# Mathematics and Actuarial Science Courses

View information regarding the frequency of course offerings.

**Core**
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**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**
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**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**
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**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**
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**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**
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**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.