| MAT 100 Elementary
Algebra |
Lec. 3. Credit
3. |
For students
whose background and placement indicate a need for basic
work. This course does not carry credit toward any degree at the University.
Concepts to be covered include arithmetic review, linear equations and
inequalities, polynomials, rational expressions and graphing.
Entry
level skills for MAT 109. |
| |
|
| MAT 105 Intermediate
Algebra |
Lec. 3. Credit
3. |
This
course is for students whose background and/or placement
indicates a need for algebra. It may be taken as an elective course, but
will not count towards the mathematical competency requirements. Concepts
to be covered include linear equations and inequalities, polynomial and
rational expressions, radicals, complex numbers, quadratics and graphing
exponential and logarithmic functions.
Entry level skills for MAT 117. |
| |
|
| MAT 109 College
Mathematics I |
Lec. 3. Credit
3. |
Sets
and simple logic. Solving linear, rational and quadratic
equations, inequalities. Graphing linear equations and inequalities, quadratic
equations. Exponential and logarithmic functions. Solving systems of equations.
Linear programming.
Prerequisite: MAT 100 or by placement. |
| |
|
| MAT 110 College
Mathematics II |
Lec. 3. Credit
3. |
Mathematics of
finance such as interest, installment buying, mortgage. Measurement,
geometry and the metric system. Elementary concepts of probability and
statistics.
Prerequisite: MAT 109 or by placement. |
| |
|
| MAT 117 Precalculus
Mathematics I |
Lec. 3. Credit
3. |
Functions
and their graphs. Polynomial and rational functions, exponential
and logarithmic functions. Systems of linear and nonlinear equations.
Sequences and series.
Prerequisite: MAT 105 or by placement. |
| |
|
| MAT 118 Precalculus
Mathematics II |
Lec. 3. Credit
3. |
Trigonometric
functions and their inverses. Analytic trigonometry. Applications
of trigonometry. Fundamentals of analytic geometry. Complex numbers. Polar
coordinates.
Prerequisite: MAT 117 or by placement. |
| |
|
| MAT 119 Mathematics
for Elementary Education |
Lec. 3. Lab
1. Credit 3. |
| Mathematics topics
central to a comprehensive elementary school curriculum covered sequentially
to parallel their development in the school curriculum. A laboratory will
provide an understanding of the use of manipulatives in teaching mathematics. |
| |
|
| MAT
120 Elementary School Mathematics |
Lec.
3. Lab 1. Credit 4. |
Mathematics topics
recommended by The National Council of Teachers of Mathematics
(NCTM) Standards for the elementary school curriculum. A laboratory will
provide an understanding of the use of manipulatives in teaching mathematics.
Prerequisite:
MAT 119. |
| |
|
| MAT 123 Introduction
to Research Topics in Mathematics |
Sem./Prj.
Credit 1-3. |
Designed for
freshman level undergraduates. Emphasis will be placed upon
introduction to areas of mathematics research, regular attendance at appropriate
seminars, techniques of literature searches, and background study. This
course may be taken twice.
Prerequisite: Consent of the department chairperson.
|
| |
|
| MAT 130 Calculus
|
Lec. 3. Credit
3. |
A
one-semester course for students with an option or a requirement
for a course in calculus. Differentiation and integration of algebraic,
exponential, and logarithmic functions. Applications from business, life,
and social sciences.
Prerequisite: MAT 117, or by placement. |
| |
|
| MAT
151 Calculus I |
Lec.
4. Prb. 1. Credit 4. |
Introduction
to limits, continuity, and derivatives. Rules of differentiation.
Differentiation of algebraic, trigonometric, inverse trigonometric, exponential,
and logarithmic functions. Differentials and tangent lines. Higher order
derivatives. Implicit differentiation. Applications of derivatives. Definite
integral. Fundamental theorem of calculus. Integration of elementary functions.
The calculus of the transcendental functions.
Prerequisite: MAT 118,
with "C" or above for mathematics majors, or by placement. |
| |
|
| MAT 152 Calculus
II |
Lec. 4. Prb.
l. Credit 4. |
Techniques of
integration. Applications of the definite integral. Indeterminate
limits. Improper integrals. Infinite series. Conic sections and curves
in three dimensions.
Prerequisite: MAT 151, with grade "C" or above for
mathematics majors, or by placement. |
| |
|
| MAT 160 Elementary
Introduction to Nuclear Fusion |
Lec. 3. Credit
3. |
Introduction
to terminology of nuclear fusion. Definitions of plasma, temperature,
Debye shielding, plasma parameters. Elementary concepts of: plasma criterion,
mass energy relation, fusion reactions, magnetic fusion, inertial fusion,
magnetic fusion devices, tokamak geometry, single particle motions in
plasmas, plasmas as fluids, waves in plasmas, equilibrium and
stability.
Prerequisite: Consent of the instructor. |
| |
|
| MAT 205 Introduction
to Statistics |
Lec. 3. Credit
3. |
Descriptive statistics
for ungrouped and grouped data. Concepts of probability. Random
variables. Binomial and normal distributions. Sampling distributions. Correlation
and regression. Hypothesis testing and estimation.
Prerequisite: MAT
109 or above. |
| |
|
| MAT 206 Mathematics
Foundations |
Lec. 3. Credit
3. |
Logic. Algebra
of sets. Nature of mathematical proofs. Mathematical induction.
Recursion. Elementary number theory. Relations and functions. Algebraic
structure.
Prerequisite: MAT 151 or above. |
| |
|
| MAT 208 Elementary
Linear Algebra |
Lec. 3. Credit
3. |
Basic concepts
of linear algebra. Linear systems. Matrix algebra. Determinants.
Vector spaces. Linear independence. Basis and dimension. Inner product
spaces. Linear transformations. Eigenvalues and eigenvectors.
Prerequisite:
MAT 206 or CSC 215. |
| |
|
| MAT 223 Directed
Research |
Credit 1-5. |
Introduction
to research problems in special areas of mathematics.
Prerequisite:
Consent of department chairperson. |
| |
|
| MAT 251 Calculus
III |
Lec. 4. Prb.
1. Credit 4. |
Vector operations.
The calculus of the vector-valued functions. Differentiation, integration,
and application in the multi-variable calculus. Vector analysis.
Prerequisite:
MAT 152, with grade "C" or above for mathematics majors, or by placement. |
| |
|
| MAT 260 Differential
Equations |
Lec. 3. Credit
3. |
Solutions and
initial value problems. First order differential equations. Linear
second order equations. Applications of linear second order equations.
Method of Laplace transforms. Series solution of linear differential equations.
Prerequisite:
MAT 251. |
| |
|
| MAT 300 Cooperative
Work-Study Experience |
Credit 3-12. |
On-the-job training
in government or industrial organizations utilizing mathematical analysis
or computer science in their operations.
Prerequisite: Approval of
the department chairperson. |
| |
|
| MAT 305 Probability
and Statistics |
Lec. 3. Credit
3. |
Random variables.
Probability and density functions. Special distributions. Point and interval
estimation. Tests of statistical hypotheses. Regression and analysis of
variance.
Prerequisite: MAT 152. |
| |
|
| MAT 310 Modern
Geometry |
Lec. 3. Credit
3. |
Deductive reasoning
and nature of proof. Basic concepts and postulates. Incidence geometry.
Congruence of segments and angles. Triangles. Circles. Proportion and
similarity. Polygon areas and volumes. Introduction to non-Euclidean geometries.
Prerequisite: MAT 206. |
| |
|
| MAT 311 Probability
|
Lec. 3. Credit
3. |
Basic concepts
of probability. Discrete random variables and their probability distributions.
Continuous random variables and their probability distributions. Multivariate
probability distributions.
Prerequisites: MAT 206 and MAT 251. |
| |
|
| MAT 312 Mathematical
Statistics |
Lec. 3. Credit
3. |
Sampling distributions
and the Central Limit theorem. Properties of point estimates and methods
of estimation. Confidence intervals. Hypothesis testing. Linear models
and estimation by least squares. Analysis of variance.
Prerequisite:
MAT 311. |
| |
|
| MAT 315 Discrete
Structures |
Lec. 3. Credit
3. |
Algebraic structures
applicable to computer sciences. Semigroups. Graphs. Lattices. Boolean
algebras. Combinatorics.
Prerequisites: MAT 152, 206 and 208. |
| |
|
| MAT 320 Modern
Algebra I |
Lec. 3. Credit
3. |
Introduction
to groups, rings, fields, and related topics. Emphasis on development
of careful mathematical reasoning.
Prerequisite: MAT 206 and 208. |
| |
|
| MAT 321 Modern
Algebra II |
Lec. 3. Credit
3. |
The symmetric
group. Vector spaces over arbitrary fields. Topics selected by
the instructor.
Prerequisite: MAT 320. |
| |
|
| MAT 323 Directed
Research |
Credit 1-5. |
Research problems
in special areas of mathematics.
Prerequisite: Consent of department
chairperson. |
| |
|
| MAT 330 Complex
Variables |
Lec. 3. Credit
3. |
Complex numbers
and functions. Analytic functions. Complex integration. Laurant and Taylor
series. Residues. Conformal mappings and applications.
Prerequisite:
MAT 251. |
| |
|
| MAT
340 History and Philosophy of Mathematics |
Lec.
3 . Credit 3. |
Historical and
philosophical aspects of mathematics and its interplay with other disciplines
from antiquity to modern times. Emphasis on the development of selected
mathematical concepts and problems in their historical settings.
Prerequisite:
MAT 206. |
| |
|
| MAT 360 Introduction
to Nuclear Fusion |
Lec. 3. Credit
3. |
Concept of plasma,
fusion, magnetic fusion, magnetic fusion devices, tokamaks, single
particle motions, plasmas as fluids, waves in plasmas, diffusion and resistivity,
equilibrium and stability, kinetic theory.
Prerequisites: MAT 152 and
PHY 204. |
| |
|
| MAT 403 Numerical
Analysis I |
Lec. 3. Credit
3. |
Finite precision
arithmetic. Interpolation. Spline approximation. Numerical integration.
Numerical solution of linear and non-linear systems of equations. Optimization
of finite - dimensional spaces.
Prerequisites: MAT 208, MAT 251, and
CSC 151. |
| |
|
| MAT 404 Numerical
Analysis II |
Lec. 3. Credit
3. |
Numerical methods
for initial value problems of ordinary differential equations. Numerical
solution of boundary value problems or ordinary differential equations.
Stability analysis. Numerical eigenvalue problems. Approximation theory.
Methods for partial differential equations.
Prerequisites: MAT 260
and 403. |
| |
|
| MAT 411 Differential
Geometry |
Lec. 3. Credit
3. |
Classical and
modern treatment. Curves, involutes, evolutes, surfaces, and transformation
groups. Space curves, tensors and lie algebras.
Prerequisites: MAT
251 and 320. |
| |
|
| MAT 416 Foundations
of Analysis I |
Lec. 3. Credit
3. |
Sequences. Series
and convergence. Topology of the real and metric spaces. Limits and continuity.
Differentiability and integrability of functions. Sequences and series
of functions.
Prerequisite: MAT 251 and 206. |
| |
|
| MAT 417 Foundations
of Analysis II |
Lec. 3. Credit
3. |
Differentiability
of functions. Integrability of functions. Uniform convergence of series
and integrals. Topology of metric spaces.
Prerequisite: MAT 416. |
| |
|
| MAT 423 Special
Projects |
Pjt. Credit
2-4. |
Introduction
to research problems in special areas of mathematics.
Prerequisite:
Advanced standing and consent of department chairperson. |
| |
|
| MAT 424 Research
Problems |
Ind. Credit
2-4. |
Participation
in research project in collaboration with faculty supervisor, or original
independent research problem.
Prerequisite: Advanced standing and consent
of department chairperson. |
| |
|
| MAT 425 Seminar
I |
Sem. 1. Credit
1. |
Topical discussion
and study in the field of mathematics.
Prerequisites: MAT 251, 260,
310, 320. |
| |
|
| MAT 426 Seminar
II |
Sem. 1. Credit
1. |
Topical discussion
and study in the field of mathematics.
Prerequisites: MAT 251, 260,
310, 320. |
| |
|
| MAT 430 Advanced
Ordinary Differential Equations |
Lec. 3. Credit
3. |
Solution methods
and basic theory of linear systems. Stability and asymptotic behavior
of linear and non-linear systems. Boundary value problems and Green's
function. Sturm-Liouville theory.
Prerequisite: MAT 260. |
| |
|
| MAT 431 Advanced
Calculus |
Lec. 3. Credit
3. |
A rigorous treatment
of multivariable calculus including gradients, multiple integrals, line
and surface integrals, Green's theorem, the divergence, and Stokes' theorem.
Prerequisite: MAT 416. |
| |
|
| MAT 435 Regression
and Analysis of Variance |
Lec. 3. Credit
3. |
Theory of least
squares. Simple linear and multiple regression. Analysis of variance.
Application of these techniques to real data.
Prerequisite: MAT 312.
|
| |
|
| MAT
436 Design and Analysis of Experiments |
Lec.
3. Credit 3. |
Experiments with
a single factor. Randomized blocks. Latin squares and related designs.
Incomplete block designs. Factorial experiments. Fractional replications.
Nested designs. Multifactor experiments with randomization restrictions.
Prerequisite: MAT 312. |
| |
|
| MAT 437 Sampling
Theory |
Lec. 3. Credit
3. |
Sampling from
finite populations: simple random sampling, stratified random sampling,
and regression estimation. Aspects of systematic sampling, cluster sampling,
and multistage sampling.
Prerequisite: MAT 312. |
| |
|
| MAT 440 Operations
Research |
Lec. 3. Credit
3. |
Deterministic
and stochastic models. Topics include mathematical programming, queuing
theory, inventory theory and non-linear programming.
Prerequisite:
MAT 311. |
| |
|
| MAT 445 Optimization
|
Lec. 3. Credit
3. |
Fundamental concepts.
Block search techniques. Least squares problem. Newton's method. Eigenvalue
problem. Gradient methods.
Prerequisite: MAT 416. |
| |
|
| MAT
450 Number Theory |
Lec.
3. Credit 3. |
Properties of
integers. Divisibility and primes. Congruences. Power residues
and quadratic reciprocity. Diophantine equations.
Prerequisite: MAT 320. |
| |
|
| |
|
| MAT 501 Infinite
Series |
Lec. 3. Credit
3. |
Foundations of
theory of infinite series of real and complex numbers. Convergence tests.
Series of functions. Summation processes. Asymptotic series.
Prerequisite:
MAT 251. |
| |
|
| MAT 502 Vector
Analysis |
Lec. 3. Credit
3. |
Vector algebra.
Vector differentiation and integration. Gradient, divergence,
and curl. General coordinates. Applications to geometry and physics.
Prerequisites:
MAT 208 and 251. |
| |
|
| MAT 503 Matrix
Algebra |
Lec. 3. Credit
3. |
Algebra matrices.
Determinants. Special Matrices. Solution of systems of linear equations.
Eigenvectors and Eigenvalues. Linear programming and the simplex method.
Prerequisite: MAT 208. |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| MAT 509 Introduction
to Probability |
Lec. 3. Credit
3. |
Probability of
finite sample spaces; counting techniques. Random variables.
Binomial distribution.
Prerequisite: MAT 206. |
| |
|
| MAT 510 Analytical
and Projective Geometry |
Lec. 3. Credit
3. |
Proposition of
incidence, point-set theory, homogeneous coordinates. Theorems
of Desargue, Pascal, Brianchon, and Klein, and the Erlanger program. Projective,
affine, and Euclidean theories of conics and quadrics including analysis
of regulus and paraboloid. General theories of transformation.
Prerequisite:
MAT 251. |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| 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
and 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. |
