# MAT (Mathematics)

MAT 111 Statistics (4 hours)
This course introduces students to both descriptive and inferential statistics. Topics include describing data graphically and numerically, discrete and continuous distributions, correlation and linear regression, basic probability, sampling distributions, the Central Limit Theorem, confidence intervals and hypothesis tests. Offered every semester.

MAT 120 Introduction to Functions (4 hours)
The objective of this course is to equip students with the algebraic reasoning and skills for MAT 121 Applied Calculus or MAT 130 Advanced Functions. The function concept is developed in algebraic, graphical and numerical forms, with attention to rates of change, domain, range and inverses. The following categories of functions are discussed in terms of their analytic, graphical, and numerical properties: linear, quadratic and other polynomials, power, rational, exponential and logarithmic. Offered every semester.

MAT 121 Applied Calculus (4 hours)
This is the recommended calculus course for students in accounting, business, economics and the social sciences. The goal of this course is to present calculus in an intuitive yet intellectually satisfying way and to illustrate the many applications of calculus to those students’ fields. Topics include functions, rates of change, the derivative, techniques of differentiation (exact and approximate), optimization and other applications of the derivative, integration, the Fundamental Theorem of Calculus, applications of integration, functions of several variables, partial derivatives and multivariable optimization (Second Derivatives Test and Lagrange multipliers). Offered every semester.

MAT 125 Precalculus (4 hours)
This course is designed to prepare a student for the Calculus sequence (Calculus I-IV). The general consideration of functions, inverse functions, and models will be illustrated using study of specific functions including polynomials, exponentials, logarithms, rational functions, and trigonometric functions. In addition, a successful student will be able to model functions and apply the models to real-world settings. Offered every semester.

MAT 130 Advanced Functions (4 hours)
The objective of this course is to equip mathematics and science students with the skills needed for Calculus I. Topics include basic analytic geometry, trigonometry (functions, equations and identities), complex numbers, polar coordinates, vectors in the plane, parametric equations and transformation of coordinates. Offered every spring semester. Prerequisite: Satisfaction of the mathematics placement requirement (Sec. 6.4.1.), or prior completion of MAT 120 with a grade of “C–” or higher.

MAT 131 Calculus I (4 hours)
Calculus I, II, III, and IV form the recommended calculus sequence for students in mathematics and the sciences. The objective of these courses is to introduce the fundamental ideas of the differential and integral calculus as they pertain to functions of both one and several variables. Topics for Calculus I include limits, continuity, rates of change, derivatives, the Mean Value Theorem, applications of the derivative, related rates, optimization problems, introduction to area and integration, and the Fundamental Theorem of Calculus. Offered every fall semester. Prerequisite: Satisfaction of the mathematics placement requirement (Sec. 6.4.1.) or prior completion of MAT 125 with a grade of “C–“ or higher, or prior completion of MAT 130 with a grade of “C–” or higher.

MAT 132 Calculus II (4 hours)
This course is a continuation of Calculus I. Topics include inverse functions, exponential and logarithmic functions, techniques of integration, and applications of integration, sequences and series. Offered every spring semester. Prerequisites: Satisfaction of the mathematics placement requirement (Sec. 6.4.1.); or prior completion of MAT 131 with a grade of “C–” or higher; or prior completion of MAT 121 with a grade of “B” or higher.

MAT 200 Independent Study in Mathematics (1-4 hours)
This course provides the opportunity for an intense study of diverse topics under the direct supervision of the instructor. The student and instructor will collaborate to develop the content of the course, which must be approved as outlined by the Independent Study Policy. (Sec. 6.15.)

MAT 210 Discrete Mathematics (4 hours)
This course introduces the ideas of finite mathematical structures. Topics include set theory, logic, proof techniques, functions and relations, graphs, and trees. Offered every spring semester. Prerequisite: MAT 120 with a grade of “C-” or higher.

MAT 233 Calculus III (4 hours)
This course is a continuation of Calculus II. Topics include the basic geometry of Euclidean 3-space (vectors, lines, planes), vector functions/curves (limits, derivatives, and integrals), and multivariable functions (limits, partial derivatives, and double integrals). Offered every fall semester. Prerequisite: MAT 132 with a grade of   “C-” or higher.

MAT 234 Calculus IV (2 hours)
This course is a continuation of Calculus III. Topics include triple integrals (Cartesian, cylindrical, and spherical coordinates), coordinate changes via the Jacobian, curves, surfaces, vector fields (field diagrams, divergence, gradient, and curl), line integrals, surface integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. Offered every spring semester. Prerequisite: MAT 233 with a grade of “C-” or higher.

MAT 236 Differential Equations (4 hours)
The objective of this course is to introduce the fundamental ideas of the theory of ordinary differential equations and to consider some of the applications of this theory to the sciences. Topics include equations of order one, applications of equations of order one, linear differential equations, linear equations with constant coefficients, nonhomogeneous equations, undetermined coefficients, variation of parameters, applications of equations of order two and power series solutions. Offered every spring semester. Prerequisite: MAT 233 with a grade of “C-” or higher.

MAT 238 Linear Algebra (4 hours)
This is an introductory course in Linear Algebra. The techniques and theory needed to solve application programs, specifically from Engineering and Economics, will be developed. Students will practice techniques initially by hand to gain understanding of the method, but mathematical software (like MATLAB or Octave) will be used as the course’s computational engine to deal with the routinely large objects created in such applications. Offered every fall semester. Prerequisite: MAT 132 with a grade of “C-“or higher.

MAT 241 Proof and Logic: An Introduction to Post-Calculus Mathematics (4 hours)
This course serves as a general introduction to advanced mathematics. As such, it will consider various methods of proof communicated through good mathematical writing. Topics are drawn from logic, set theory, functions, relations, combinatorics, graph theory and Boolean algebra. Offered every fall semester. Prerequisite: MAT 132 with a grade of “C-” or higher.

MAT 250 Financial Mathematics (4 hours)
This course provides an introduction to financial mathematics. The course starts with time value of money and annuities/cash flows with non-contingent payments. Loans and bonds will be followed by general cash flows and portfolios. The course will culminate with immunization, interest rate swaps, and determinants of interest rates. Offered the fall semester of even years. Prerequisite: MAT 132 with a grade of “C-” or higher.

MAT 290 Special Topics in Mathematics (1-4 hours)
Courses of selected topics will be offered periodically as determined by the needs of the curriculum. Prerequisites can vary based on the topic selected. See individual course listings for each semester for the specific topic and any prerequisites.

MAT 300L Advanced Linear Algebra Lab: Proofs & Vector Spaces (1 hour)
This laboratory course extends the computationally intensive foundation laid in MAT 238 to the theoretical realm of the mathematics major. The laboratory’s first focus is taking the results used without proof in the canonical course and proving them mathematically true. As such, students will practice extensively with mathematical precision, proof techniques, and good communication. The laboratory’s second focus is taking the concepts grounded in Euclidean space in the canonical course and extending them more broadly. Thus, this course will give a formal treatment of abstract vector spaces. Offered every fall semester. Corequisite or Prerequisite: MAT 238 (with a grade of “C–“ or higher if prerequisite).

MAT 340 Probability (4 hours)
This course provides a calculus-based study of probability. The course starts with set-theoretic, axiomatic and combinatorial foundations of probability, followed by basic rules/laws, conditional probability, and Bayes Theorem.  Students will master key concepts of univariate random variable theory for discrete and continuous random variables.  The course will culminate with key concepts of multivariate random variable theory for discrete random variables.  Offered the spring semester of odd years. Prerequisite: MAT 233, with a grade of “C-” or higher

MAT 345 Mathematical Statistics (4 hours)
This course provides a calculus-based study of statistics as a follow-up to a formal study of probability. The course starts with order statistics, linear combinations of independent random variables, random sampling, statistical inference, and sampling distributions.  The main methods of estimation will be followed by the main properties of estimators.  The course will culminate with constructing confidence intervals (one and two means, variances, and proportions) and hypothesis testing (one and two means, variances, contingency tables, and goodness-of-fit).  Offered the fall semester of odd years. Prerequisite: MAT 340

MAT 350 Statistical Learning (4 hours)
This course provides an introduction to statistical learning as a follow-up to the formal study of calculus-based probability and statistics.  The course starts with an overview of statistical learning along with simple and multiple linear regression.  Resampling methods will be followed by linear model selection and regularization.  The course will culminate with tree-based methods, unsupervised learning, and cluster analysis.  Offered the spring semester of even years.  Prerequisite:  MAT 345 with a grade of “C-” or higher.

MAT 355 Fundamental Actuarial Mathematics I (4 hours)
This course provides a fundamental understanding of short-term actuarial mathematics. The course starts with the modeling process linked to random variables, basic probability distributions, and related calculations.  Actuarial modeling will be followed by estimation and an introduction to credibility theory.  The course will culminate with insurance types, coverages, loss reserving, and ratemaking.  Offered the fall semester of odd years.  Prerequisite:  MAT 340 with a grade of “C-” or higher.

MAT 360 Fundamental Actuarial Mathematics II (4 hours)
This course provides a fundamental understanding of long-term actuarial mathematics. The course starts with an introduction to life and long-term health insurance and survival models.  Life tables, selection, and insurance benefits will be followed by premium calculation and annuities.  The course will culminate with policy values, option pricing, and estimating survival models.  Offered the spring semester of even years.  Prerequisite:  MAT 355 with a grade of “C-” or higher.

MAT 400 Advanced Independent Study in Mathematics (1-4 hours)
This course provides the opportunity for an advanced, intense study of diverse topics under the direct supervision of the instructor. These offerings are generally suited for junior or senior students. The student and instructor will collaborate to develop the content of the course, which must be approved as outlined by the Independent Study Policy. (Sec. 6.15.)

MAT 455 Advanced Short-Term Actuarial Mathematics (4 hours)
This course serves as one of two possible capstones for Actuarial Science, and it provides an advanced understanding of short-term actuarial mathematics. The course starts with a quick review of basic distributional quantities and actuarial models.  Frequency and severity with coverage modifications will be followed by advanced aggregate loss models, Bayesian estimation, construction of empirical models, and model selection.  The course will culminate with greatest accuracy credibility, empirical Bayes parameter estimation, and advanced loss reserving and ratemaking.  Offered the spring semester of even years.  Prerequisite:  MAT 355 with a grade of “C-” or higher.

MAT 460 Advanced Long-Term Actuarial Mathematics (4 hours)
This course serves as one of two possible capstones for Actuarial Science, and it provides an advanced understanding of long-term actuarial mathematics. The course starts with policy values, multiple state models, and multiple decrement models.  Joint life and last survivor benefits will be followed by pension mathematics and emerging costs for both traditional life insurance and equity-linked insurance.  The course will culminate with embedded options and estimating survival models.  Offered the fall semester of even years.  Prerequisite:  MAT 360 with a grade of “C-” or higher.

MAT 471 Abstract Algebra (4 hours)
The objective of this course is to introduce the fundamental ideas of modern algebra. Topics include sets, mappings, the integers, groups, rings and fields. Offered the spring semester of even years. Prerequisites: MAT 241 and MAT 372, each with grade of “C-” or higher.

MAT 482 Real Analysis (4 hours)
Real analysis is a very natural extension of calculus. In the first part of the course, we will develop rigorous proofs of many key calculus theorems – theorems whose validity was only assumed in the Calculus sequence. From there, we will move to a formal consideration of real numbers and point-set topology, which are extensions of the more elementary notions learned in calculus. Offered the fall semester of odd years. Prerequisites: MAT 233 and MAT 241, each with grade of “C-” or higher.

MAT 490 Advanced Special Topics in Mathematics (1-4 hours)
Advanced courses of selected topics will be offered periodically as determined by the needs of the curriculum. These offerings are generally suited for junior or senior students. Prerequisites can vary based on the topic selected. See individual course listings for each semester for the specific topic and any prerequisites.

Specifically, this Mathematics course will explore selected topics in advanced mathematics, such as advanced abstract Algebra, combinatorics, differential geometry, dynamical systems, game theory, graph theory, number theory, numerical analysis, set theory, and topology. Offered the spring semester of odd years. Prerequisite: Will depend on the topic but will include a minimum of MAT 241 with a grade of “C-” or higher.

MAT 495 Internship in Mathematics (1-12 hours)
An internship designed to provide a formalized experiential learning opportunity to qualified students. The internship generally requires the student to have an application (which satisfies all internship requirements developed by the academic program that oversees the internship) and to obtain a faculty supervisor in the relevant field of study. All internships are graded on a Satisfactory/Unsatisfactory basis. Prerequisites are determined by the academic program overseeing the internship course.