The study of mathematics is a hallmark of enlightened society, as it has been for millennia. Mathematics helps us understand our world and ourselves, and it is fun.
Mathematics is one of the oldest of the liberal arts. The study of mathematics has been used for centuries to train students to think clearly and creatively. Mathematical applications enlighten other disciplines and inform society.
Mathematical thought requires curiosity, creativity, discipline and logic. As students progress through the mathematics curriculum, they are expected to become increasingly adept at developing conjectures, constructing correct proofs and refuting weak ones, creating and using mathematical models to describe physical phenomena, working with abstract structures and clearly communicating results.
A major in Mathematics requires completion of MAT 109, 110, 111, 211 and 229; MAT 330 and 331; one course from MAT 323, 329, 337, 339 or other courses in mathematical modeling as offered by the department; one mathematics course numbered 400 or higher, other than 490 or 491; and sufficient electives so that the total number of mathematics courses taken beyond MAT 111 is nine. One of the electives may be chosen from PHY 226, ECO 310, PHI 244, CHM 321, PSY 360, or, with approval of the department, other mathematically intensive courses; 100-level courses may not be used as electives for the Mathematics major.
The writing requirement in Mathematics is met by the completion of MAT 211.
A student planning to major in Mathematics should take MAT 211 as soon as possible, no later than the first semester of the junior year. A student planning to major in Mathematics and study abroad should complete 211 before going abroad.
We suggest the following guidelines for course selection:
Students intending to pursue graduate study in mathematics should take MAT 442, 446, 490 and CPS 111. We also recommend studying at least one of French, German and Russian.
Prospective teachers of secondary school mathematics should take MAT 216, 316, 445 and CPS 111.
Students interested in actuarial science or statistics should take MAT 216, 316, 323 and 338 and CPS 111. We also recommend taking courses in Economics and in Business, Organizations, and Society.
Students planning to enter other fields of applied mathematics should take MAT 323, 329, 337, 338, 339 and 442. Knowledge of probability, statistics and computer science is essential in many areas of applied mathematics.
A minor in Mathematics may be completed in one of two tracks. The “theoretical math track” consists of MAT 110, 111 and 211; and three courses chosen from MAT 325, 330, 331, 442, 445, 446 or other theoretical courses as designated by the department, at least one of the three courses must be at the 300-level or beyond. The “applied math track” consists of MAT 110 and 111; and four courses from MAT 215, 216, 229, 316, 323, 329, 337, 338, 339, or other applied modelling courses as designated by the department, at least one of the four courses must be at the 300-level or beyond.
Majors in the Department of Mathematics have studied abroad in the following programs in recent years: Institute for Study Abroad at Butler University Programs in England, Ireland, Scotland, Australia and New Zealand; American University in Cairo, Egypt. See the International Programs section of the Catalog for further information.
A list of regularly offered courses follows. Please note the key for the following abbreviations: (A) Arts; (H) Humanities; (S) Social Sciences; (N) Natural Sciences with Laboratory; (LS) Language Studies requirement; (NSP) Natural Science in Perspective; (NW) Non-Western Cultures requirement.
105. Preparation for College Mathematics.
Introductory logic and algebra, elementary functions: polynomial, rational, trigonometric, exponential, logarithmic. Prerequisite: Permission of the department. Not for credit toward the mathematics major or minor.
109. Calculus I.
Introduction to the basic concepts of calculus and their applications. Functions, derivatives and limits; exponential, logarithmic and trigonometric functions; the definite integral and the Fundamental Theorem of Calculus. Prerequisite: Twelfth-grade mathematics or MAT 105.
110. Calculus II.
Techniques of integration, applications of integration, separable first-order differential equations, convergence tests for infinite series, Taylor polynomials and Taylor series. Prerequisite: MAT 109 or permission of the department.
111. Calculus III.
Vectors and parametric equations; functions of two variables; partial and directional derivatives; multiple integrals; line integrals. Prerequisite: MAT 110 or permission of the department.
211. Introduction to Higher Mathematics.
A course designed as a transition from calculus to advanced mathematics courses. Emphasis on developing conjectures, experimentation, writing proofs and generalization. Topics will be chosen from number theory, combinatorics and graph theory, polynomials, sequences and series and dynamical systems, among others. Prerequisite: MAT 111.
215. Introduction to Statistical Modeling.
This course is about the construction, analysis, and application of statistical models to real data. We emphasize the use of models to untangle and quantify variation in observed data. Basic statistical concepts such as randomness, confidence intervals, hypothesis tests, causal inference, etc., are explored in the context of statistical models which include multivariate regression, analysis of variance, and logistic regression. We use a modern statistics software package (R) throughout the course. Prerequisite: MAT109
216. Probability and Statistics I.
Introduction to single variable probability and statistics. Random variables. Binomial, geometric, Poisson, exponential and gamma distributions, among others. Counting techniques. Estimation and hypothesis tests on a single parameter. Prerequisite: MAT 110.
229. Linear Algebra and Differential Equations.
Systems of linear equations and matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, nth order linear differential equations, systems of first order differential equations. Prerequisite: MAT 111.
237. Discrete Mathematics.
Basic set theory, basic proof techniques, combinatorics (the theory of counting), and graph theory with related algorithms. Prerequisite: MAT 109. Offered every Fall. Same as CPS 237.
245. Projective Geometry Applied to Perspective Art.
This course deals with projective geometry as applied to perspective art. In particular, we will use problems from perspective art to motivate geometric concepts. Solutions to these problems will include both simple drawings and also rigorous mathematical proofs. Mathematical topics include projective maps from three-space to the plane, Desargues’ theorem, and the Fundamental Theorems of Projective Geometry. Prerequisite: MAT 111.
270 – 279. Selected Topics.
Intermediate level courses.
291. Directed Reading.
Reading directed by the Mathematics staff. Permission of chairperson.
316. Probability and Statistics II.
Continuation of MAT 216. Multivariate distributions. Estimation and hypothesis tests for multiple parameters. Regression and correlation. Analysis of variance. Prerequisites: MAT 111, MAT 216.
323. Stochastic Processes.
Properties of stochastic processes, Markov chains, Poisson processes, Markov processes, queueing theory. Applications of stochastic modeling to other disciplines. Prerequisites: MAT 111, MAT 216.
325. Number Theory.
Properties of the natural numbers and integers: divisibility, primes, number theoretic functions, Diophantine equations, congruences, quadratic reciprocity, additive number theory, unsolved problems. Prerequisite: MAT 211.
329. Fourier Series.
Fourier series, orthogonal series, boundary value problems, applications. Prerequisite: MAT 229.
330. Abstract Algebra.
Algebraic systems and their morphisms including sets, functions, groups, homomorphisms, factor groups, rings and fields. Prerequisite: MAT 211.
331. Introduction to Analysis.
An introduction to the ideas and proof techniques specific to mathematical analysis. Real numbers, sequences, limits, derivatives, integrals, infinite series, cardinality; other topics as chosen by instructor. Prerequisite: MAT 211.
337. Mathematics for Optimization.
Discrete, deterministic models of interest to the social sciences. Linear programming, duality, simplex method, sensitivity analysis, convex sets. Selections from: assignment, transportation, network flow, nonlinear programming problems. Prerequisite: MAT 229.
338. Computational Mathematics.
Numerical analysis as implemented on computers. Polynomial and rational approximations, numerical differentiation and integration, systems of linear equations, matrix inversion, eigenvalues, first and second order differential equations. Prerequisites: CPS 111, MAT 229. Same as CPS 338.
339. Mathematical Models.
An introduction to the art of creating and analyzing deterministic mathematical models. Models of physical, biological and social phenomena. Topics vary with instructor; examples are predator-prey interactions, spread of epidemics, arms races and changes in global temperature. Mathematical techniques include phase-plane analysis of systems of differential equations and function iteration. Prerequisite: MAT 229.
370 – 379. Selected Topics.
Advanced Algebra, Advanced Multivariable Calculus, Measure Theory, Algebraic Topology, History and Development of Calculus.
375. Topics in Algebra.
Courses of an algebraic nature such as Ring Theory, Advanced Linear Algebra and Algebraic Number Theory, that can be taken in place of, or in addition to, MAT 330 to satisfy the major requirements. May be repeated with permission of department. Prerequisite: MAT 211.
390. Independent Study.
Independent study directed by the Mathematics staff. Permission of chairperson.
391. Directed Reading.
Reading directed by the Mathematics staff. Permission of chairperson.
442. Complex Analysis.
Functions of one complex variable: analytic functions; mappings; integrals; power series; residues; conformal mappings. Prerequisite: MAT 331.
Selections from: advanced synthetic geometry; groups of transformations; affine geometry; metric geometry; projective geometry; inversive geometry. Prerequisite: MAT 330.
An introduction to topological spaces and continuous functions. Prerequisite: MAT 330. Corequisite: MAT 331.
470 – 479. Selected Topics.
Study of advanced specialized areas of mathematics.
490. Independent Study.
Independent study directed by the Mathematics faculty. Permission of chairperson.
491. Directed Reading.
Reading directed by the Mathematics faculty. Permission of chairperson.
Topics Courses Expected to be Offered in 2017-2018
- Analytic Number Theory.