**General enumeration methods,

difference equations , generating

functions. Elements of

graph theory, including transport

networks, matching theory

and graph algorithms. Introduction

to finite geometries and

block designs. Prerequisites:

MATH 301 or permission of

instructor.

**MATH 476
Introduction to Game Theory.
**Purely non-cooperative or zerosum

games between two players

are introduced. In simple cases ,

solutions of such games use

techniques of saddle points or

other geometric means. VonNeumann’s

Min-Max theorem

assures optimal mixed strategies.

In general, linear programming

techniques must be

employed. Study of convex sets

in Euclidean spaces, in particular

of polyhedra, and polytopes is

necessary for full understanding

of the general case. In non-zero

sum situations with two or more

players, the fundamental results

of John Nash assuring equilibria

in mixed strategies and on arbitration

or bargaining schemes

are studied. For cooperative

games with many players, several

solution concepts are studied,

including Shapley values and

core allocations. Diverse application

are considered. Purely noncooperative

or zero-sum games

between two players are introduced.

Solutions of such entail

techniques of finding saddle

points or geometric means in

simple cases. Prerequisites:

Math 221 and Math 251.

**MATH 479
Mathematics
Problem-Solving Seminar. [1]
**Mathematical problem-solving

techniques, mathematical communication

skills. Problem sessions

with problems ranging

from pre-calculus to analysis,

algebra, geometry, combinatorics

and probability. Problems

ranging from quickies to mini

research problems. Students

will develop and reinforce skills

from previous mathematics

courses and will be introduced

to topics from more advanced

courses. Note: Repeatable for

credit. Prerequisite: Permission

of instructor.

**MATH 480
Senior Seminar. [1]
**Note: Repeatable for credit.

**MATH 481
Mathematical Modeling. [3]
**Derivation and analysis of mathematical

models of phenomena

from physics, engineering and

other exact sciences. Topics

include stability of equilibria of

dynamical systems with emphasis

on the qualitative aspects of

solutions, phase plane analysis

and linearization of non-linear

systems. Additional topics from

catastrophe theory, bifurcation,

optimization and chaos will be

covered as time permits. Examples

will be drawn from population

dynamics, flywheel governor,

a model for heartbeat,

bang-bang controls, self-sustained

oscillations and morphogenesis.

Prerequisites: MATH

221, 225 and 251.

**MATH 482
Non-linear Optimization. [3]
**Introduction to convex analysis.

One-dimensional minimization.

Unconstrained optimization in

algorithms, global convergence

and rates of convergence.

Quasi-Newton techniques. Convex

programming: optimality

conditions and duality. Penalty

and Barrier methods. Prerequisite:

MATH 251. Corequisite:

MATH 301.

**MATH 483
Linear and Combinatorial
Optimization. [3]
**Integer programming. The traveling

salesman problem.

Advanced linear programming

techniques. Complexity. Projective

methods in linear programming.

The Karmarkar method.

Prerequisite: MATH 381.

**MATH 484
Stochastic Methods in
Operations Research . [3]
**Topics of this course include:

introduction to Markov chains,

Poisson processes, introduction

to queuing theory, Stochastic

programming, introduction to

deterministic and Stochastic

dynamic programming. Prerequisite:

STAT 355 or 451.

**MATH 485
Introduction to the
Calculus of Variations. [3]
**This course will provide a modern

introduction to basic results

of the classical calculus of variations.

Special emphasis will be

given to the theory of secondorder

conditions. Considerable

attention will be devoted to

physical applications of variational

methods. Prerequisites:

MATH 221, 225, 251 and 301.

**MATH 486
Introduction to
Dynamical Systems.
**The course will address ideas

from discrete dynamical systems,

including fixed points,

periodic points, bifurcations,

and an explanation of period 3

implied chaos. Fractals such as

Sierpinski’s gasket, Julia sets

and Mandelbrot sets also will

be introduced. Prerequisite:

MATH 221 and 225 and some

programming experience; Math

301 or permission or instructor.

**MATH 490
Special Topics
in Mathematics. [1-4]**

**MATH 495
Topics in Mathematics of
Operations Research. [3]
**Introduction to recent and

advanced techniques of optimization

and operations

research. The course will be

redefined from time to time and

will reflect the instructor’s interests.

Prerequisite: Permission

of instructor.

**MATH 496
Mathematics Practicum. [1-4]
**Under faculty direction, students

will write a report dealing

with mathematical concepts or

techniques utilized or implemented

in internships or cooperative

education or in the workplace.

Note: This course is

repeatable up to four times .

Prerequisite: Permission of

instructor.

**MATH 497
Senior Thesis. [3]
**The student will be required to

prepare an exposition of either

a significant area of mathematics

or of the results of a student

research project. Typically,

the former will be in connection

with an upper- division course

the student has completed or

independent study (MATH 499).

**MATH 499
Independent Study
in Mathematics. [1-4]
**Under this heading, a student

may agree to a course with a

particular faculty member on a

topic not covered in the regular

curriculum. The arrangements

with the faculty member must

be made before the student

registers for the course.

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