2009-11 Marian University Course Catalog, fall 2010 edition

MAT 215
Fundamentals and Special
Applications of Calculus 3 credits
Designed for non-mathematics majors. Study of functions and
their graphs, the process and techniques of differentiation
and integration, and applications in the students’ respective
fields of interest. This course partially satisfies the general
education requirement in the scientific and quantitative
understanding category. (SPR)
MAT 230
Calculus and Analytic Geometry I 4 credits
This course begins the formal study of limits, differentiability
of algebraic and transcendental functions, applications of
differentiation, and an introduction to integration. This
course partially satisfies the general education requirement
in the scientific and quantitative understanding category.
(FAL)
MAT 231
Calculus and Analytic Geometry II 4 credits
Prerequisite: 230. Study of integration by standard forms and
special methods, indeterminate forms and improper
integrals, transcendental functions, analytic geometry, and
polar coordinates. (SPR)
MAT 305
Calculus and Analytic Geometry III 4 credits
Prerequisite: 231. Study of lines, curves, planes, and surfaces
by means of coordinate systems and vectors; differentiation
and integration of functions of several variables; infinite
series; functions represented by power series; applications.
(FAL)
MAT 310
Linear Algebra 3 credits
Prerequisite: 231. Study of systems of linear equations, vector
spaces, matrices, determinants, linear dependence, bases,
dimension, linear transformations, eigenvectors, and
applications. (2SE)
MAT 315
Differential Equations 3 credits
Prerequisite: 305. Study of ordinary differential equations.
Solution methods for first order equations, higher order
linear equations and systems of linear equations,
approximate methods of solution, and applications. (2SO)
MAT 320
Mathematical Probability and Statistics I 3 credits
Prerequisite: 231. Elements of modern probability theory and
its application in statistical inference. Representative topics:
variability; probability in finite spaces; random variables;
discrete and continuous distributions including normal,
binomial, Poisson and hypergeometric; sampling; estimates
of location; tests of hypotheses; regression and correlation;
introduction to analysis of variance; rudiments of decisionmaking.
(2FE)
MAT 321
Mathematical Probability and Statistics II 3 credits
Prerequisite: 320. A continuation of MAT 320. (2SO)
MAT 330
Advanced Geometry 3 credits
Study of Euclidean geometry, both classical and modern,
finite geometries, geometric transformations, and convexity.
Axiomatic structure is emphasized. (2FO)
MAT 331
Modern Geometries 3 credits
An introduction to several geometries developed after 1800.
Study of non-Euclidean geometries, particularly hyperbolic
geometry, projective geometry, geometric topology, and
geometry of inversion. Axiomatic structure and invariant
properties are emphasized. (2SE)
MAT 335
Number Theory 3 credits
Study of integers, their properties, and relationships. Topics:
representation of integers, Euclid’s algorithm, the
fundamental theorem of arithmetic, the number-theoretic
functions, Diophantine equations, congruences, residues.
(2SO)
MAT 340
Abstract Algebra I 3 credits
An axiomatic study of important algebraic systems, including
groups, rings, fields, and vector spaces. (2FE)
MAT 341
Abstract Algebra II 3 credits
Prerequisite: 340. A continuation of MAT 340. (2SO)
MAT 350
Numerical Methods 4 credits
Prerequisite: 305. An introduction to numerical algorithms
essential in scientific computation. Elementary discussion of
error, interpolation, quadrature, solution of non-linear
equations, and systems of linear equations. Programming
concepts needed for implementing numerical algorithms.
Selected algorithms are implemented on a computer or
programmable calculator. (2SE)
MAT 420
Real Analysis I 3 credits
Prerequisite: 305. Introduction to analysis in Euclidean
spaces. Elementary topological concepts; limits, continuity,
and differentiation of mappings; integration of functions;
convergence of sequences; and series of numbers and
functions. (ADD)
108