# 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 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 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 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 for Engineering and Economics (4 hours)
This course in Linear Algebra is intended for students in Engineering and Economics, and it focuses on applications from those disciplines. The techniques and theory needed to solve such applications will be developed. Students will practice techniques initially by hand to gain understanding of the method, but mathematical software (like MATLAB or Maple) will be used as the course’s computational engine to deal with the routinely large objects created in such applications. (Note: Students may not receive credit for both MAT 238 and MAT 372. MAT 238 may not be used toward completing either the Mathematics major or minor.) Offered in the fall semester of even years. 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 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 361 Probability (4 hours)
This course provides a calculus-based study of probability. Topics include set-theoretic, axiomatic and combinatorial foundations, basic rules, conditional probability, independence, discrete and continuous random variable theory, special discrete and continuous models, probability plots and joint distributions. Offered the fall semester of even years. Prerequisites: MAT 132 and MAT 241, each with a grade of “C-” or higher.

MAT 371 Mathematical Statistics (4 hours)
This course provides a calculus-based study of statistics as a follow-up to a formal study of probability. Topics include functions of random variables, sampling distributions, the Central Limit Theorem, estimator theory, confidence intervals, hypothesis testing, and linear models via simple and multiple regression. Offered the spring semester of odd years. Prerequisite: MAT-361 with a grade of “C-” or higher.

MAT 372 Linear Algebra (4 hours)
The objective of this course is to introduce the fundamental ideas of linear algebra. Topics include linear equations, matrices, determinants, vector spaces, inner products, linear transformations, eigenvalues and eigenvectors. Offered the fall semester of odd years. Prerequisites: MAT 132 and MAT 241, each with 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 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.

MAT 496 Senior Seminar in Mathematics (2 hours)
This course stresses the communication of mathematical ideas – both in written and oral/multimedia forms. Content will be appropriate for a senior level course in areas like complex analysis, dynamical systems, and topology. Course topics will be chosen taking into consideration recent offerings and the needs of the Oglethorpe community. Offered every spring semester. Prerequisites: MAT 241 with a grade of “C–” or higher and Senior standing.