Mathematics (MATH)

College of Arts and Sciences

 

(GE) = Approved General Education Course

131 Intermediate Algebra, 3 credit hours
Fundamental concepts and operations of algebra. For students who do not qualify for regular placement in mathematics.

144 Pre-Calculus Algebra, 3 credit hours (GE)
The algebra of polynomial, rational, exponential, and logarithmic functions, systems of equations and inequalities, quadratic inequalities, and the binomial theorem. Prerequisite: MATH 131 or equivalent.

147 Finite Mathematics, 3 credit hours (GE)
Topics in finite mathematics and their applications. The course includes sets, counting, permutations, combinations, basic probability (including Baye’s Theorem), an introduction to statistics (including work with Binomial and Normal Distributions), matrices and their applications to Markov chains, and decision theory. Prerequisite: MATH 131 or equivalent.

149 Pre-Calculus Trigonometry, 3 credit hours (GE)
Trigonometric functions (circular), inverse trigonometric functions along with identities and trigonometric equations, vectors, complex numbers, DeMoivre’s Theorem, and polar coordinates. Prerequisite: MATH 144 or equivalent.

150 Pre-Calculus Algebra and Trigonometry, 4 credit hours (GE)
The algebra of polynomial, rational, exponential, and logarithmic functions, systems of equations and inequalities, quadratic inequalities, and the binomial theorem. Trigonometric functions (circular), inverse trigonometric functions along with identities and trigonometric equations, vectors, complex numbers, DeMoivre’s Theorem, and polar coordinates. Prerequisite: MATH 131 or equivalent.

154 The Nature of Mathematics, 3 credit hours (GE)
Basic concepts from set theory, logic, geometry, statistics; the fundamental ideas of calculus, and a survey of the development and application of modern mathematics. This course is designed to satisfy the general education requirement in mathematics while providing an overview of the discipline. Prerequisite: MATH 131 or equivalent.

157 Introduction to Statistics, 3 credit hours (GE)
Descriptive and inferential statistics, frequency distributions, measures of central tendency and dispersion, probability and sampling, estimation, hypothesis testing, confidence intervals, linear regression, correlation, and design of experiments. Prerequisite: MATH 131 or equivalent.

160 Basic Mathematics for Elementary Teachers I, 3 credit hours
An overview of induction and deduction, sets, numbers, and numeration. Topics include patterns and sequences, counting techniques, sets, relations and functions, logic (implication and validity), numeration (base and place syntax and algorithms), number systems (axioms, rational operations, and modular arithmetic), and measurement. Where appropriate, these topics are applied to problem-solving strategies. This course is intended for Elementary Education majors and is aligned with the Alabama Course of Study—MATHEMATICS, but is open to any student meeting the prerequisite. (Note: Students who have completed MATH 164 with a “C” or better will not get credit for MATH 160.) Prerequisite: A grade of C or better in MATH 144 and MATH 147.

162 Basic Mathematics for Elementary Teachers II, 3 credit hours
A continuation of MATH 160. Topics include the real number system (irrational numbers), geometry (geometric shapes, angles, constructions, and measures of length, area, and volume), the metric system, symmetries, descriptive statistics (frequency distributions, measures of central tendency and variation, and normal distributions), and elementary inferential statistics. This course is intended for Elementary Education majors and is aligned with the Alabama Course of Study–MATHEMATICS, but is open to any student meeting the prerequisite. Prerequisite: A grade of C or better in MATH 160.

164 Basic Mathematics, 3 credit hours
Topics (selected in concert with Alabama Course of Study-MATHEMATICS) include an introduction to logic, basic number theory, arithmetic algorithms, elementary geometry and measurement, congruence and similarity, and skills and strategies for problem solving. Prerequisite: A grade of C or better in both MATH 144 and 147.

170 Calculus I, 4 credit hours (GE)
The study of the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; the definite integral and its basic applications to area problems. Applications of the derivative are covered in detail, including approximations of error using differentials, maximum and minimum problems, and curve sketching using calculus. Prerequisite: MATH 149 or 150 or equivalent.

171 Calculus II, 4 credit hours
The study of vectors in the plane and in space, lines and planes in space, applications of integration (such as volume, arc length, work, and average value), techniques of integration, infinite series, polar coordinates, and parametric equations. Prerequisite: MATH 170 or equivalent.

185 Survey of Mathematics, 1 credit hour
This course provides an overview of the nature of mathematics in both a historical and modern context, and its relationship to other disciplines. Students will learn about what mathematicians do and why, and will hear a variety of speakers discuss career opportunities in mathematics and related disciplines. The course is graded pass/fail, and is open to all majors. Prerequisite: MATH 144 or higher.

202 Mathematics of Games, 3 credit hours
Introduction to various mathematics concepts as they apply to games. This will include counting techniques, probability, decision trees, and an introduction to game theory. Prerequisite: MATH 144 or higher.

205 Introduction to the History of Mathematics, 3 credit hours
Introduction to the history of mathematics, from early numeration systems through the beginnings of calculus. Prerequisite: MATH 170.

222 Algorithm Development, 3 credit hours
Introduction to programming and algorithm development. Includes basic I/O and file operations, data types, loops and decisions, functions and procedures, and the use of these topics in developing algorithms applicable to various mathematical problems. Prerequisites: MATH 144 and CIS 161 or consent of instructor.

226 Fractal Geometry, 2 credit hours
Introduction to the concepts of iteration, fractals, fractal dimension, and chaos. Prerequisites: CIS 161 and MATH 170.

247 Introduction to Discrete Mathematics, 3 credit hours
Introduction to various topics in discrete mathematics, including the study of sets, logic, relations, functions, counting techniques, graphs, trees, and mathematical induction. Prerequisite: MATH 170 or consent of instructor.

261 Introduction to Programming and Computer Algebra Systems, 3 credit hours (GE)
Fundamentals of computing, computer programming in BASIC, Maple V, and other computer algebra systems, internet resources, and the PCTeX typesetting language. Prerequisite: MATH 170.

271 Sequences, Series, and Indeterminate Forms, 2 credit hours
Sequences and series of numbers and functions, along with supporting theory and applications. Topics include convergence tests, Taylor’s theorem, L’Hôpital’s rule, and an introduction to uniform convergence. Prerequisite: MATH 171.

272 Calculus III, 4 credit hours
The study of vector functions, functions of two or more variables, partial derivatives (including applications), quadric surfaces, multiple integration, and vector calculus (including Green’s Theorem, curl and divergence, surface integrals, and Stoke’s Theorem). Prerequisite: MATH 171 or equivalent.

287 Introduction to Graph Theory, 3 credit hours
An introduction to the basic concepts of graph theory, including the properties and applications of various types of graphs. Although some material will be presented in the standard theorem-proof format, most of the classwork will be computational in nature. Prerequisite: MATH 170 or consent of instructor.

295 Special Topics, 3 credit hours
Topic will be announced prior to registration. Topics vary. Course may be repeated for credit as topic changes. Prerequisite: A grade of C or better in MATH 170.

299 Independent Study, 1–3 credit hours
Independent study in a selected mathematics area to further a student’s knowledge and competence in that area. Material to be studied will be determined in consultation with the faculty member supervising the course, the student’s adviser, and the department chair. Topics vary. Course may be repeated for credit as topic changes.

310 Foundations of Mathematics, 3 credit hours
Introduction to abstract mathematical reasoning, including set theory, logic, mathematical analysis, and the structure of the real number system. Prerequisite: MATH 247. Corequisite: MATH 272 or consent of instructor.

320 College Geometry, 3 credit hours
Concepts and methods of geometry for advanced study and for teaching geometry at the secondary-school level. Includes Euclidean, solid, and spherical geometry. Prerequisite: MATH 170 or consent of instructor.

330 Numerical Analysis, 3 credit hours
The use of computers to obtain numerical solutions to systems of linear equations, root approximations of other equations, least squares, numerical integration. Prerequisites: MATH 261 and 272.

336 Mathematical Statistics, 3 credit hours
Probability basics, discrete and continuous random variables, multivariate distributions, properties of expectation, laws of large numbers, special distributions, moment generating functions, the Central Limit Theorem, sampling, estimation of parameters, hypothesis testing, nonparametric methods, and linear regression. Prerequisite: MATH 171.

350 Differential Equations, 3 credit hours
Introduction to ordinary differential equations, their solutions and practical applications. Prerequisite: MATH 272 or equivalent.

376 Complex Analysis, 3 credit hours
Representations of complex numbers, complex arithmetic, complex functions of a complex variable, calculus of complex functions, harmonic functions, analytic functions, contour integrals, Cauchy’s theorem, and selected topics. Prerequisite: MATH 272.

385 Mathematics Colloquium, 1 credit hour
Topics will be announced prior to registration. This course provides students with the opportunity to explore areas of mathematics not normally found in the undergraduate curriculum, in an informal, lecture/discussion format. The course is graded pass/fail, and may not be used as an upper-level mathematics elective. Topics vary. Course may be repeated for credit as topic changes. Prerequisite: MATH 310.

387 Graph Theory, 3 credit hours
Advanced topics in graph theory, including graphs and diagraphs, vertex and edge colorings, planar graphs, and Ramsey numbers. Although some of the class will be computational, much of it will be presented in theorem-proof format. Prerequisite: MATH 310 or consent of instructor.

390 Linear Algebra, 3 credit hours
Coordinate systems, vector algebra, linear transformations, solutions of systems of linear equations, and introduction to matrix theory. Prerequisite: MATH 272 (may be taken concurrently).

395 Special Topics, 3 credit hours
Topics will be announced prior to registration. Topics vary. Course may be repeated for credit as topic changes.

399 Independent Study, 1–3 credit hours
Independent study in a selected mathematics area to further a student’s knowledge and competence in that area. Material to be studied will be determined in consultation with the faculty member supervising the course, the student’s adviser, and the department chair. Topics vary. Course may be repeated for credit as topic changes.

440 Abstract Algebra, 3 credit hours
An introduction to algebraic systems, including groups, rings, and fields. Prerequisite: MATH 310.

470 Real Analysis, 3 credit hours
A study of functions, including convergence, continuity, differentiability, infinite series expansions, and the supporting theory. Prerequisites: MATH 272 and 310.

480 Topology, 3 credit hours
Theory of sets, metric spaces, topological spaces, connectedness, and compactness. Prerequisite: MATH 310.

484 Directed Reading in Mathematics, 1 credit hour
In this course students will explore areas of interest in mathematics and propose a topic for the senior seminar project. The course is graded pass/fail. Prerequisite: MATH 310 or permission of department chair.

485 Senior Seminar, 1 credit hour
This course provides students with the opportunity to synthesize previous work through the preparation and presentation of a research paper. Prerequisite: MATH 484.

495 Special Topics, 3 credit hours
Topic will be announced prior to registration. Topics vary. Course may be repeated for credit as topic changes.

498 Mathematics Colloquium, 1 credit hour
Opportunity to engage in mathematics at the professional level, through weekly talks given by UM mathematicians and invited speakers. Graded pass/fail. Topics vary. Course may be repeated for credit as topic changes. Corequisite: MATH 310 and junior standing.

499 Independent Study, 1–3 credit hours
Independent study in a selected mathematics area to further a student’s knowledge and competence in that area. Material to be studied will be determined in consultation with the faculty member supervising the course, the student’s adviser, and the department chair. Topics vary. Course may be repeated for credit as topic changes.