21&62:640:037Study Skills for Mathematics Development (N2)
Prerequisite: 21&62:003:102 or placement by examination. Corequisite: 21&62:640:112. |
21&62:640:103Mathematics 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&62:003:102 or placement by examination. Successful completion of this course with a grade of C or better fulfills the mathematics proficiency requirement. Credit not given for 21&62:640:103 after receiving credit for any other mathematics course. Intended for students in a liberal arts major who do not plan to enroll in additional courses in mathematics. |
21&62:640:112College Algebra Intensive (3) Covers the same material as 21&62:640:113, but meets for three 80-minute sessions each week. Intended for students who need extra class time and individualized attention. Prerequisite: 21&62:003:102 or placement by examination. Corequisite: 21&62:640:037. Credit is not given for both 21&62:640:112 and 113. Successful completion of this course with a grade of C or better fulfills the mathematics proficiency requirement. |
21&62:640:113College Algebra (3) 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. Prerequisite: 21&62:003:102 or placement by examination. Successful completion of this course with a grade of C or better fulfills the mathematics proficiency requirement. |
21&62:640:114Precalculus (3) Algebraic, rational, trigonometric, logarithmic, and exponential functions; functions and inverse functions; solutions of nonlinear inequalities; advanced factoring techniques. Prerequisite: 21&62:640:112 or 113 or placement by examination. Intended for students who plan to enroll in additional courses in mathematics. |
21&62:640:119Basic Calculus (3) Intuitive approach to calculus, with emphasis on applications, differential and integral calculus, and multivariable calculus. Prerequisite: 21&62:640:112 or 113 or placement by examination. Credit not given for both 21&62:640:119 and 135. Intended for students majoring in information systems, business, social science, or the liberal arts. |
21&62:640:135Calculus I (4) Introduction to analytic geometry; inequalities, functions, limits, continuity, differentiation of algebraic functions, applications, and introduction to definite and indefinite integration, calculus of exponential and logarithmic functions. Prerequisite: 21&62:640:114 or placement by examination. Credit not given for both 21&62:640:119 and 135. |
21&62:640:136Calculus II (4) Applications of integrals, calculus of trigonometric and inverse
trigonometric functions, techniques of integration, indeterminate
forms, infinte series and Taylor's series, polar coordinates. Prerequisite: 21&62:640:135 or 155 (4 credits). Students who took 21&62:640:135 or 155 for 3 credits, prior to spring 2000, should arrange with the department to complete the missing credits before taking Calculus II. |
21&62:640:155-156Honors Calculus (4,4) Covers material selected from 21&62:640:135, 136 in greater depth with emphasis on mathematical rigor. Prerequisite: Invitation by department based on placement examination. Open to all majors. |
21&62:640:219Basic 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&62:640:119 or 135 or 155 or permission of instructor. Credit not given for both 21&62:640:219 and 350. Intended for students majoring in business, social science, information systems, or the liberal arts. Mathematics majors and minors cannot get credit for 21&62:640:219. |
21&62:640:235Calculus III (4) Introduction to vectors in the plane, solid analytic geometry, and vectors in three dimensions; partial differentiaion; multiple integrals; applications. Prerequisite: 21&62:640:136 or 156 (4 credits). Students who took 21&62:640:136 or 156 for 3 credits, prior to fall 2000, should arrange with the department to complete the missing credits before taking Calculus III. |
21&62:640:237Discrete 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&62:640:119 or 135 or 155. |
21&62:640:238Foundations 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 stucture of the real number system and elements of real analysis. Proof techniques are stressed. Prerequisite: 21&62:640:136 or 156 or permission of instructor. |
21&62:640:311-312Advanced Calculus I,II (3,3) The calculus of functions of one or more real variables; transformations and implicit functions; line and surface integrals. Prerequisites: 21&62:640:235, 238, and 350, or permission of instructor. |
21&62:640:314Elementary Differential Equations (3) Ordinary differential equations, including solution by series and their applications; emphasis on linear equations. Prerequisite: 21&62:640:136 or 156. |
21&62:640:327Probability 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&62:640:119 or 135 or 155 or permission of instructor. |
21&62:640:350Linear 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&62:640:136 or 156 or permission of instructor. Credit not given for both 21&62:640:219 and 350. |
21&62:640:353Theory of Equations (3) Algebraic equations, including methods of solving equations; introductory theory of solvability; tranformations; algebraic invariants; the fundamental theorem of algebra. Prerequisite: 21&62:640:350. |
21&62:640:397,398Mathematics Teaching Apprenticeship (3,3) Practice in the teaching of mathematics supervised by members of the faculty. |
21&62:640:403Introductory Theory of Functions of a Complex Variable (3) Analytic functions; Cauchy's integral theorem; contour integration; residues; series; and conformal mapping. Prerequisite: 21&62:640:311 or permission of instructor. |
21&62:640:410Vector 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&62:640:235 or permission of instructor. |
21&62:640:423Elementary 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&62:640:314. |
21&62:640:424Operations Research (3) Major topics and techniques in operations research; topics chosen from transportation problems, scheduling problems, linear programming, dynamic programming, mathematical inventory theory, and game theory. Prerequisite: 21&62:640:235 or permission of instructor. |
21&62:640:432Introductory 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&62:640:235, 238. |
21&62:640:433Projective Geometry (3) Projective and affine curves; polynomial rings; ideals; Hilbert's basis
theorem; the nullstellungsatz; local rings; singularities. Prerequisite: 21&62:640:238. |
21&62:640:435-436Geometry I,II (3,3) Axiomatic systems; finite geometries; Euclidean geometry; non-Euclidean geometry. Prerequisites: 21&62:640:235, 350. |
21&62:640:441-442Topology 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 isometrics. Prerequisite: 21&62:640:238 or permission of instructor. |
21&62:640:451-452Abstract Algebra I,II (3,3) Elementary set theory; fundamental structures of algebra, including semigroups, groups, rings, and fields; homomorphisms and isomorphisms; factor group, rings of residue classes, and other factor structures. Prerequisites: 21&62:640:238, 350, or permission of instructor. |
21&62:640:456Theory of Numbers (3) Divisibility of integers; the series of primes; number-theoretic functions; continued fractions; congruences; diophantine equations; quadratic residues; the Pell equation. Prerequisite: 21&62:640:238 or permission of instructor. |
21&62:640:473Numerical Analysis (3) Error analysis; interpolation theory; numerical solution of equations; polynomial approximations; numerical differentiation and integration; solution of differential equations. Prerequisites: 21&62:198:101 and 21&62:640:136 or 156. |
21&62:640:475-476Applied Mathematics I,II (3,3) Fourier series and integrals; boundary value problems; matrices; finite differences; special functions; numerical methods. Prerequisite: 21&62:640:314 or permission of instructor. |
21&62:640:477Fundamental Mathematical Probability (3) Fundamentals of probability theory for discrete and continuous
distributions; random variables and probability distributions; Bayes's
theorem; the Bernoulli and Poisson distributions; central limit
theorem; strong law of large numbers. Prerequisite: 21&62:640:136 or 156 or permission of instructor. |
21&62:640:491,492Mathematics Seminar (3,3) Selected topics in mathematics; individual study stressed. Prerequisite: Permission of instructor. Students may enroll multiple times. |
21&62:640:493,494Individual Studies in Mathematics (3,3) Individual studies of selected topics in mathematics. Prerequisite: Permission of instructor. Students may enroll multiple times. |
