The College of Liberal Arts and Sciences - Butler University

174
and Galois theory. Prerequisite: MA312. (U/G)
(3). Fall only.
MA326, Real Analysis I: A rigorous study of
the principles underlying real-variable calculus.
Topics include limits, continuity, differentiation
and Riemann integration. Prerequisites:
MA107, 200, 205. (U/G)(3). Fall only.
MA327, Real Analysis II: Continuation of
MA326. Includes a variety of topics, such as
sequences, series, uniform convergence, introduction
to Lebesgue measure and integration,
line and surface integrals. Prerequisite: MA326.
(U/G)(3). Spring only.
MA330, Complex Analysis: Complex numbers,
analytic functions, complex integration,
Cauchy’s Theorem, Taylor and Laurent series,
contour integrals and the residue theorem.
Prerequisite: MA208. (U/G)(3). Spring only.
MA334, Differential Equations: Analytical,
numerical and qualitative approaches to differential
equations, including linear equations and
systems, and nonlinear equations. Prerequisite:
MA107. (U/G)(3). Fall and spring.
MA341, Theory of Computation: Basic
theoretical principles of computer science that
are embodied in formal languages, automata,
computability and computational complexity.
Includes regular expressions, context-free grammars,
Turing machines, Church’s thesis and
unsolvability. Prerequisites: MA208 and CS142
or equivalent. (U/G)(3). Spring odd-numbered
years.
MA351, Geometry: Various topics from
Euclidean, projective and non-Euclidean
geometry. Prerequisite: MA107. (U/G)(3).
Spring only.
MA354, Topology: Introduction to topological
spaces, separation axioms, compactness,
connectedness, metric and function spaces.
Prerequisite: MA326. (U/G)(3). Fall evennumbered
years.
MA360, Probability Theory I: Combinatorics,
general probability, conditioning, discrete/
continuous random variables, transformed
random variables, joint, marginal and conditional
continuous densities, covariance, and the
central limit theorem. Topics may include order
Butler University
statistics, conditional expectation. Prerequisite:
MA107 or permission. (U/G)(3). Fall only.
MA361, Statistical Theory: Tests of statistical
hypotheses, linear models, nonparametric
methods, multivariate distributions and theory
of statistical inference. Prerequisite: MA360.
(U/G)(3). Spring only.
MA362, Applied Statistical Methods: Simple
linear regression, correlation, multiple regression
and time series. Regression topics to be discussed
include dummy variables, transformations
of data and multicollinearity. Time series
topics cover model identification, parameter
estimation, diagnostic checking and forecasting.
Prerequisites: MA215, 361. (U)(3). Fall evennumbered
years.
MA363, Probability Theory II: Poisson
process, multistate Markov transition models,
mixed continuous-discrete distributions
(including expectation and cumulative
distribution), moment generating functions,
order statistics, conditional densities, conditional
expectation, and actuarial applications,
such as net benefit. Prerequisite: MA360.
(U/G)(3). Spring only.
MA365, Numerical Analysis: Solutions of
equations and systems, error analysis, numerical
differentiation and integration, interpolation,
least squares approximation, and numerical
solution of ordinary differential equations.
Prerequisite: MA107. (U/G)(3). Fall oddnumbered
years.
MA372, Loss Models: Models for the amount
of a single payment, models for the number of
payments, and aggregate loss models. Prerequisite:
MA361. (U/G)(3). Spring odd-numbered
years.
MA395, Financial Mathematics: Time value
of money, annuities, loans, bonds, general
cash flows, immunization, and introduction
to financial derivatives. Prerequisite: MA107.
(U/G)(4). Fall only.
MA397, Actuarial Mathematics I: Survival
distributions and life tables; the mathematics of
life insurance, life annuities, net premiums and
net premium reserves. Prerequisites: MA360,
395. (U/G)(3). Fall odd-numbered years.