Contact Persons: Theodore Erickson, Ph.D. (Chair)
John Karwin, S.J.
Vasile Lauric, Ph.D.
Onkar Pandit
Elizabeth Prather
Kimberly Roth, Ph.D.
The essence of orderliness, form and elegance, mathematics is a basic tool for many disciplines and careers. The mathematics curriculum is designed to provide the student with a strong mathematics background enhanced by technological tools, such as the graphing calculator and symbolic algebra software. It also is flexible enough to accommodate the diverse interests of mathematics majors, including those preparing for graduate work, those preparing to become an actuary and those seeking to teach on the elementary or secondary level.
Upon completion of the Mathematics program, students will be able to:
1. Comprehend and simplify mathematical expressions.
2. Build or solve mathematical models.
3. Prove or disprove a theory with logical steps.
4. Understand and use modern technology in mathematics.
5. Pursue high level mathematical theory.
Core Fulfilling Courses
Mathematics Requirement 1 courseCSC 108 Introduction to Structured Programming (3 crs)
CSC 110 Computer Science I (4 crs)
MAT 102 Math in Society (3 crs)
MAT 105 Introduction to Statistics I (3 crs)
MAT 108 Pre-Calculus (3 crs)
MAT 111 Calculus I (4 crs)
(A student with advanced placement may substitute a higher level MAT or CSC course to fulfill the core requirement.)
Requirements for Mathematics Major
Bachelor of Science Degree
In addition to completing the core curriculum requirements, outlined on pg. 14-15 of this catalog, (plus 6 more already included in courses below,) all majors in mathematics must complete the following courses:
MAT 111, 112 Calculus I, II (8 crs)
MAT 211 Calculus III (4 crs)
MAT 212 Ordinary Differential Equations (3 crs)
MAT 235 Discrete Mathematics (4 crs)
MAT 240 Linear Algebra (4 crs)
MAT 351 or 352 Introduction to Abstract Algebra I or II (3 crs)
MAT 411, 412 Introduction to Real Variables I, II (6 crs)
MAT 482 Senior Seminar in Mathematics (2 crs)
MAT, PHY, CSC Electives (two courses from MAT, PHY or CSC)
CSC 110 Electives (three courses to be chosen from: MAT 331, MAT 335,MAT 413, MAT 422, MAT 424, MAT 431, MAT 310, MAT 336, MAT352) (15 crs)
PHY 110, 121 Physics I and Lab I (5 crs)
Total : 51 crs
Requirements for Certification in Mathematics Education
The student wishing to pursue certification for teaching mathematics in the intermediate and/or secondary schools should consult the director of the teacher preparation program for specific requirements. Generally, the student completes the mathematics major as described above with the upper-level electives being specified as MAT 424 and MAT 335. PSY 110 should be taken as early as possible.
Requirements for Mathematics Minor
Mathematics minors must complete a minimum total of 15 credit hours in mathematics beyond MAT 112.
Course Descriptions
DEVELOPMENTAL MATHEMATICS:
These courses are preparatory and will not satisfy the University’s core curriculum requirement in mathematics. They are offered as parallel semester courses each academic year so that students with deficient background in mathematics will be prepared to successfully complete the core requirement in mathematics. Students with weaker backgrounds in mathematics should take MAT 090 while students with fewer deficiencies should take MAT 092. The algebra background in either of these courses is a prerequisite for every other course in mathematics or computer science. Students can not take both of these courses for credit since MAT 090 includes the content of MAT 092.
MAT 090 Developmental Mathematics (4 crs)
A review of arithmetic operations, variable expressions, translation, polynomials, exponents, factoring, rational expressions, first degree equations, inequalities, radical expressions and quadratic equations. This course also requires a weekly one-hour lab session.
MAT 092 Developmental Mathematics II (2 crs)
A study of intermediate algebra including rational expressions, linear equations in two variables, systems of equations, radical expressions and quadratic equations.
COLLEGE LEVEL MATHEMATICS:
The following courses carry a minimum prerequisite of the above two courses or the equivalent. Any of these, except MAT 110, can satisfy the mathematics core requirement provided the necessary prerequisites are met by the student. Those typically taken as such are marked “core.”
MAT 102 Math in Society (3 crs) (core)
This course is designed to meet the needs of students who do not have a specific course needed for support of their major. The fundamental properties of numbers, geometry and statistics are covered through the collection of modern and useful applications of mathematics. The course contains a collection of topics of modern society: Social Choice, Management Science, Growth and Symmetry and Statistics.
MAT 105 Introduction to Statistics I (3 crs) (core)
Descriptive statistics including measures of central tendency and variability, graphic representation, probability, the binomial, normal and T distributions, hypothesis testing and linear regression.
MAT 106 Introduction to Statistics II (3 crs)
Descriptive statistics continued, including hypothesis testing of the mean and proportion (two populations), analysis of variance (ANOVA), goodness of fit (chi-square distribution), multiple regression and non-parametric methods. Prerequisite: MAT 105
MAT 108 Pre-Calculus (3 crs) (core)
A thorough preparation for calculus with analytic geometry, including conic sections, and the transcendental functions: logarithmic, exponential and trigonometric functions.
MAT 110 Business Calculus (4 crs)
A survey of the basic techniques of differential and integral calculus including polynomial, logarithmic and exponential functions. Applications to finance and economics. (Taught concurrently with MBA 495.) Does not satisfy the core requirement in mathematics.
MAT 111 Calculus I (4 crs)
A theoretical introduction to differential calculus including limits,
continuity, the basic rules for derivatives and applications including optimization problems. A brief introduction to integration leading to the Fundamental Theorem of Calculus completes this course.
Prerequisite: MAT 108 or equivalent.
MAT 112 Calculus II (4 crs)
Transcendental functions, applications of integrals, volumes of revolution, surface areas; techniques of integration, including powers of trigonometric functions, integration by parts and by partial fractions, improper integrals, infinite series, Taylor’s expansion and indeterminate forms. Prerequisite: MAT 111.
MAT 211 Calculus III (4 crs)
Vectors and vector valued functions, extreme of multivariate functions and the method of Lagrange multipliers, surfaces in three dimensions, line and surface integrals; multiple integration and Stokes Theorem. Prerequisite: MAT 112.
MAT 212 Ordinary Differential Equations (3 crs)
ODEs of first order: linear, homogeneous, separable and exact, with applications; orthogonal trajectories; those of second order: reducible to first order, general and particular solutions by the methods of undetermined coefficients, variations of parameters and power series; and an introduction to numerical methods. Prerequisite: MAT 211.
MAT 222 Applied Calculus (4 crs)
Survey of various topics in calculus including: simple and multiple integration, partial differentiation, infinite series and differential equations; with emphasis on applications. Prerequisite: MAT 111.
MAT 235 Discrete Mathematics (4 crs)
Sets and relations, logic and truth tables, Boolean algebra, logic gates, graph theory, combinatorics, algorithms, matrix algebra and determinants. Prerequisites: MAT 111.
MAT 240 Linear Algebra (4 crs)
Solution spaces for systems of linear equations, elementary row operations, vector spaces, linear independence, linear transformations, change of basis, inner products, projections, the Gram-Schmidt process, eigenvalues and eigenvectors. Prerequisite: MAT 211 or MAT 235.
MAT 310 History of Mathematics (3 crs)
History of the development of mathematical concepts in algebra, geometry, number theory, analytical geometry and calculus from ancient times through modern times. Theorems with historical significance will be studied as they relate to the development of modern mathematics. Prerequisite: MAT 112 or MAT 235
MAT 331 Numerical Analysis (3 crs)
Numerical solution of linear systems and of non-linear equations; interpolation, approximation and numerical differentiation and integration (computer methods and programming will be utilized.) Prerequisite: MAT 112.
MAT 335 Applied Probability and Statistics I (3 crs)
Introduction to Probability: discrete and continuous random
variables (binomial, geometric, hypergeometric, Poisson, normal, exponential, Chi-square, gamma), sampling distribution (including CLT), multivariate distributions, stochastic processes. Prerequisite: MAT 211
MAT 336 Applied Probability and Statistics II (3 crs)
Introduction to mathematical statistics: elimination and inferences for means (confidence intervals and tests of significance), differences of two means, proportions, differences of two proportions and variances; linear models (simple and multi-variable), nonparametric methods. Prerequisite: MAT 335
MAT 351 Introduction to Abstract Algebra I (3 crs)
Introduction to groups: finite groups and subgroups, cyclic groups, permutation groups, homomorphisms and isomorphisms, cosets and Lagrange’s theorem, direct products of homomorphisms. Prerequisite: MAT 240
MAT 352 Introduction to Abstract Algebra II (3 crs)
Introduction to rings, integral domains; ideals and factor rings; homomorphisms and isomorphisms; polynomial rings, unique factorization, irreducible polynomials; extension fields, algebraic extensions, finite fields; geometric constructibility. Prerequisite: MAT 240
MAT 411 Introduction to Real Variables I (3 crs)
Development of the real numbers; topology of the real line; limits and limit points, continuity and the properties of continuous functions; convergence of sequences and series. Prerequisite: MAT 351.
MAT 412 Introduction to Real Variables II (3 crs)
Uniform continuity, sequences of functions, uniform convergence, differentiation, integration and measure and elementary functional analysis. Prerequisite: MAT 411.
MAT 413 Introduction to Complex Variables (3 crs)
Analytic functions; power series; complex integration and Cauchy’s theorem; entire functions; analytic continuation. Prerequisite: MAT 211, 212.
MAT 422 Topology (3 crs)
An introduction to point set topology including topological spaces, connected spaces, compact spaces, metric spaces and separation axioms. Prerequisite: MAT 411.
MAT 424 Geometry (3 crs)
Euclid’s Axioms, the parallel postulate, leading to non-Euclidean geometries, and an introduction to projective and affine geometries.
MAT 431 Foundations of Mathematics (3 crs)
The fundamental notions of a system of postulates, their consistency, independence and categoricalness. Introduction to ordinal and cardinal numbers. Prerequisite: MAT 211.
MAT 482 Senior Seminar in Mathematics (2 crs)
Independent study of topics not usually covered in the MAT curriculum leading to a presentation of an elementary research or survey paper by the student under the direction of a professor. Required for all mathematics majors in the junior or senior year.
