 Mathematics, Statistics & Actuarial Science

# Course Descriptions & Frequency of Offerings

Below is a listing of classes that may be offered by the Mathematics and Actuarial Science Department during your studies at Butler. For the most current information, please review our Course Catalog.

### Core

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.

### MA 100

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. (U)(3) Fall and spring.

MA102 Precalculus: 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: Appropriate score on the Butler math placement test. (U)(3) Fall and spring.

MA106 Calculus and Analytic Geometry 1: The beginning calculus course for properly prepared students. Topics include differentiation, integration, elementary differential equations, and exponential, logarithmic, and trigonometric functions. Applications are emphasized. The Analytic Reasoning core course is waived for students who successfully complete this course. Prerequisite: Placement, or C- in MA102. (U)(4) 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.

MA108 First Year Problem Solving: This one credit course gathers together first-year students to practice and learn about effective techniques to solve problems and think about proofs in mathematics. Students work together with faculty in a team-oriented spirit and approach to problem solving. (Note: This course does not satisfy the Core Curriculum FYS requirement.) Must be a first year student to enroll in MA108. (U)(1) Fall.

MA125 Business Calculus: Introduces students to the concepts and methods of calculus by studying differentiation
and integration with applications to business. Additionally, the mathematics of finance, including simple and compound interest, future and present annuity values, and amortization, is developed. Other topics may include a brief introduction to probability and counting techniques. Prerequisite: C- in MA101. (U)(3) Fall and spring

MA162 Elementary Statistics: An introduction to inferential statistics with applications in the natural, social, and managerial sciences. This course is especially designed to meet the needs of students who will later pursue postgraduate studies in social and natural sciences or professional programs in medicine. The course introduces elementary probability and uses it to develop a sound understanding of confidence intervals and hypothesis testing. Topics include data analysis, descriptive statistics, linear regression, chi-square tests, analysis of variance, and tests and confidence intervals for means and proportions. The Analytic Reasoning core requirement is waived for students who successfully complete MA162. Credit will not be awarded for both AR 210-MA and MA162. Prerequisite: MA101 or equivalent. (U)(3) Fall and spring.

### MA 200

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: MA107. (U)(3). Spring only.

MA205 Discrete Mathematics: Introduces students to the study of mathematical objects and number systems associated with discrete sets, which are distinct from continuous sets over the real number line. Topics include proofs by induction, simple diagonalization proofs, combinatorial theory, relations and functions, the inclusion/exclusion principle, recurrence relations, and generating functions. Prerequisite: MA106. (U)(3). Fall only.

MA208 Calculus and Analytic Geometry III: Continuation of MA107. The calculus (limits, integration, and differentiation) of real-valued functions of one variable in MA106 and MA107 is extended in this course to more than one variable.  Topics include multivariable calculus, partial differentiation, multiple integration, line integrals, vector calculus, Green’s Theorem, and Stokes' Theorem. Prerequisite: MA107. (U)(4). Fall and spring.

MA215 Linear Algebra: The course studies linear maps between vector spaces. These simplest of transformations are quite sophisticated and useful when the dimensions are higher than one.  Topics include the structure of vector spaces, matrices, determinants, orthogonal bases, applications such as solving systems of linear equations, and eigenvalues and eigenvectors. Prerequisite: MA107. (U)(3). Fall and spring.

### MA 300

MA301 History of Mathematics: This course provides an overview of the historical evolution of major concepts in mathematics from ancient development of various number systems from Egypt, Greece, China, India, through mathematical developments in early to modern Europe, and up to discoveries of living mathematicians. Topics may include arithmetic, algebra, theory of equations, geometry, trigonometry, number theory, combinatorics, probability, and the theory of functions. Prerequisites: MA200. (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: Emphasizes 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: This course studies the properties of the integers. Topics include 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: MA200. (U/G)(3). Offered periodically.

MA312 Algebra: Groups: This course studies a general algebraic structure called a group, a set that has four fundamental properties under an operation. Groups arise in many settings, including the arithmetic study of the integers, the rational numbers, and the reals.  Applications exist in a variety of situations, such as in the advanced study of polynomials and in coding theory. Topics include basic definitions, subgroups, cosets and quotient groups, isomorphism theorems, and structure theorems of groups. Prerequisites: MA200 and MA215. (U/G)(3). Spring only.

MA313 Algebra: Rings and Fields: This course studies two algebraic structures called rings and fields—sets that have numerous fundamental properties under two operations that act like addition and multiplication.  They arise in many settings, including the study of polynomials and matrices, as well as rational, real, and complex numbers.  Topics include basic definitions, ideals, quotient rings, prime factorization, integral domains, ring homomorphisms, and filed extensions.  Prerequisites: MA200, and MA215. (U/G)(3). Fall only.

MA326-W Analysis: Theory of Calculus: This course studies the theoretical foundations of single variable calculus,  It describes real-valued functions, using precise definitions and properties of real numbers and limits to prove theorems about sequences, derivatives, Riemann integrals, and infinite series.  Prerequisite: MA200. (U/G)(3). Fall only.

MA327 Analysis: Lebesgue Integral:  The Lebesgue definite integral generalizes the Riemann integral learned in calculus. The Lebesgue integral effectively determines a geometry on complete spaces of functions, helping us understand the functions’ properties. This course studies the definition and properties of the Lebesgue integral on real-valued functions, along with important associated function spaces Prerequisite: MA200. (U/G) (3) Spring only.

MA328 Analysis: Calculus n Manifold: This course provides students with an opportunity to explore the proof-based mathematical analysis with several real variables with two goals in mind: to provide mathematical rigor to the calculus of sever real variables and to generalize the context of the calculus to manifolds.  Topics will include the topology of higher dimensional spaces, Stokes' Theorem, the Divergence Theorem, the Implicit Function Theorem, differential forms, integration of forms, and the exterior derivative. Prerequisites:  MA 200, MA208, and MA215.  (U/G)(3).  Occasionally.

MA330 Complex Analysis: This course extends the calculus of real functions to complex functions-those that have complex-numbered sets for their domain and range. Topics include the algebra of 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: Ordinary differential equations relate functions of one independent variable to their derivatives.  They have been used extensively to describe a wide variety of natural phenomena in physics, chemistry, biology, and engineering.  This course introduces many types of analytical, qualitative, and numerical techniques to find and interpret solutions to ordinary differential equations, including linear equations, nonlinear equations, and systems of equations.  Prerequisite: MA215. (U/G)(3). Fall and spring.

MA337 Applied Dynamics: Explore applications of differential equations in contexts of physics, biology, chemistry and engineering. Introduction to nonlinear dynamics including flows, phase plane analysis and more. Prerequisite: MA334 and MA215 (U)(3) Offered periodically.

MA351 Geometry: This course presents the core concepts and principles of ancient and modern geometry in two and three dimensions.  Axiomatic systems and proofs are emphasized. Various topics may be offered from Euclidean, differential, projective, and non-Euclidean geometry. Prerequisite: MA200. (U/G)(3). Spring only.

MA354 Topology: Introduction to topological spaces, separation axioms, compactness, connectedness, metric and function spaces. Prerequisite: MA326. (U/G)(3). Offered periodically.

MA 359 Probability and Statistics:   An advanced calculus-based study of probability and inferential statistics especially designed to meet the needs of engineering, secondary education, and mathematics majors by covering probability and statistical inference wthin a single course.  The course introduces the theory of discrete and continuous random variables and uses it to develop a sound understanding of cofidence intervals, hypothesis testing, andlinear regression.  Topics may include multivariate probability, chi-square tests, andanalysis of variance.  credit will not be awarded for both MA 359 and MA 360.  Prerequisite or co-requisite: MA 107.  (U) (3). Fall only.

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: Sampling distributions, methods of estimation, properties of estimators, confidence intervals, theory and application of hypothesis testing, analysis of variance, chi-squared tests, and fundamental concepts and applications of Bayesian statistics.  Prerequisite: MA360. (U/G)(3). Spring only.

MA362 Linear Regression and Time Series: 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: MA361. (U)(3). Fall only.

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.

MA364 Design of Experiments: An introduction to the basic principles of experimental design: analysis of variance for experiments with a single factor; randomized blocks and Latin square designs: multiple comparison of treatment means; factorial and nested designs; analysis of covariance; an introduction to response surface methodology.  Prerequisite: MA 361 or 162. (U/G)(3)

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.

MA369 Multivariate Statistical Methods: The course reviews matrix theory, univariate normal, T, chi-squared, F and multivariate normal distributions, and introduces inference about multivariate means including Hotelling's T squared, multivariate analysis of variance, multivariate regression and multivariate repeated measures. Additional topics include inference about covariance structure including principal components, factor analysis and canonical correlation, along with multivariate classification techniques including discriminant and cluster analyses. Prerequisites: MA 360, 361. (U/G)(3)

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-W 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.

### MA 400

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.

MA 467 Nonparametric Statistical Methods:  Introduction to nonparametric statistics, including one and two sample testing and estimation methods, one and two way layout models and correlation and regression models. Prerequisites: MA 360, 361. (U/G)(3)

MA 468 Predictive Analytics and Data Mining: This course provides an experiential overview of data mining and machine learning algorithms to analyze huge sets of data having large numbers of random variables and/or large numbers of entries.  Topics include manipulation of databases, statistics, machine learning, information retrieval, and uses of a software such as RapidMiner/R. Prerequisite: MA 369 and CS 142. (U/G)(3)

MA 469 Advanced Statistical Computing: Topics involve numerical analysis useful for statistical modeling and analysis. Methods used include deterministic and stochastic methods for optimization and integration, the EM algorithm, Monte Carlo simulation (both non-iterative and iterative), and kernel density estimation. Applications include Bayesian hierarchical models, mixture models, time series, nonlinear regression, smoothing, classification, and modern variable selection.
(U/G)(3)

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-S 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.

MA 495: Mathematics for Investment Portfolios: This course together with MA 399 completes the coverage of the SOA Exam IFM syllabus. (U/G)(1).Spring only.

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

### Frequency of Course Offerings

Course No. Course Name Fall
Odd
Spring
Even
Fall
Even
Spring
Odd
Credit Hours
AR 210-MA Statistically Speaking (U)(3)
AR 211-MA Codes & Secret Messages (U)(3)
AR 212-MA Win, Lose or Draw (U)(3)
MA 101 Algebra (U)(3)
MA 102 Precalculus (U)(3)
MA 106 Calculus and Analytic Geometry I (U)(4)
MA 107 Calculus and Analytic Geometry II    (U)(4)
MA 162 Statistical Methods (U)(3)
MA 200 Basics of Advanced Mathematics  ●  ● (U)(3)
MA 205 Discrete Mathematics     (U)(3)
MA 208

Calculus and Analytic Geometry III

(U)(4)
MA 215 Linear Algebra (U)(3)
MA 301 History of Mathematics     (U/G)(3)
MA 305* Graph Theory   *   * (U/G)(3)
MA 308* Problem Seminar * * * * (U/G)(1)
MA 311* Number Theory     *   (U/G)(3)
MA 312 Algebra:  Groups     (U/G)(3)
MA 313 Algebra:  Rings and Fields     (U/G)(3)
MA 326W Analysis:  Theory of Calculus  ●         ●        (U/G)(3)
MA 327 Analysis:  Lebesgue Integral     (U/G)(3)
MA 328 Analysis:  Calcuus on Manifold * * * * U/G)(3)
MA 330 Complex Analysis     (U/G)(3)
MA 334 Differential Equations (U/G)(3)
MA 337* Applied Dynamics         (U/G)(3)
Course No. Course Name Fall
Odd
Spring
Even
Fall
Even
Spring
Odd
Credit Hours
MA 351 Geometry     (U/G)(3)
MA 354* Topology     *   (U/G)(3)
MA 359 Probability and Statistics
MA 360 Probability Theory I     (U/G)(3)
MA 361 Statistical Theory     (U/G)(3)
MA 362 Applied Statistical Methods       ●   (U/G)(3)
MA 363 Probability Theory II     (U/G)(3)
MA 364** Design of Experiments       (U/G)(3)
MA 365* Numerical Analysis *       (U/G)(3)
MA 369** Multivariate Statistical Methods       (U/G)(3)
MA 372 Loss Models       (U/G)(3)
MA 395 Financial Mathematics     (U/G)(4)
MA 397 Actuarial Mathematics I  ●       (U)(3)
MA 398 Actuarial Mathematics II     ●        (U)(3)
MA 399 Financial Derivatives           ● (U)(3)
MA 401, 402, 403*** Independent Study         (U/G)(1-3)
MA 411*** Internship         (U/G)(3)
MA 467 Nonparametric Statistical Methods       (U/G)(3)
MA 468 Predictive Analytics and Data Mining         (U/G)(3)
MA 469* Advanced Statistical Computing           (U/G)(3)
MA 471 ,472, 473***     Topics of Mathematics         (U/G)(1-3)
MA 490-S Senior Seminar       (U)(1)
MA 495 Mathematics for Investment Portfolios     (U/G)(1)
MA 499 Honors Thesis (U)(3)

*These courses are offered fairly regularly but not strictly in any given term
**Beginning no later than academic year 2019-2020
***These courses are offered on an as-needed basis and require a faculty sponsor.
For more information, visit the Mathematics, Statistics, and Actuarial Science website at www.butler.edu/math-actuarial.

Revised August 2017