50:640:041 Elementary Algebra (NC) The system of integers, exponentiation, graphing, solution of equations, and basic notions of geometry. For students who do not have the usual background in mathematics for college admission.

50:640:042 Intermediate Algebra (NC) Study of algebraic operations on polynomials, integral and rational exponents, linear and quadratic equations, systems of equations, and the function concept. Prerequisite: 50:640:041 or placement by basic skills test.

50:640:103 Introduction to Math for Liberal Arts (R) (4) Topics in mathematics and statistics, including Mathematics of Elections, Power,
Appointment, Touring, Networks, and Scheduling; Growth Models; Financial Math; Surveys and Polls; Graphs and Charts; Probability; and Statistics. This course also incorporates review sessions for arithmetic operations involving integers, decimals, and fractions. Prerequisite: Mathematics placement examination. For students who have no intention of taking additional mathematics courses. Students who plan to take additional courses in mathematics should take 640:104, 640:113, or 640:115 instead.

50:640:104 Introduction to College Algebra for Science and Business (R) (4) A review of algebra intended to prepare the student for Pre-Calculus. Topics include: solving linear equations and inequalities, equations and graphs of lines and conic sections, polynomials, exponents, factoring, rational expressions and equations, completing the square, quadratic equations, and radicals. This course satisfies the LQR, MAT, and QNT requirements. Prerequisite: Mathematics placement examination. For students majoring or planning to major in business or the sciences who will need to take at least 640:113 or 640:115.

50:640:105 Finite Mathematics (R) (3) Introduction to important and fundamental areas of mathematics that do not require calculus. Topics include set theory; functions and relations; and the algebra of vectors and matrices with applications to systems of linear equations, linear programming, and game theory. Particularly suitable for business and economics majors.

50:640:106 An Introduction to Mathematical Thought (R) (3) The topics covered are: set and number theory, the concept of functions and inverses, logic and reasoning, validity of arguments, inductive vs. deductive reasoning, group concepts, coordinate and transformational geometry in 2-D/3-D, the concept of measurement, and networks. Prerequisite: Appropriate score on mathematics placement examination. For the student who has serious interest in learning something about mathematical thought and its applications, but who is not planning to major in mathematics.

50:640:108 Numbers and Beyond (R) (3) Study of the properties and qualities of number systems and spatial relationships in geometry. Topics needed to explore the developmental beauty of mathematics discussed. Some are logic and reasoning; set theory and number theory; function (not limited to linear); sequences; basic concepts from calculus; group and field concepts; and spatial concepts such as rotations, translations, and geometric objects. Prerequisite: Appropriate score on the mathematics placement examination. This course is designed for students who are considering secondary certification. In addition, it also satisfies the 3-credit mathematics requirement for any other major.

50:640:113 Precalculus for Business and Economics (R) (3) A study of real numbers with regard to algebraic operations and order properties. Introduction to complex numbers and logarithmic and exponential functions. Prerequisite: 50:640:104 or appropriate score on the mathematics placement examination. Credit not given for both this course and 50:640:115. A nonrequired preparatory course for those students who must take 50:640:130.

50:640:114 Trigonometry and Analytic Geometry (R) (3) Elements of plane trigonometry and trigonometric identities. Plane loci, properties of the conic sections, and transformations of coordinates. The line, plane, and quadric surface in three dimensions.

50:640:115 Precalculus College Mathematics (R) (3) Algebraic expressions; algebraic equations; functions; graphing; and exponential, logarithmic, and trigonometric functions. Prerequisite: 50:640:104 or appropriate score on the mathematics placement examination. Credit not given for both this course and 50:640:113. A nonrequired preparatory course for those students who must take 50:640:121-122.

50:640:116 Elements of Calculus (R) (3) A one-semester survey of the elements of calculus, with emphasis on applications. Topics include elementary functions and their derivatives, rate of change, curve tracing, velocity, minimum and maximum, law of growth and decay, antiderivatives, and definite integral. Students who plan to take more than one semester of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 130.

50:640:121 Calculus I (R) (4) An introduction to analytic geometry, differentiation of algebraic and transcendental functions, applications of differentiation, and a brief introduction to integration. Prerequisite: 50:640:115 or appropriate score on the mathematics placement examination. Students who plan to take more than one semester of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 130.

50:640:122 Calculus II (R) (4) An extensive introduction to integration and the definite integral, transcendental functions, methods of integration, applications, and infinite series. Prerequisite: 50:640:121 or equivalent.

50:640:129 Linear Mathematics for Business and Economics (R) (3) Basic algebra, matrices, and linear programming with applications to problems in business and economics. Prerequisite: 50:640:113 or appropriate score on the mathematics placement examination. A mathematics foundations course for the student majoring in business and economics.

50:640:130 Calculus for Business and Economics (R) (3) A one-semester survey of the elements of calculus with emphasis on applications in business, economics, and life sciences. Topics covered are basic algebra, derivatives, maximum/minimum problems, integration, and partial differentiation. Prerequisite: 50:640:113 or appropriate score on the mathematics placement examination. Students who plan to take more than one semester of calculus should follow the sequence 50:640:121-122. Credit will not, in general, be given for more than one of the courses 50:640:116, 121, or 130.

50:640:182 Elements of Probability (R) (3) A gentle introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Topics include: axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, and Markov chains. Prerequisite: 50:640:122.

50:640:190 Introduction to Higher Mathematics (R) (3) An encyclopedic survey of different branches of mathematics. Designed primarily for mathematics majors.

50:640:221 Calculus III (4) Solid analytic geometry, partial differentiation, multiple integrals, and applications. Prerequisite: 50:640:122.

50:640:237 Discrete Mathematics (3) Sets, relations, and functions. Mathematical induction; recursion; propositional logic; introduction to first order logic; Boolean algebra; and elements of combinatorics. Introduction to graphs and trees. Prerequisites: 50:640:113 and 121, or placement.

50:640:250 Linear Algebra (3) Vector spaces, the calculus of matrices, and the theory of determinants. Prerequisite: 50:640:121 or permission of instructor.

50:640:253 Linear Algebra with Applications (3) The topics from 640:250 plus applications using MatLab. Students may not receive credits for this course and 640:250. Prerequisite: 50:640:121 or permission of instructor.

50:640:300 Mathematical Reasoning with Proofs (3) Course develops two fundamental components of "writing mathematics": reasoning (thinking about the proof) and writing (formulating and writing the ideas precisely using logical statements). Begins with illustrative examples and general guidelines. Prerequisite: 50:640:122.

50:640:311-312 Introduction to Real Analysis I,II (3,3) A study of convergence, uniform convergence, and continuity, with applications to series expansions in one and several variables; partial differentiation; multiple, line, and surface integrals. Prerequisite: 50:640:221.

50:640:314 Elementary Differential Equations (3) Theory of ordinary differential equations. Power series methods and existence and uniqueness theorems. Applications to problems in economics, biology, chemistry, physics, and engineering. Prerequisite: 50:640:221 or permission of instructor.

50:640:331 Probability and Stochastic Processes (3) A mathematically precise introduction to the basic concepts and essential introductory results of probability: a branch of math aimed at the description and study of random phenomena. Prerequisite: 50:640:122, or permission of instructor.

50:640:345 Mathematics on the Web (3) Designed to get acquainted with using the World Wide Web for finding mathematical information and communicating mathematics.
Prerequisites: 50:640:121, 122, 221, 250, or permission of instructor. Recommended also as an elective for students majoring in computer science.

50:640:347 Visualizing Mathematics by Computer (3) A comprehensive introduction to symbolic computational packages and scientific visualization through examples from calculus and geometry. Covers two-dimensional, three-dimensional, and animated computer graphics using Maple, Mathematica, and Geomview. No programming knowledge required. Prerequisites: 50:640:121, 122, 221, or permission of instructor. Recommended also as an elective for students majoring in computer science.

50:640:351-352 Introduction to Modern Algebra (3,3) The study of groups, rings, field, and linear spaces.
Prerequisites: 50:640:250 and 300, or permission of instructor.

50:640:356 Theory of Numbers (3) Properties of the natural numbers, simple continued fractions, congruences, and elementary arithmetical functions. Prerequisites: 50:640:122 and 300, or permission of instructor.

50:640:357 Introduction to Computational Mathematics (3) An introduction to numerical techniques for solving mathematical problems on a computer: the IEEE internal representation of floating point numbers, interpolation, root finding, numerical integration, numerical differentiation, optimization. Prerequisite: 50:640:221, 50:640:250/253, or permission of instructor. Recommended also as an elective for students majoring in computer science.

50:640:358 Advanced Discrete Mathematics (3) Covers recurrent problems, generating functions: exponential and Dirichlet, number theory, special numbers, graphs, trees, asymptotics, difference equations, and other topics. Prerequisite: 50:640:237.

50:640:363-364 Computational Engineering Mathematics I,II (3,3) Covers integral theorems of vector analysis, complex variables, series solutions to differential equations, Laplace and Fourier transforms, and use of mathematical software languages such as Maple and Mathematica. Prerequisite: 50:640:314.

50:640:368 Mathematics for Economic and Business Analysis (3) Emphasizes the mathematical foundations of analysis in optimization of multivariate functions; differential and difference equations; linear programming; problems with particular consideration to business and economic interpretation. Prerequisites: 50:640:129, 130.

50:640:375 Fourier Series (3) Introduction to the solution of boundary value problems in the partial differential equations of mathematics, physics, and engineering by means of Fourier series, Fourier transforms, and orthogonal functions. Prerequisite: 50:640:314.

50:640:396 Honors Program in Mathematics (3)

50:640:401 Foundations of Analysis I (3) Introduction to basic concepts of topology and analysis, including point sets, uniform continuity, uniform convergence, compactness, metric spaces, Jordan curves, and the Riemann-Stieljes integral. Pre- or corequisite: 50:640:311.

50:640:402 Foundations of Analysis II (3) Hilbert Space, Banach Space, Lebesgue integral, and elements of functional analysis. Prerequisite: 50:640:401.

50:640:403 Complex Analysis (3) Topological concepts, analytic functions, elementary conformal mappings, line integrals, Cauchy's theorem, Cauchy's integral formula, and the calculus of residues. Taylor and Laurent series, normal families, Riemann mapping theorem, and harmonic functions. Prerequisite: 50:640:311 or permission of instructor.

50:640:427 Advanced Differential Equations (3) Autonomous and nonautonomous systems of differential equations; phase plane analysis and stability of critical points; the perturbation method applied to nonlinear equations; modeling and analysis of environmental, biological, chemical, and economic systems. An article interdisciplinary in nature discussed in detail. Prerequisites: 50:640:250 and 314.

50:640:432 Introduction to Differential Geometry (3) Space, curves, curvature, torsions, Frenet formulas, curvilinear coordinates, fundamental forms, mean and Gaussian curvature, and the general theory of surfaces. Prerequisites: 50:640:221 and 300, or permission of instructor.

50:640:435 Geometry (3) Euclidean and non-Euclidean geometries, geometric transformations. Complex language in geometry. Moebius transformations. Symmetries and tessellations. Projective geometry. Regular polytopes. Prerequisite: 50:640:300 or permission of instructor.

50:640:441 Introductory Topology (3) A study of the standard topics of set theoretic topology. Prerequisites: 50:640:221 and 300, or permission of instructor.

50:640:450 Advanced Linear Algebra (3) Continuation of 50:640:250/253. Abstract vector spaces, linear transformations, inner product spaces, diagonalization, singular value decomposition, Jordan canonical form, numerical techniques, and applications. Prerequisites: 50:640:250/253, 50:640:300, or permission of instructor.

50:640:463-464 Applied Partial Differential Equations (3,3) An advanced course in methods of applied mathematics. Covers elementary partial differential equations in the engineering and physical sciences. Simple models (heat flow, vibrating strings, and membranes) are emphasized. Discusses method of separation of variables, Fourier series, methods of characteristics for linear wave equations, introduction to finite-difference numerical methods for partial differential equations, and other topics. Prerequisites: 50:640:221, 50:640:314, or permission of instructor.

50:640:466-467 Mathematical Methods in Systems Biology (3,3) Introduction to the use of mathematical methods in biology. Basics of ordinary differential equations and classical examples in mathematical biology systems and control theory, system biology, advanced models, and biological networks. Prerequisites: 50:640:300 and 314.

50:640:477-478 Mathematical Theory of Probability (3,3) An introduction to the mathematical treatment of random phenomena with a focus on proofs and rigorous mathematical theory. Topics include: axioms of probability theory; combinatorial analysis; conditional probability and Bayes' Methods; independence; random variables; Borel-Cantelli, law of large numbers, weak and almost sure convergence, and central limit theorems. Prerequisites: 50:640:122, 182, and 250, or permission of instructor.

50:640:491,492 Mathematics Seminar I,II (3,3) Members of the seminar present individually developed reports on topics of mathematical interest. Prerequisite: 50:640:300 or permission of instructor.

50:640:493-494 Individual Study in Mathematics (BA,BA)

50:640:495-496 Honors Program in Mathematics (3,3)

50:640:497 Advanced Computational Mathematics (3) Numerical techniques for solving scientific problems with aid of a computer. Topics include: Numerical linear algebra, in particular numerical solution of linear systems of equations and the algebraic eigenvalue problem, and numerical solution of initial and boundary value problems of differential equations. Prerequisites: 50:640:221, 50:640:250/253, 50:640:314, 50:640:357, or permission of instructor.

50:640:499 Data Visualization (3) An introduction to data visualization techniques. Mathematical techniques for transforming data. Prerequisites: 50:640:250/253, or permission of instructor.