# Courses (Mathematics 640)

 Note: Some upper-level courses may be given in alternate years. Please check with departmental advisers. 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 Fundamental Mathematics Systems I (R) (3) Sets, logic, number systems, algebraic structures, and the concept of functions and inverses.  Prerequisite: 50:640:042 or appropriate score on mathematics placement examination. Particularly suitable for students of elementary education. 50:640:104 Fundamental Mathematics Systems II (R) (3) Informal geometry, measurement in 2-D and 3-D, coordinate geometry, transformational geometry, similarity vs. congruence, and functions. Prerequisite: 50:640:042 or appropriate score on mathematics placement examination. Particularly suitable for students of elementary education. 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: 50:640:042 or 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: 50:640:042 or 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, Economics, and Biology (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: 50:640:042 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: 50:640:042 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 Unified 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 Unified 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, Economics, and Life Sciences (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 Unified 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: 50:640:115 or permission of instructor. 50:640:252 Linear Algebra (3) A more rigorous treatment of topics in Vector spaces, the calculus of matrices, and the theory of determinants. Prerequisite: 50:640:122 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. Prerequisites: 50:640:121, 122. 50:640:311-312 Advanced Calculus 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. Prerequisites: 50:640:221, 250, and 300. 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. Prerequisites: 50:640:221 and 250, or permission of instructor. 50:640:331 Introduction to Actuarial Mathematics (3) Survey of calculus and linear algebra, with particular emphasis on topics such as complex exponents and logarithms. Pre- or corequisite: 50:640:221. Preparation course for the first exam of the college of actuaries. 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, 300, and 356, 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 Computational Mathematics (3) Designed to emphasize the computational aspect of number theory. The most important topics to treat are the prime numbers, pseudo primes, and their applications, especially cryptography; prime factorization of composite numbers via several different methods explored. Computer simulation emphasized. Prerequisite: 50:640:250 or permission of instructor. Alternate substitute for 50:640:356. 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 Introductory Theory of Functions of a Complex Variable (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. Prerequisites: 50:640:221, 300, and 311; or permission of instructor. 50:640:410 Vector Analysis (3) Vector calculus and its application to physics. Gauss, Stokes, Green theorems. Potentials. Prerequisite: 50:640:221. 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. Prerequisites: 50:640:121, 122, 221, and 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. 50:640:463-464 Partial Differential Equations and Boundary Value Problems (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: 50:640:363-364. 50:640:465 Introduction to the Fundamentals of Mathematics (3) Selected topics from the different areas of mathematics. Prerequisite: 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. 50:640:472 Special Functions (3) Theory and applications of functions frequently used in modern analysis such as the gamma function, delta function, Green's functions, Legendre functions, Bessel functions, Schwarz distributions, and others. Prerequisite: 50:640:314. 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)