# Descriptions of Mathmatics

**MATH 215
Finite Mathematics for
Information Sciences.
**This course focuses on the

area of mathematics of particular

use in the information sciences.

The basic linear algebra

of matrices used for solutions

of large scale systems of linear

equations is treated. Applications

of matrices such as Leontieff

models of multi-sector economics

and the basics of the

simples method for solving linear

economic optimization problems

are discussed. Fundamental

concepts of probability

including basic combinatorial

methods for probabilistic computations

are studied. An introduction

is given to decision theory.

This treatment is in the

context of Bayesian or statistical

decision theory, though

game theorectic versions may

be discussed. Possible optional

topics may include elementary

Markov chains or the matrix

algebra of spreadsheet operations.

This course is intended

for IFSM majors only. Prerequisite:

MATH 141, 151, 155 or

380.

**MATH 221
Introduction to
Linear Algebra. [3]
**Topics of this course include:

linear equations, Gauss-Jordan

reduction, matrices and determinants

and their properties,

vector spaces and subspaces,

basis and dimension, linear

transformations, kernel and

range, eigenvalues and eigenvectors,

and matrix diagonalization.

Prerequisites: MATH 141,

151, 155 or 380.

**MATH 225
Introduction
to Differential Equations. [3]
**Topics of this course include:

solutions of first- and secondorder

linear differential equations,

non-linear exact and separable

equations, integrating

factors, homogeneous equations,

higher-order linear equations.

initial and boundary value

problems, solutions as functions

of the equation parameters,

Laplace transforms, power

series solutions for Bessel and

Legendre equations, difference

equations and numerical methods.

Note: Recommended for

science majors who need a

basic knowledge of differential

equations. Recommended:

MATH 251. Prerequisite: MATH

142 or 152.

**MATH 233
Fundamentals
of Geometry. [3]
**In this course, the student will

learn and apply the principles of

geometry as well as recognize

and understand their relevance

to the real world. Topics include

fundamental concepts and patterns;

geometric reasoning and

proof; parallel and perpendicular

lines as they relate to

Euclidean, hyperbolic and elliptical

geometry; triangle relationships

and triangle congruence;

exploring quadrilaterals; transformations

and similarity; investigating

right triangles, polygons,

surface area and volume,

and circles. Throughout the

course, special emphasis is

given to problem-solving techniques.

Prerequisite: MATH

132 or 150 or placement into

MATH 140 or 151.

**MATH 251
Multivariable Calculus. [4]
**Topics of this course include:

vectors, lines, planes and surfaces

in three dimensions. Vector

functions and their derivatives.

Partial derivatives, gradients,

directional derivatives,

maxima, minima and Lagrange

multipliers. Multiple integrals,

area, volume, surface area,

integration in different coordinate

systems. Line integral,

Green’s theorem, Stokes’ theorem

and divergence theorem.

Prerequisite: MATH 142 or

152.

**MATH 290
Special Topics
in Mathematics. [1-4]**

**MATH 299
Independent Study
in Mathematics. [1-4]
**Prerequisite: Permission of

instructor.

**MATH 301
Introduction to
Mathematical Analysis I. [4]
**This course is a systematic

study of basic analysis with an

emphasis on formal proofs,

examples and counter examples.

Topics include properties

of the real line, sequences,

series, limits, continuity and differentiation

of functions, and

Riemann Integration. Highly

recommended: CMSC 203. Prerequisite:

MATH 142 or 152

and 221.

**MATH 302
Introduction to
Mathematical Analysis II. [3]
**Topics of this course include:

continuity, differentiation of

functions of several variables,

uniform convergence of

sequences of functions, multiple

integration, contraction mapping

principle, and implicit and

inverse function theorems.

Note: Credit will not be given for

both MATH 302 and 401. Prerequisites:

MATH 251 and 301.

**MATH 306
Geometry. [3]
**Topics of this course are to be

selected from foundations of

geometry, modern Euclidean

geometry, non-Euclidean geometry,

projective geometry and its

subgeometries. Prerequisite:

MATH 301.

**MATH 341
Computational Methods. [3]**

Basic computational methods

for interpolation, systems of linear

equations, least squares

approximation, numerical quadrature,

numerical solution of

polynomial and transcendental

equations. Emphasis on the

methods and their computational

properties, rather than on

their analytic aspects. Prerequisites:

MATH 142 or 152, 221,

CMSC 201 or permission of

instructor.

**MATH 380
Introduction to Operations
Research (MS). [3]
**Linear programming, including

the simplex method. Transportation,

assignment and

trans-shipment problems. Network

problems. Not recommended

for mathematics/

statistics or computer science

majors. Note: Credit will not be

given for both MATH 380 and

381. Prerequisite: MATH 115

or 150.

**MATH 381
Linear Methods in
Operations Research. [3]
**Introduction to convex sets.

Theory of linear programming.

Applications to transportation

and assignment problems.

Introduction to graphs with

applications to network problems,

including shortest route

and maximum flow problems.

Introduction to game theory.

Note: Credit will not be given

for both MATH 380 and 381.

Prerequisite: MATH 221.

**MATH 385
Introduction to
Mathematical Modeling. [3]
**This is a project-oriented course

offering the opportunity to discover

how various real-world

problems can be described and

analyzed with the aid of simple

mathematical models and computer

simulations. Possible project

topics include operation of

a fuse, spread of pollutants in a

river, propagation of an infectious

disease, traffic flow on a

highway, oscillating chemical

reactions, etc. Specific selection

of problems will depend on

the background and interests of

the students enrolled in the

course. Students seeking elementary

teacher certification in

science or math are particularly

welcome. This course incorporates

constructivist principles

and has been designed as an

MCTP course for students in

the Maryland Collaborative for

Teacher Preparation Program.

Prerequisite: MATH 225.

**MATH 390
Special Topics
in Mathematics. [1-4]**