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2000-2001 Catalog |
| SOU Catalog Home >> Schools and Departments >> Mathematics >> Courses | |
Note: Mathematics prerequisites must be completed with a grade of C- or better unless otherwise noted.
(These are extra fee courses.)
4 credits eachA three-quarter sequence designed for students who lack adequate algebra and geometry preparation for college-level mathematics. Initiates students into the curriculum by presenting general principles and procedures in the context of specific, concrete problems. Students integrate ideas from algebra and geometry; make connections among tabular, graphical, and symbolic information; and apply mathematics to real-world settings. Coursework includes the use of the graphing calculator as a learning tool and resource.
Mth 111 College Algebra
4 creditsDevelops skills in algebra and deductive thinking in the real number setting. Uses algebraic and function concepts to solve problems and analyze applications. Topics include real number properties, absolute value, theory of equations, inequalities, graphs, polynomial and rational functions, and an introduction to complex numbers. Recommended as preparation for Elementary Functions (Mth 112). Prerequisite: Mth 95 or satisfactory placement.
4 creditsStudies exponential, logarithmic, and trigonometric functions and their graphs and applications. Intended as preparation for Mth 251. Prerequisite: Mth 111 or satisfactory placement.
4 creditsAcquaints students with limited mathematical background to the basic theory and applications of finite probability. Topics include elementary set theory, sample spaces, probability basics, combinatorics, random variables, distributions, and expectation. Credit is not given to students who have received credit for Mth 361. Prerequisite: Mth 95 or satisfactory placement.
4 creditsIntroduces analytic geometry, with an emphasis on linear functions of one or more variables and their graphs. Applications are drawn primarily from the social and management sciences. Topics include lines, planes, systems of linear equations, matrix algebra, and linear programming problems. Credit for Mth 158 is not given to students who have received credit for Mth 261. Prerequisite: Mth 95 or satisfactory placement.
1-4 credits
Credit to be arranged
4 creditsIntroduces the theory of arithmetic for prospective teachers. Topics include set theory, numeration, place value, computational algorithms for whole numbers and integers, computational estimation, mental arithmetic, relations and functions, and number theory. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 95 or satisfactory placement.
4 creditsCovers rational number arithmetic for prospective teachers. Topics include theory and modeling of fractions, decimals, and percentages; rational and irrational numbers; mental arithmetic and computational estimation; graphing linear and nonlinear functions; and probability and statistics. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 211.
4 creditsCovers informal geometry and measurement for prospective teachers. Topics include properties of two- and three-dimensional space, the metric system, measurement, estimation, perimeter, area, volume, surface area, congruence motions, similarity motions, and topological motions. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 211.
4 creditsIntroduces the mathematical structures fundamental to the study of computer science. Topics selected from sets, functions, combinatorics, statistics, coding theory, logic networks, and Boolean expressions. Prerequisite: Mth 251.
4 creditsSurvey course for nonmathematics majors. Develops the basic concepts and techniques of descriptive and inferential statistics. Topics include graphing, measures of the center and variability, binomial and normal probability distributions, estimation and testing of means, proportions and variances, correlation, and regression. Assigns problems to enhance the statistical reasoning in the student's major. Introduces appropriate technology to display and analyze data. Prerequisite: Mth 95 or satisfactory placement.
4 creditsIntroduces limits, continuity, and differentiation. Applications include graphing techniques, related rates, and maximum/minimum problems. Students are introduced to writing precise mathematical arguments. Prerequisite: Mth 112 or satisfactory placement.
4 creditsIntroduces integration, developed as a limit of Riemann sums. Covers the first and second forms of the Fundamental Theorem of Calculus. Applications selected from length, area, volume, work, and motion. Students are expected to write precise mathematical arguments. Prerequisite: Mth 251.
4 creditsIntroduces sequences and series, including power series representations of functions. Other topics include symbolic and numerical techniques of integration, improper integrals, and indeterminate limit forms. Students are expected to write precise mathematical arguments. Prerequisite: Mth 252.
4 creditsProvides the basic linear algebra necessary for multivariable calculus, differential equations, and abstract algebra. Develops skills for constructing rigorous mathematical proofs. Topics include finite dimensional vector spaces, matrices, linear transformations, and eigenvalue problems. Prerequisite: Mth 252.
4 creditsApplies concepts of limit, continuity, differentiability, and integrability to multivariate and vector-valued functions. Topics include the study of motion, partial derivatives, and multiple and line integrals. Students are expected to write precise mathematical arguments. Prerequisites: Mth 252, and Mth 261 or Ph 221.
1 creditSeminar for mathematics majors and others. Presents mathematics as a way of thought and body of knowledge important to the development of civilization and the concerns of modern society. Prerequisite: Mth 252 (may be taken concurrently).
1-4 credits
Mth 311 Number Structures
5 creditsStudies essential features of the real number system and the organization of number systems in general. Stresses logical development, precise notation, and written exposition. Includes axiomatic developments, set and function theory, division algorithm, congruence, completeness, Archimedean Principle, denseness, and infinite sets. Prerequisites: Mth 261, and Wr 122 or Core 103.
4 creditsIntroduces the theory and application of ordinary differential equations. Analyzes problems from the natural and physical sciences. Emphasizes finding and interpreting solutions. Topics selected from separable equations, linear equations, power series solutions, Laplace Transforms, and systems of linear equations. Prerequisites: Mth 253 and 261.
4 creditsStudies the basic analytic structure of real numbers. Topics include sequences, continuity, uniform continuity, properties of functions on closed bounded sets, and an introduction to metric spaces. Prerequisite: Mth 311.
4 creditsPresents abstract groups to demonstrate the fundamental strategies used to study algebraic structures such as subsystems, morphisms, and quotient systems. Includes a brief overview of some alternative algebraic systems. Prerequisite: Mth 311.
4 creditsCovers the theory and applications of probability. Topics include laws of probability, Bayes' theorem, principles of counting, combinatorics, random variables, discrete and continuous probability distributions, and expected values. Prerequisite: Mth 281.
1-4 credits
1-3 credits
1-3 credits
1-4 credits
Credit to be arranged
Credit to be arranged
4 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Geometry. An axiomatic development of a variety of geometries. Prerequisite: Mth 311.
4 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Partial Differential Equations. Introduces diffusion, wave, and Laplace equations; separation of variables; and Fourier series. Prerequisites: Mth 281 and 321.
Optimization. Introduces linear programming and nonlinear optimization. Prerequisites: Mth 261 and CIS 200 or CS 257.
4 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Metric Spaces. Extends analytic concepts to general metric spaces and mappings. Includes metric topology, convergence, continuity, and compactness. Prerequisite: Mth 331.
Complex Analysis. Studies complex numbers, mappings, differentiation, and integration. Prerequisite: Mth 331.
Integration. Introduces Lebesque and Riemann integration.
Infinite Series. Extends the analysis of infinite series to series of functions. Topics include uniform convergence, power series, and trigonometric series. Prerequisites: Mth 253 and 331.
4 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Groups. A careful study of groups, including normal subgroups, group morphisms, isomorphism theorems, and the Sylow or equivalent structure theorems. Prerequisite: Mth 341.
Rings. A careful study of rings, including integral domains, Euclidean domains, and other algebraically related structures. Uses quotient rings, ideals, and ring homomorphisms to establish the existence of solutions to certain polynomials. Prerequisite: Mth 341.
Linear Algebra. A general study of vector spaces and linear transformations. Topics include basis and dimension theorems for vector spaces, similarity relations, eigenvalues, and canonical forms for matrices. Prerequisite: Mth 341.
4 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Statistics. Explores theory and applications of inferential statistical procedures. Topics include interval estimation and testing for means, variances, proportions, tests of independence and goodness-of-fit, linear regression and correlation, and nonparametric statistics. Prerequisite: Mth 361.
3-5 credits eachThe following and other topics are offered as needed. Repeated credit is given for distinct topics.
Arithmetic and Algebraic Structures.
Study of the real number system and its subsystems leads to the introduction of more general algebraic structures and their applications. Involves applications to middle school mathematics, high school general mathematics, and first-year algebra curriculum. Prerequisite: Mth 212 or 251.
Experimental Probability and Statistics.
Examines probability and statistics through laboratory experiments, simulations, and applications. Involves applications to middle school and high school general mathematics curriculum. Prerequisite: Mth 212, 243, or 251.
Informal Geometry. Focuses on understanding the theory behind selected topics in the high school geometry curriculum. Attention is given to the informal background necessary for appreciation of formal development. Prerequisite: Mth 213 or 251.
A total of 4 creditsA directed individual or group project organized around a theme that necessitates a synthesis of a variety of concepts in the undergraduate mathematics curriculum. Includes a major writing component. Prerequisites: senior standing, Mth 311, 331, 341, and 321 or 361.
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This
material is from the 2000-2001 |