21:640:079 College Algebra Bridging Course - 107 to 109 (1) Prerequisite: 21:640:107. Optional corequisite: 21:640:114 or 21:640:119. This is a bridging course to allow students who have taken 21:640:107 to take 21:640:114 or 21:640:119. Intended for students who change their major from the humanities or social sciences to the physical sciences, mathematics, or computer science. Students who intend to major in the physical sciences, mathematics, or computer science should not plan to take 21:640:107 and this bridging course, but should take 21:640:109 instead.

21:640:104 Intermediate Algebra Intensive (3) Intended to give students the necessary numerical and algebraic skills to allow for success in subsequent courses requiring a solid foundation in quantitative reasoning. The topics contained in this course include numerical systems such as the integers and the rational numbers (fractions), variable expressions, equations and applications, graphing simple equations, polynomials, and factoring. Prerequisite: Placement by examination. Corequisite: 21:640:038.

21:640:105 Intermediate Algebra (3) Intended to give students the necessary numerical and algebraic skills to allow for success in subsequent courses requiring a solid foundation in quantitative reasoning. The topics contained in this course include numerical systems such as the integers and the rational numbers (fractions), variable expressions, equations and applications, graphing simple equations, polynomials, and factoring. Prerequisite: Placement by examination.

21:640:106 Mathematics for the Liberal Arts (3) Fundamental ideas of mathematics, selected from graph theory, game theory, mathematical logic, number theory, geometry, probability, and statistics. Prerequisite: 21:640:104 or 21:640:105 or placement by examination. Intended for students in a liberal arts major who do not plan to enroll in additional courses in mathematics. Students who have passed college algebra (107, 108, or 109), or any other higher level math course cannot receive degree credit for this course.

21:640:107 College Algebra for Humanities (3) Designed for students who intend to major or minor in one of the following subjects: humanities, social sciences, criminal justice, nursing, or public administration. The course covers functions and operations of functions, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, elementary probability and statistics. Prerequisite: 21:640:104 or 21:640:105 or placement by examination.

21:640:109 College Algebra for Science Business (3) Designed for students who intend to major or minor in one of the physical sciences, mathematics, or economics. The course covers functions and operations of functions, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, functions, polynomial and rational functions, inverse functions, systems of linear equations, algebra of matrices, and series. Prerequisite: 21:640:104 or 21:640:105 or placement by examination.

21:640:114 Precalculus (4) Algebraic, rational, trigonometric, logarithmic, and exponential functions; functions and inverse functions; solutions of nonlinear inequalities; advanced factoring techniques. Prerequisite: 21:640:109 or placement by examination. Intended for students who plan to enroll in additional courses in mathematics.

21:640:119 Applied Calculus (4) Intuitive approach to calculus, with emphasis on applications, differential and integral calculus, and multivariable calculus. Prerequisite: 21:640:108, 21:640:109, or placement by examination. Intended for students majoring in information systems, business, social science, or the liberal arts. Students minoring in mathematics or majoring in mathematics, computer science, or the physical sciences should take 21:640:114 and 21:640:135 instead.

21:640:134 Trigonometry Bridging Course (1) Prerequisite: 21:640:119. Option corequisite: 21:640:135. This is a bridging course to allow students who have taken 21:640:119 to take 21:640:135 and higher-level math courses. Intended for students who minor in mathematics, or who major in mathematics, computer science, or the physical sciences. Students who intend to minor in mathematics or major in the physical sciences, mathematics, or computer science should not plan to take 21:640:119 and this bridging course, but should take 21:640:114 instead.

21:640:135 Calculus I (4) Functions; limits; continuity; the derivative; rules of differentiation, exponential, log, trigonometric, and inverse trigonometric functions; applications; definite and indefinite integrals; the fundamental theorems of calculus; and simple substitution. Prerequisite: 21:640:114 or placement by examination.

21:640:136 Calculus II (4) Applications of the integral, volumes and arc length, exponential and trig functions revisited, techniques of integration, L'Hopital's Rule, numerical integration, improper integrals, sequences and series, Taylor's Theorem, and polar coordinates. Prerequisite: 21:640:135 or 155.

21:640:155-156 Honors Calculus (4,4) These courses rigorously cover the theory and applications of differential and integral calculus. Substantially more theory with deeper applications will be covered than in the regular calculus sequence 21:640:135-136. Prerequisite: Invitation by department based on placement exam. Open to all majors.

21:640:211 Statistics I (3) Principles, methods, and application of statistical methodology; includes frequency distributions, measures of central tendency and dispersion, simple probability, sampling, regression and correlation analysis, curve fitting, and tests of significance. Applications to natural and social sciences. Prerequisite: Math placement above 21:640:106, 107, 108, 109, or successful completion, with a grade of C or better, of one of the following courses: 21:640:106, 107, 108, 109, or any other higher-level mathematics course.

21:640:219 Basic Linear Algebra (3) Solving linear systems and Gauss-Jordan elimination; matrix algebra, determinants; vectors, affine transformations in the plane; applications to linear programming, economics, and computer graphics; eigenvalues and eigenvectors. Prerequisite: 21:640:119 or 135 or 155, or permission of instructor. Credit not given for both 21:640:219 and 350. Intended for students majoring in business, social science, or the liberal arts. Mathematics majors, applied math majors, and math minors cannot get credit for 21:640:219.

21:640:235 Calculus III (4) Introduction to vectors in the plane, solid analytic geometry, vectors in three dimensions, partial differentiation, multiple integrals, and applications. Prerequisite: 21:640:136 or 156.

21:640:237 Discrete Structures (3) Sets, relations, functions, graphs, trees, formal expressions, mathematical induction, and some algebraic structures; applications to probability and computer science; and enumerative problems in combinatorial analysis. Prerequisite: 21:640:119 or 135 or 155.

21:640:238 Foundations of Modern Mathematics (3) Basic concepts on which modern mathematics is founded; language and logical structure of mathematics; elementary set theory, including set operations, relations, and mappings; the structure of the real number system and elements of real analysis. Proof techniques are stressed. Mathematics majors should take 21:640:238 immediately after completing 21:640:136/156.
Writing intensive. Prerequisite: 21:640:136 or 156, or permission of instructor.

21:640:311-312 Advanced Calculus I,II (3,3) A rigorous development of the calculus of functions of one or more real variables: topology of Euclidean space, limits and continuity, the derivative, the Riemann integral, the Lebesgue integral, and selected topics from Fourier series, transformations and implicit functions, and line and surface integrals. Prerequisites: 21:640:235 and 238, or permission of instructor.

21:640:314 Elementary Differential Equations (3) Ordinary differential equations and their applications, includes solution by series; emphasis on linear equations. Applied mathematics majors should take 21:640:314 immediately after completing 21:640:136/156. Prerequisite: 21:640:136 or 156.

21:640:327 Probability and Statistics (3) Modern probability, statistics, and statistical inference; discrete and continuous distributions of random variables, statistical inference, hypothesis testing, linear regression, and correlation. Prerequisite: 21:640:119 or 135 or 155, or permission of instructor.

21:640:331 Introduction to Partial Differential Equations (3) Partial differential equations of science and engineering. Topics include initial and boundary value problems for parabolic, hyperbolic, and elliptic second-order equations. Stress on separation of variables, special functions, transform methods, and numerical techniques. Prerequisite: 21:640:314.

21:640:350 Linear Algebra (3) Row reduction, solving linear systems; vector spaces, subspaces, bases; linear transformations, images, and kernels; eigenvalues, eigenvectors, and diagonalization of matrices; applications to differential equations, computer graphics, and numerical calculation. Prerequisite: 21:640:136 or 156, or permission of instructor. Credit not given for both 21:640:219 and 350.

21:640:353 Theory of Equations (3) Algebraic equations, including methods of solving equations; introductory theory of solvability; tranformations; algebraic invariants; the fundamental theorem of algebra. Prerequisite: 21:640:350.

21:640:397,398 Mathematics Teaching Apprenticeship (3,3) Practice in the teaching of mathematics supervised by a member of the faculty.

21:640:403 Introductory Theory of Functions of a Complex Variable (3) Analytic functions, Cauchy's integral theorem, contour integration, residues, series, and conformal mapping. Prerequisite: 21:640:311 or permission of instructor.

21:640:410 Vector Analysis (3) Vector algebra and vector calculus, including line and surface integrals and the theorems of Green, Gauss, and Stokes; applications to physics and geometry. Pre- or corequisite: 21:640:235 or permission of instructor.

21:640:423 Elementary Partial Differential Equations (3) Partial differential equations of science and engineering. Topics include initial and boundary value problems for parabolic, hyperbolic, and elliptic second-order equations. Stress on separation of variables, special functions, transform methods, and numerical techniques. Prerequisite: 21:640:314.

21:640:432 Introductory Differential Geometry (3) Differential geometry; curves in Euclidean 3-space; regular surfaces in space; parametrization of surfaces; first fundamental form for surfaces; Gauss map and second fundamental form; intrinsic geometry of surfaces; intrinsic geometry of manifolds. Prerequisites: 21:640:235, 238.

21:640:435-436 Geometry I,II (3,3) Axiomatic systems, finite geometries, Euclidean geometry, and non-Euclidean geometry. Prerequisites: 21:640:235, 350.

21:640:441-442 Topology I,II (3,3) General topological spaces and continuous mappings; linear point set theory and plane point set theory; separation, connectedness, and compactness; localization; topological products and Tychonoff's theorem; metric spaces and isometries. Prerequisite: 21:640:238 or permission of instructor.

21:640:451-452 Abstract Algebra I,II (3,3) Fundamental structures of algebra: groups, rings and ideals, fields, homomorphisms, isomorphisms, quotients, the fundamental theorem of finite abelian groups, group actions, the Sylow theorems, Euclidean and Unique Factorization Domains, splitting fields, ruler and compass constructions, and the fundamental theorem of Galois theory. Prerequisites: 21:640:238 and 350, or permission of the instructor.

21:640:456 Theory of Numbers (3) Divisibility of integers; prime numbers; number-theoretic functions; continued fractions; congruences; diophantine equations; quadratic residues; the Pell equation. Prerequisite: 21:640:238 or permission of instructor.

21:640:473 Numerical Analysis (3) Error analysis; interpolation theory; numerical solution of equations; polynomial approximations; numerical differentiation and integration; solution of differential equations. Prerequisite: 21:640:136 or 156.

21:640:475-476 Applied Mathematics I,II (3,3) Fourier series and integrals; boundary value problems; matrices; finite differences; special functions; numerical methods.
Writing intensive. Prerequisite: 21:640:314 or permission of instructor.

21:640:491,492 Mathematics Seminar (3,3) Selected topics in mathematics; individual study stressed.
Writing intensive. Prerequisites: 21:640:238 and senior standing, or permission of instructor. Students may enroll multiple times.

21:640:494 Individual Studies in Mathematics (3) Individual studies of selected topics in mathematics. Prerequisite: Permission of instructor. Students may enroll multiple times.