110 Finite Mathematics
GER: MR (Mathematics & Formal Reasoning)
Topics include: set theory, combinatorics, probability, statistics,
matrix algebra, linear programming, Markov chains, graph theory, and
mathematics of finance. A student cannot receive credit for this course
after credit has been received for MTH-260 or any mathematics
course numbered 301 or greater. Satisfies the pre-fall 2008 general
education requirement in mathematics for the bachelor of arts degree
only. 4 credits.
140 Integrated Precalculus/Calculus I
Introduction to the theory and methods of differential calculus. Topics
include functions, graphs, limits, continuity and derivatives.
Enrollment by department established criteria only. May not be enrolled
on a pass-fail basis. 4 credits.
141 Integrated Precalculus/Calculus II
GER: MR (Mathematics & Formal Reasoning)
Introduction to applications of the derivative and the theory and
applications of the definite integral. Topics include: trigonometric
functions and their derivatives, applications of derivatives,
antiderivatives, the definite integral and applications of the integral.
Satisfies the pre-fall 2008 general education requirement in
mathematics. 4 credits.
150 Analytic Geometry and Calculus I
GER: MR (Mathematics & Formal Reasoning)
Prerequisite: criteria established by department
First course in the standard calculus sequence. Introduction to the
theory, methods, and applications of differential calculus and an
introduction to the definite integral. Topics include: algebraic and
trigonometric functions, limits and continuity, rules for
differentiation, applications of the derivative, antiderivatives, and
the definition and basic properties of the definite integral. Satisfies
the pre-fall 2008 general education requirement in mathematics. 4
151 Analytic Geometry and Calculus II
Prerequisite: MTH-141 or 150
The second course in the standard calculus sequence. An introduction to
the logarithmic and exponential functions, the applications of the
definite integral, techniques of integration, indeterminate forms,
improper integrals, numerical methods, and infinite series. 4 credits.
160 Vectors and Matrices
Introduction to the theory of vectors and matrices. Among the topics
included are: vectors, vector operations, the geometry of Euclidean
space, systems of equations, matrices, matrix operations, special
transformations, eigenvalues, and applications of matrix theory. 4
235 Operations Research
Application of mathematical modeling and analytical methods to make
better decisions. Topics include modeling, algorithm design, discrete
linear function optimization with linear constraints, convexity,
duality, sensitivity analysis, and optimality criteria. 4 credits.
241 Introduction to Statistics
Prerequisite: MTH-110, 141 or 150
Non-calculus based course in elementary probability and statistics.
Counting problems, probability, various distributions, random variables,
estimation, hypothesis testing, regression and correlation, analysis of
variance, and nonparametric methods. A student cannot receive credit
for this course and ECN-225 or MTH-341. 4 credits.
250 Vector Calculus
Introduction to multivariate and vector calculus. Topics include vector
functions and the differential and integral calculus of functions of
several variables including Green’s Theorem and Stokes’ Theorem. 4
255 Differential Equations
Introduction to the theory, methods, and applications of ordinary
differential equations, including first- and higher order differential
equations, series solutions, systems, approximate methods, Laplace
transforms, and phase plane analysis. 4 credits.
260 Introduction to Discrete Mathematics
Introduction to the main ideas and proof techniques of discrete
mathematics. Among the topics covered are mathematical logic, relations,
functions, partitions, recursion, induction, combinatorial principles,
inclusion/exclusion, enumeration, and introductory graph theory (trees,
connectivity, planarity, colorings, etc.). 4 credits.
301 Mathematics for Elementary School Teachers I
Problem solving and mathematical reasoning; sets and set operations;
functions; numeration systems; the systems of whole numbers, integers,
and rational numbers; algorithms; mental computation; elementary number
theory; teaching strategies, materials, and technologies for these
topics in grades pre-K-6. 4 credits.
302 Mathematics for Elementary School Teachers II
Decimals and percents; elementary probability; descriptive statistics;
geometry of shapes in two and three dimensions; congruence and
similarity; measurement; geometric transformations; teaching strategies,
materials, and technologies for these topics in grades pre-K-6 and
field-based experiences in area schools. 4 credits.
320 Number Theory
Introduction to the arithmetic properties of the integers including
divisibility, congruences, diophantine equations, primes and their
distribution, quadratic forms and quadratic reciprocity. Additional
topics will be chosen from continued fractions, cryptography,
partitions, elliptic curves, modular forms and number fields. 4 credits.
325 Modern Geometry
Development of Euclidean and non-Euclidean geometries. Topics include
axiom systems, models, congruence theorems, parallel postulates, and the
philosophical and historical background to geometry. 4 credits.
330 Combinatorics and Graph Theory
A study of the primary methods and fundamental ideas of combinatorics
and graph theory. Topics covered include generating functions, set
partitions, recurrence relations, inclusion-exclusion, trees, graph
connectivity, independence, and graph colorings. Additional topics will
be chosen from Ramsey theory, set systems, planarity, directed graphs,
matchings, and Hamiltonian and Eulerian graphs. 4 credits.
335 Mathematical Models and Applications
Prerequisite: MTH-250 and 255
A selection of mathematical models using various continuous and discrete
methods and having applications in business and the social and
biological sciences. Included are ecological models, epidemic models,
Richardson’s arms race model, and population growth models. Other topics
discussed are linear programming, voting problems, and Markov chains. 4
Calculus-based course in probability, covering counting, discrete and
continuous probability, random variables, important probability
distributions, joint distributions, expectation, moment generating
functions, and applications of probability. 4 credits.
341 Mathematical Statistics
Calculus based course in statistics covering sampling, estimation,
hypothesis testing, chi-square tests, regression, correlation, analysis
of variance, experimental design, and nonparametric statistics. 4
350 Complex Variables
Study of the complex plane and the calculus of functions of a complex
variable. Topics to be considered include the algebra and geometry of
complex numbers, limits and derivatives of functions of a complex
variable, the Cauchy- Riemann equations, contour integrals, Taylor and
Laurent series, and residues. 4 credits.
360 Linear Algebra and Matrix Theory
Prerequisite: MTH-160 and 260
Study of finite dimensional real vector spaces, linear transformations,
determinants, inner product spaces, eigenvalues and eigenvectors. 4
Introduction to concepts in topology including the following:
topological spaces, metric spaces, continuity, homeomorphisms,
neighborhoods, closed sets and closure, basis and sub-basis for a
topology, subspaces, product spaces, connectivity, compactness, and
separation axioms. 4 credits.
450 Real Analysis
A theoretical introduction to some of the basic ideas of real analysis:
real numbers and the topology of the real line, sequences and series of
real numbers, limits of functions, continuity, uniform continuity,
differentiation, the Riemann integral, and sequences and series of
functions. 4 credits.
451 Topics in Analysis
An in-depth investigation of selected topics in analysis. 4 credits.
460 Modern Algebra
A theoretical introduction to some of the basic ideas of modern abstract
algebra. Included is a study of groups, rings, domains, polynomial
rings and fields as well as an investigation of their sub-structures and
of the fundamental homomorphism theorems. 4 credits.
461 Topics in Algebra
An in-depth investigation of selected topics in abstract algebra. 4 credits.
504 Directed Independent Study
Study of an area of mathematics of interest to the student that is not
part of one of the listed courses. The student must choose a faculty
member to direct the study and, together with this faculty member,
prepare a description of the material to be covered and submit it to the
department chair for approval. Variable credit.