21&62:640:037
Study Skills for Mathematics Development (N2)
Prerequisite: 21&62:300:102 or placement by examination. Corequisite: 21&62:640:112.
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21&62:640:103
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&62:300:102 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.
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21&62:640:112
College 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&62:300:102 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.
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21&62:640:113
College 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&62:300:102 or placement by examination. Successful completion of this course with a grade of C or better fulfills the mathematics proficiency requirement.
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21&62:640:114
Precalculus (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.
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21&62:640:119
Basic 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.
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21&62:640:135
Calculus I (4)
Introduction to analytic geometry; inequalities, functions, limits, continuity, differentiation of algebraic functions, applications; introduction to definite and indefinite integration; and 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.
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21&62:640:136
Calculus II (4)
Applications of integrals, calculus of trigonometric and inverse
trigonometric functions, techniques of integration, indeterminate
forms, infinite series and Taylor's series, and 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.
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21&62:640:155-156
Honors 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.
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21&62:640:219
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&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.
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21&62:640:235
Calculus III (4)
Introduction to vectors in the plane, solid analytic geometry, and vectors in three dimensions; partial differentiation; 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.
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21&62:640:237
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&62:640:119 or 135 or 155.
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21&62:640:238
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.
Prerequisite: 21&62:640:136 or 156, or permission of instructor.
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21&62:640:311-312
Advanced 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.
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21&62:640:314
Elementary Differential Equations (3)
Ordinary differential equations, including solution by series and their applications; emphasis on linear equations.
Prerequisite: 21&62:640:136 or 156.
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21&62:640:327
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&62:640:119 or 135 or 155, or permission of instructor.
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21&62:640:350
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&62:640:136 or 156, or permission of instructor. Credit not given for both 21&62:640:219 and 350.
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21&62:640:353
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&62:640:350.
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21&62:640:397,398
Mathematics Teaching Apprenticeship (3,3)
Practice in the teaching of mathematics supervised by members of the faculty.
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21&62:640:403
Introductory Theory of Functions of a Complex Variable (3)
Analytic functions, Cauchy's integral theorem, contour integration, residues, series, and conformal mapping.
Prerequisite: 21&62:640:311 or permission of instructor.
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21&62:640:410
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&62:640:235 or permission of instructor.
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21&62:640:423
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&62:640:314.
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21&62:640:424
Operations 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.
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21&62:640:432
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&62:640:235, 238.
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21&62:640:433
Projective Geometry (3)
Projective and affine curves; polynomial rings; ideals; Hilbert's basis
theorem; the nullstellungsatz; local rings; singularities.
Prerequisite: 21&62:640:238.
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21&62:640:435-436
Geometry I,II (3,3)
Axiomatic systems, finite geometries, Euclidean geometry, and non-Euclidean geometry.
Prerequisites: 21&62:640:235, 350.
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21&62:640:441-442
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 isometrics.
Prerequisite: 21&62:640:238 or permission of instructor.
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21&62:640:451-452
Abstract 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.
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21&62:640:456
Theory 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.
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21&62:640:473
Numerical 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.
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21&62:640:475,476
Applied 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.
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21&62:640:477
Fundamental 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.
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21&62:640:491,492
Mathematics Seminar (3,3)
Selected topics in mathematics; individual study stressed.
Prerequisite: Permission of instructor. Students may enroll multiple times.
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21&62:640:493,494
Individual Studies in Mathematics (3,3)
Individual studies of selected topics in mathematics.
Prerequisite: Permission of instructor. Students may enroll multiple times.
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