21:640:038
Intermediate Algebra Intensive (Noncredit)
Prerequisite: Placement by examination.
Corequisite: 21:640:104.
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21:640:104
Intermediate Algebra Intensive (3)
This course is 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.
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21:640:105
Intermediate Algebra (3)
This course is 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.
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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.
Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 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.
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21:640:107
College Algebra for Humanities (3)
This course has been 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.
Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or placement by examination.
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21:640:108
College Algebra for Business (3)
This course has been designed for students who intend to major or minor in business. The course covers functions and operations of function, operations on polynomials, fractions, solution of linear and quadratic equations and inequalities, graphing of linear and quadratic functions, solution of word problems, functions, inverse functions, systems of equations, algebra of matrices.
Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or placement by examination.
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21:640:109
College Algebra for Physical Sciences (3)
This course has been 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.
Prerequisites: 21:003:102 or 21:300:102 or 21:640:102 or 21:640:104 or 21:640:105 or by placement by examination.
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21:640:114
Precalculus (3)
Algebraic, rational, trigonometric, logarithmic, and exponential functions; functions and inverse functions; solutions of nonlinear inequalities; advanced factoring techniques.
Prerequisite: 21:640:112 or 113, or placement by examination. Intended for students who plan to enroll in additional courses in mathematics.
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21:640:119
Basic Calculus (3)
Intuitive approach to calculus, with emphasis on applications, differential and integral calculus, and multivariable calculus.
Prerequisite: 21:640:112 or 113, or placement by examination. Credit not given for both 21:640:119 and 135. Intended for students majoring in information systems, business, social science, or the liberal arts.
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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 integration, the fundamental theorems of calculus, and simple substitution.
Prerequisite: 21:640:114 or placement by examination. Credit not given for both 21:640:119 and 135.
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21:640:136
Calculus II (4)
Applications of the integral, volumes and arc length, exponential and trig functions revisited, techniques of integration, L'Hospital's Rule, numerical integration, improper integrals, sequences and series, Taylor's Theorem, and polar coordinates.
Prerequisite: 21:640:135 or 155.
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21:640:155-156
Honors Calculus (4,4)
These courses will rigorously cover the theory and applications of differential and integral calculus. Substantially more material 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.
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21:640:211
Statistics (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: Placement by examination or successful completion, with a grade of C or better, of one of the following courses: 21:640:103, 112 and 113, 107, 108, 109, or any other higher level mathematics course.
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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, information systems, or the liberal arts. Mathematics majors and minors cannot get credit for 21:640:219.
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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.
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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.
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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.
Prerequisite: 21:640:136 or 156, or permission of instructor.
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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, 238, and 350, or permission of instructor.
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21:640:314
Elementary Differential Equations (3)
Ordinary differential equations, including solution by series and their applications; emphasis on linear equations.
Prerequisite: 21:640:136 or 156.
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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.
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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.
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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.
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21:640:397,398
Mathematics Teaching Apprenticeship (3,3)
Practice in the teaching of mathematics supervised by members of the faculty.
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21:640:403
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.
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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.
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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.
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21:640:424
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: 21:640:235 or permission of instructor.
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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.
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21:640:433
Projective Geometry (3)
Projective and affine curves; polynomial rings; ideals; Hilbert's basis
theorem; the nullstellungsatz; local rings; singularities.
Prerequisite: 21:640:238.
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21:640:435-436
Geometry I,II (3,3)
Axiomatic systems, finite geometries, Euclidean geometry, and non-Euclidean geometry.
Prerequisites: 21:640:235, 350.
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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 isometrics.
Prerequisite: 21:640:238 or permission of instructor.
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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.
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21:640:456
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: 21:640:238 or permission of instructor.
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21:640:473
Numerical Analysis (3)
Error analysis; interpolation theory; numerical solution of equations; polynomial approximations; numerical differentiation and integration; solution of differential equations.
Prerequisites: 21:198:101 and 21:640:136 or 156.
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21:640:475-476
Applied Mathematics I,II (3,3)
Fourier series and integrals; boundary value problems; matrices; finite differences; special functions; numerical methods.
Prerequisites: 21:640:314 or permission of instructor.
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21:640:477
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: 21:640:136 or 156 or permission of instructor.
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21:640:491,492
Mathematics Seminar (3,3)
Selected topics in mathematics; individual study stressed.
Prerequisite: Permission of instructor. Students may enroll multiple times.
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21:640:493,494
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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