|
Mathematics
Professor Jung,
chair
Professor Mest, Professor
Emeritus Hilt
Assistant Professor Nawrocki
Lecturer Gattone
The Department of Mathematics offers a Bachelor
of Science degree (B.S.) in mathematics. The mathematics courses
are designed to provide a thorough undergraduate training in mathematics
for those students who wish to pursue graduate study in the subject,
teach mathematics in the secondary or elementary schools, or to
work in various fields in business and industry.
Students concentrating in mathematics are required to complete MAT
107, 108, 207, 307, 308 or 312, 311, 491, and 492; three mathematics
courses at the 300 level to be chosen with departmental approval;
and PHY 201 and 202. MAT 100, 103, 104, 105 and 210 do not satisfy
concentration requirements.
Students intending to pursue graduate work in
mathematics are advised to take 302, 304, 307, 308, 312, 315, 316,
and 317.
Combined concentrators will take MAT 107 as a general studies quantitative
reasoning course plus MAT 108, 207, 311, 492, and three 300-level
elective mathematics courses.Those intending to pursue secondary
education certification in mathematics should include MAT 107, 108,
207, 307, 308, 311, 302 or 317, 312 or 318, 316, 491 and 492.
All mathematics courses satisfy the general studies
quantitative reasoning requirement.
Please note that, at the discretion of the individual
instructor, the TI-89 graphing calculator may be used in certain
courses. For these courses it is highly recommended that the student
purchase a TI-89 or comparable (TI-92) graphing calculator.
COURSES
| MAT
100 |
Pre-Calculus Mathematics
A review of algebra and trigonometry intended to be taken
before 107 or 105 by those students whose background in algebra
and trigonometry is insufficient. The major emphasis will be
on the function concept. Elementary analytic geometry will be
discussed, along with the algebra and composition of functions,
inverse functions, trigonometry, and logarithmic and exponential
functions. |
| MAT
103 |
Discrete Mathematics I
An introduction to the theory and application of discrete
mathematics. Topics include logic, sets, functions and relations,
combinations, and elementary probability. |
| MAT
104 |
Discrete Mathematics II
A continuation of MAT 103, this course includes trees and
graphs, recurrence relations, elementary group theory, and selected
topics in computer science. |
| MAT
105 |
Discrete
Mathematics and Calculus with Business/Economics Applications
Designed as a one-semester course for concentrators in business
administration or economics, topics such as linear functions
and models; matrices and matrix algebra; linear systems; functions
and graphs; derivatives and integrals; and extremization will
be included. Partial differentiation also will be introduced. |
| MAT
107 |
Calculus and Analytic Geometry I
Fundamental concepts of functions of one variable: limits,
continuity, and
differentiability. Derivative applications in curve stretching,
related rates, and maxima-minima problems. Introduction to indefinite
and definite integration including the fundamental theorem.
This is the first course taken by students entering a math or
math-related curriculum. |
| MAT
108 |
Calculus and Analytic Geometry II
Continuation of 107. Applications of definite integration
finding areas, volumes, work, and so forth. Study of transcendental
functions. Integration techniques, indeterminate forms, improper
integrals.
Prerequisite: MAT 107.
|
| MAT
207 |
Calculus III
Continuation of 108. Topics include sequences and infinite
series, polar coordinates, parametric representation, vectors,
analysis of functions of two (or more) variables, multiple
integrations, and line integrals.
Prerequisite: MAT 108.
|
| MAT
210 |
Biostatistics
The course begins with an introduction to descriptive
statistics, organizing and summarizing data, and basic concepts
of probability. Random variables of discrete and continuous
type are considered along with their appropriate distribution
functions. Use of statistical tests for inferential statistics
ó both for estimating parameters and for hypothesis
testing – is emphasized. Correlation, regression, confidence
intervals, hypothesis testing about means, proportions, paired
comparisons, population variances, difference between means,
and difference between populations proportions are all included.
Analysis of variance and some nonparametric tests also are
covered, with emphasis on the use of these procedures in decision
making. All applications are taken from the area of biology.
(This course is not intended for concentrators in mathematics
but is aimed at biology concentrators or any students planning
to enter graduate or professional school in biology or the
life sciences.)
|
| MAT
302 |
Differential Equations
A study of the solution of ordinary differential equations,
including the principal
types of equations of first and second order, linear equations
with constant coefficient, simultaneous equations, and operational
methods. Runge-Kutta and other numerical approximation methods,
Series solutions, Ordinary and singular points, and the method
of Frobenius will be discussed.
Prerequisite: MAT 207.
|
| MAT
304 |
Functions of a Complex Variable
An introduction to the theory of functions of complex
variables: derivatives and
integrals; Cauchy’s theorem; power series; theory of
residues; and conformal mapping.
Prerequisite: MAT 207.
|
| MAT
307 |
Linear Algebra
An introduction to matrix algebra; linear equations; linear
dependence, determinants; vector spaces; linear transformations;
and eigen problems.
Prerequisites: MAT 108 and 311, or permission of the
department.
|
| MAT
308 |
Modern Algebra
An introduction to groups with topics selected from number
theory, rings, fields, ideals, and polynomial rings.
Prerequisite: MAT 311, or permission of the department.
|
| MAT
311 |
Foundation of Mathematics
An introduction to abstract mathematics. Topics covered are
symbolic logic, methods of proof, set theory, relations, functions,
and induction. Should be taken by mathematics concentrators
the second semester of their sophomore year. |
| MAT
312 |
Introduction to Topology
Definitions and properties of topological spaces, metric spaces,
continuity, homeomorphisms, separation axioms, compactness,
connectedness.
Prerequisites: MAT 207, 311, or permission of the
department.
|
| MAT
315 |
Partial Differential Equations
Orthogonal functions; Sturm-Liouville system; initial and
boundary value problems; Fourier series; higher transcendental
functions; separation-of-variables method, and other methods
of solution of equations of mathematical physics.
Prerequisite: MAT 207.
|
| MAT
316 |
Mathematical Statistics
An introduction to mathematical statistics at the level presupposing
a knowledge of the calculus. Descriptive and inferential statistics
are included. Hypothesis testing, estimation, analysis of
variance, and nonparametric methods will be discussed.
Prerequisite: MAT 108.
|
| MAT
317 |
Numerical Methods
A study of numerical methods involved in interpolation;
differentiation and integration; solution of equations and
systems of equations; solution of differential equations;
and fitting of empirical data, with emphasis in those procedures
that can be most readily programmed for an electronic digital
computer. Applications are made to science and engineering.
Computer programming knowledge is assumed.
Prerequisite: MAT 207.
|
| MAT
318 |
Geometry
This course is intended primarily for those students planning
to enter the field of
secondary education. It begins with a study of the most important
ideas of Euclidean plane geometry, but will also consider
the tutorial significance of Euclid’s original postulates.
Special attention is given to the notion of parallelism of
lines and the resulting non-Euclidean geometrics when the
axiom of parallelism is altered. Differential geometry also
will be introduced as a means of studying curves, surfaces,
and curves on surfaces.
Prerequisites: MAT 207 and 311.
|
| MAT
321 |
Advanced Calculus I
Designed to take a rigorous look at definitions, theorems,
and concepts taken from the foundational calculus courses.
Rigorous treatment given to topics such as continuity, mean-value
theorems, analysis of functions of several variables, extremization,
and limits. Other topics include sequences, series, and the
Heine-Borel covering theorem.
Prerequisites: MAT 207, 311.
|
| MAT
322 |
Advanced Calculus II
A logical continuation of 321 with a concentration on
integration. Topics include theory of Riemann integration,
improper integrals, gamma and beta functions, and Fourier
analysis. Generalized integrals (Stieltje’s, Lebesgue,
and so forth) and notions or real analysis are included as
time permits.
Prerequisite: MAT 321.
|
| MAT
340 |
Topics
Designed to cover topics of interest that are not covered in
other courses. |
| MAT
491 |
Seminar I (W)
A seminar in topics selected by the course instructor in which
independent learning is stressed. The student will be expected
to present both oral and written reports on topics covered
in the seminar.
Prerequisite: Senior standing or permission of the
department.
|
| MAT
492 |
Seminar II (W)
A seminar in which each student selects a topic with the approval
of the course instructor. The student will be expected to
present both oral and written reports. This seminar is to
be taken in the final semester of the student’s course
work. Exceptions will require the approval of the department.
Prerequisite: Senior standing or permission of the
department.
|
top of page
|
