2 0 1 3 bulletin - Butler University
2 0 1 3 bulletin - Butler University
2 0 1 3 bulletin - Butler University
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174<br />
and Galois theory. Prerequisite: MA312. (U/G)<br />
(3). Fall only.<br />
MA326, Real Analysis I: A rigorous study of<br />
the principles underlying real-variable calculus.<br />
Topics include limits, continuity, differentiation<br />
and Riemann integration. Prerequisites:<br />
MA107, 200, 205. (U/G)(3). Fall only.<br />
MA327, Real Analysis II: Continuation of<br />
MA326. Includes a variety of topics, such as<br />
sequences, series, uniform convergence, introduction<br />
to Lebesgue measure and integration,<br />
line and surface integrals. Prerequisite: MA326.<br />
(U/G)(3). Spring only.<br />
MA330, Complex Analysis: Complex numbers,<br />
analytic functions, complex integration,<br />
Cauchy’s Theorem, Taylor and Laurent series,<br />
contour integrals and the residue theorem.<br />
Prerequisite: MA208. (U/G)(3). Spring only.<br />
MA334, Differential Equations: Analytical,<br />
numerical and qualitative approaches to differential<br />
equations, including linear equations and<br />
systems, and nonlinear equations. Prerequisite:<br />
MA107. (U/G)(3). Fall and spring.<br />
MA341, Theory of Computation: Basic<br />
theoretical principles of computer science that<br />
are embodied in formal languages, automata,<br />
computability and computational complexity.<br />
Includes regular expressions, context-free grammars,<br />
Turing machines, Church’s thesis and<br />
unsolvability. Prerequisites: MA208 and CS142<br />
or equivalent. (U/G)(3). Spring odd-numbered<br />
years.<br />
MA351, Geometry: Various topics from<br />
Euclidean, projective and non-Euclidean<br />
geometry. Prerequisite: MA107. (U/G)(3).<br />
Spring only.<br />
MA354, Topology: Introduction to topological<br />
spaces, separation axioms, compactness,<br />
connectedness, metric and function spaces.<br />
Prerequisite: MA326. (U/G)(3). Fall evennumbered<br />
years.<br />
MA360, Probability Theory I: Combinatorics,<br />
general probability, conditioning, discrete/<br />
continuous random variables, transformed<br />
random variables, joint, marginal and conditional<br />
continuous densities, covariance, and the<br />
central limit theorem. Topics may include order<br />
<strong>Butler</strong> <strong>University</strong><br />
statistics, conditional expectation. Prerequisite:<br />
MA107 or permission. (U/G)(3). Fall only.<br />
MA361, Statistical Theory: Tests of statistical<br />
hypotheses, linear models, nonparametric<br />
methods, multivariate distributions and theory<br />
of statistical inference. Prerequisite: MA360.<br />
(U/G)(3). Spring only.<br />
MA362, Applied Statistical Methods: Simple<br />
linear regression, correlation, multiple regression<br />
and time series. Regression topics to be discussed<br />
include dummy variables, transformations<br />
of data and multicollinearity. Time series<br />
topics cover model identification, parameter<br />
estimation, diagnostic checking and forecasting.<br />
Prerequisites: MA215, 361. (U)(3). Fall evennumbered<br />
years.<br />
MA363, Probability Theory II: Poisson<br />
process, multistate Markov transition models,<br />
mixed continuous-discrete distributions<br />
(including expectation and cumulative<br />
distribution), moment generating functions,<br />
order statistics, conditional densities, conditional<br />
expectation, and actuarial applications,<br />
such as net benefit. Prerequisite: MA360.<br />
(U/G)(3). Spring only.<br />
MA365, Numerical Analysis: Solutions of<br />
equations and systems, error analysis, numerical<br />
differentiation and integration, interpolation,<br />
least squares approximation, and numerical<br />
solution of ordinary differential equations.<br />
Prerequisite: MA107. (U/G)(3). Fall oddnumbered<br />
years.<br />
MA372, Loss Models: Models for the amount<br />
of a single payment, models for the number of<br />
payments, and aggregate loss models. Prerequisite:<br />
MA361. (U/G)(3). Spring odd-numbered<br />
years.<br />
MA395, Financial Mathematics: Time value<br />
of money, annuities, loans, bonds, general<br />
cash flows, immunization, and introduction<br />
to financial derivatives. Prerequisite: MA107.<br />
(U/G)(4). Fall only.<br />
MA397, Actuarial Mathematics I: Survival<br />
distributions and life tables; the mathematics of<br />
life insurance, life annuities, net premiums and<br />
net premium reserves. Prerequisites: MA360,<br />
395. (U/G)(3). Fall odd-numbered years.