College of Liberal Arts and Sciences
Department of Math & Actuarial Science

Mathematics and Actuarial Science Courses

View information regarding the frequency of course offerings.

Core ~ Show Courses

AR210-MA, Statistically Speaking: Who needs statistics in the 21st century? Anyone looking critically at numerical information who does not want to be misled by incorrect or inappropriate calculations or anyone dealing with issues in their environment, state/nation or career would benefit from studying the methodology of statistics. These problems include finding ways to improve our environment and living standards or studies conducted in an effort to fight diseases. This course is an introduction to applied statistics in the natural, social and managerial sciences through the use of current environmental and global issues. Topics include sampling, data analysis, experimental design and the use of computer-based statistical software. (U)(3). Fall and spring.

AR211-MA, Codes & Secret Messages: How can sensitive information such as credit card numbers or military strategy be exchanged between two people without being intercepted by a third party? Are there ways to detect and correct errors resulting from a mistyped identification number or a scratched CD? Can information be exchanged securely among multiple individuals without anyone revealing his or her own decryption scheme? In this course, students will investigate various strategies for storing and transmitting information accurately, efficiently and securely. Students will design several types of ciphers for sending secret messages, construct various error detecting and error-correcting codes, and implement secure public-key cryptosystems for exchanging messages with classmates. As these issues are explored, students will discover the need for mathematical notions such as modular arithmetic, permutations and combinations, probability and statistics, vectors and matrices, and formal logic. Students will also become aware of the central role played by cryptology and coding throughout history and modern society. (U)(3). Fall and spring.

AR212-MA, Win, Lose or Draw: Why do we play games? Whatever the reason, games are a big piece of life. The world has played games for a long, long time - every time period, every culture. We will study games and gambling in our culture as well as those in other cultures. To better understand games, the students will study probability theory and its application to gaming. Applications include casino games, lotteries, racing, wagering systems, as well as other games. Some analytical tools that will arise during the course are counting methods, expected value, trees, gambler's ruin and distributions. (U)(3). Fall and spring.

MA106, Calculus and Analytic Geometry I: The beginning calculus course for properly prepared students. Topics include differentiation, integration, elementary differential equations, exponential and logarithmic functions, and trigonometric functions. Applications are emphasized. The Analytic Reasoning core course is waived for students who successfully complete this course. Prerequisite: MA102 or equivalent. (U)(5). Fall and spring.

MA125, Business Calculus: This course introduces students to the concepts and methods of calculus and the mathematics of finance. Topics include interest, future and present annuity values, differentiation, integration, exponential and logarithmic functions, elementary differential equations, functions of several variables, partial derivatives and extrema of functions of several variables. Prerequisite: MA101 or equivalent. (U)(3). Fall and spring.

MA162, Statistical Methods: An introduction to applied statistics for students in the natural, social and managerial sciences. Topics include sampling, data analysis, experimental design and the use of computer-based statistical software. Three hours lecture, one hour recitation weekly. The Analytic Reasoning core course is waived for students who successfully complete this course. Prerequisite: MA101 or equivalent. (U)(4). Fall and spring.

MA100 ~ Show Courses

MA101, Algebra: Provides students with the necessary background to continue in mathematics. Topics include the number system, equations, inequalities, graphs, polynomials, algebraic functions and exponents. Students who have successfully completed any other mathematics course will not be given credit for MA101. Does not satisfy core curriculum requirement.  Must not be taken pass/fail. Prerequisite: high school algebra. (U)(3). Fall and spring.

MA102, Precalculus: This course provides students with the necessary mathematical background to successfully complete a calculus course or a course that has calculus as a major topic. Topics include solving equations and inequalities, exponents, factoring, complex numbers, and functions - linear, quadratic, polynomial, rational, exponential, logarithmic and trigonometric. Students who have successfully completed any other mathematics course, MA106 or above, will not be given credit for MA102. Does not satisfy core curriculum requirement.  Must not be taken pass/fail. Prerequisite: high school algebra and appropriate score on the Butler Math Placement Exam. (U)(3). Fall and spring.

MA106, Calculus and Analytic Geometry I: The beginning calculus course for properly prepared students. Topics include differentiation, integration, elementary differential equations, exponential and logarithmic functions, and trigonometric functions. Applications are emphasized. The Analytic Reasoning core course is waived for students who successfully complete this course. Prerequisite: MA102 or equivalent. (U)(5). Fall and spring.

MA107, Calculus and Analytic Geometry II: Continuation of MA106. Topics include methods of integration, improper integrals, infinite series, conic sections and polar coordinates. Prerequisite: MA106. (U)(4). Fall and spring.

MA125, Business Calculus: This course introduces students to the concepts and methods of calculus and the mathematics of finance. Topics include interest, future and present annuity values, differentiation, integration, exponential and logarithmic functions, elementary differential equations, functions of several variables, partial derivatives and extrema of functions of several variables. Prerequisite: MA101 or equivalent. (U)(3). Fall and spring.

MA162, Statistical Methods: An introduction to applied statistics for students in the natural, social and managerial sciences. Topics include sampling, data analysis, experimental design and the use of computer-based statistical software. Three hours lecture, one hour recitation weekly. The Analytic Reasoning core course is waived for students who successfully complete this course. Prerequisite: MA101 or equivalent. (U)(4). Fall and spring.

MA200 ~ Show Courses

MA200, Basics of Advanced Mathematics: Introduces students to the concepts and methods of higher mathematics with an emphasis on techniques of mathematical proof. Topics include foundations of logic, set theory, relations, partial orders, well-ordering, isomorphisms, induction, equivalence relations, and functions. Prerequisite or corequisite: MA106 or equivalent. (U)(3). Spring only.

MA205, Discrete Mathematics: Proofs by induction, simple diagonalization proofs, combinatorial theory, relations and functions, inclusion/exclusion principle, derangements, recurrence relations and generating functions. Prerequisite: MA106. (U)(3). Fall only.

MA208, Calculus and Analytic Geometry III: Continuation of MA107. Topics include vector calculus, multivariable calculus, partial differentiation, multiple integration, line integrals and Green's Theorem. Prerequisite: MA107. (U)(3). Fall and spring.

MA215, Linear Algebra: Systems of linear equations, matrices, determinants, vector spaces, linear transformations and the eigenvalue problem. Prerequisite: MA107. (U)(3). Fall and spring.

MA300 ~ Show Courses

MA301, History of Mathematics: Historical development of number systems, including contributions from Egypt, Greece, China, India and medieval to early modern Europe. Topics may include arithmetic, algebra, theory of equations, geometry, trigonometry, number theory, combinatorics, probability and the beginnings of calculus. Prerequisites: MA107 and MA205. (U/G)(3). Fall only.

MA305, Graph Theory: Graphs and sub-graphs, planar graphs, graph coloring and chromatic polynomials, trees, weighted trees and prefix codes, transport networks, and matching theory. Prerequisite: MA205. (U/G)(3). Spring only.

MA308, Problem Seminar: A course emphasizing the process of solving mathematical problems. Problems will be drawn from various sources. Students and faculty will meet weekly to exchange ideas and present solutions. Students may earn up to three credits by repeated registrations. Prerequisite: MA107. (U/G)(1). Fall and spring.

MA311, Number Theory: Divisibility, the Euclidean algorithm, prime numbers, unique factorization, linear congruences, the Chinese Remainder Theorem, and applications to public-key cryptography. Additional topics may include primitive roots, quadratic residues, factorization algorithms, Diophantine equations, continued fractions and the distribution of primes. Prerequisite: MA205. (U/G)(3). Fall even-numbered years.

MA312, Modern Algebra I: Relations and graphs, groups, subgroups, normal subgroups, homomorphism theorems, rings and fields. Prerequisite: MA200, 205, 215. (U/G)(3). Spring only.

MA313, Modern Algebra II: This course is a continuation of MA312. Topics include Euclidean rings, principal ideal domains, unique factorization domains, field extensions 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 even-numbered 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 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 even-numbered 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 odd-numbered 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.

MA398, Actuarial Mathematics II: Multiple state models, multiple decrement models, valuation theory for pension plans and ruin models. Prerequisite: MA397. (U/G)(3). Spring even-numbered years.

MA399, Financial Derivatives: Put-call parity, binomial options, Black-Scholes formula, delta-hedging, lognormal distribution, Brownian motion and Ito's lemma. Prerequisite: MA395. (U)(3). Spring odd-numbered years.

MA400 ~ Show Courses

MA401, 402, 403, Independent Study: Provides an opportunity for qualified students to pursue special topics under the guidance of a department staff member. Prerequisite: permission of department. (U/G)(1, 2 or 3). Fall and spring.

MA411, Internship: Supervised work experience directly related to the major area of study. The student is required to present his or her internship work in a seminar to a group of students and faculty. Prerequisites: junior or senior standing and permission of department. (U/G)(3). Fall and spring.

MA471, 472, 473, Topics in Mathematics: In-depth study of special topics not covered in regular courses. Prerequisite: permission of department. (U/G)(1, 2 or 3). Fall and spring.

MA490, Senior Seminar: Intended for seniors majoring in mathematics, this seminar features student presentations on mathematical topics and selected readings. Prerequisites: 15 hours of mathematics and junior standing or permission of department. (U)(1). Spring only.

MA499, Honors Thesis: (U)(3). Fall and spring.