Mathematics
Courses
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Mathematics |
SOU CATALOG HOME : SCHOOLS AND DEPARTMENTS : MATHEMATICS : COURSES
See Course Prerequisites Policy.
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. These courses initiate 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. Algebraic and function concepts are used 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. This course is recommended as preparation for Elementary Functions (Mth 112). Prerequisite: Mth 95 or satisfactory placement.
4 creditsStudies exponential, logarithmic, and trigonometric functions; their graphs and applications. Intended as preparation for Mth 251. Prerequisite: Mth 111 or satisfactory placement.
4 creditsAcquaints students with limited mathematical background with 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.
1-4 credits
Credit to be arranged
4 creditsIntroduction to 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, and number theory. Content is taught within a problem-solving framework using calculators and computers as problem-solving aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 95 or satisfactory placement.
4 creditsRational number arithmetic for prospective teachers. Topics include theory and modeling of fractions, decimals, and percent; rational and irrational numbers; mental arithmetic and computational estimation; probability and statistics. Content is taught within a problem-solving framework using calculators and computers as problem-solving aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 211.
4 creditsInformal 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 problem-solving aids. Three hours of lecture and three hours of laboratory. Prerequisite: Mth 211.
4 creditsIntroduction to 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 students not majoring in mathematics. 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, contingency tables, correlation, and simple linear regression. Problems are assigned to enhance the statistical reasoning in the student's major. Three hours of lecture and two hours of laboratory. Prerequisite: Mth 95 or satisfactory placement.
4 creditsIntroduction to 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 creditsIntroduction to integration developed as a limit of Riemann sums. The first and second forms of the Fundamental Theorem of Calculus are studied. Applications selected from length, area, volume, work, and motion. Students are expected to write some precise mathematical arguments. Prerequisite: Mth 251.
4 creditsIntroduction to 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 creditsConcepts of limit, continuity, differentiability, and integrability are applied to multivariate and vector-valued functions. Topics include the study of motion, partial derivatives, multiple and line integrals. Students are expected to write precise mathematical arguments. Prerequisites: Mth 252 and 261, or Mth 252 and 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).
14 credits
Mth 311 Number Structures
4 creditsStudies essential features of the real number system and the organization of number systems in general. Logical development, precise notation, and written exposition are stressed. Includes axiomatic developments, set and function theory, division algorithm, congruence, completeness, Archimedean Principle, denseness, and infinite sets. Three hours of lecture and two hours of laboratory. Prerequisites: Mth 261 and Wr 122.
4 creditsIntroduces the theory and application of ordinary differential equations. Problems from the natural and physical sciences are analyzed. Emphasis is placed on finding and interpreting solutions. Topics selected from separable equations, linear equations, power series solutions, Laplace Transforms, and systems of linear equations. Prerequisites: Mth 253, 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 creditsAbstract groups are presented to demonstrate the fundamental strategies used to study algebraic structures such as subsystems, morphisms, and quotient systems. Includes a brief overview of some alternate algebraic systems. Prerequisite: Mth 311.
4 creditsTheory 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 252 required, Mth 281 recommended.
14 credits
13 credits
13 credits
14 credits
Credit to be arranged
Credit to be arranged
4 credits eachThe following and other topics are offered as needed. Repeated credit 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 given for distinct topics.
Partial Differential Equations. Introduction to diffusion, wave, and Laplace equations; separation of variables; and Fourier series. Prerequisites: Mth 281, 321.
Optimization. Introduction to linear programming and nonlinear optimization. Prerequisites: Mth 261 and CIS 200 or CS 257 or equivalent.
4 credits eachThe following and other topics are offered as needed. Repeated credit 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. An introduction to 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, 331.
4 credits eachThe following and other topics are offered as needed. Repeated credit 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. Quotient rings, ideals, and ring homomorphisms are used 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 given for distinct topics.
Statistics. 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. Prerequisites: Mth 281 and 361. Mth 281 may be taken concurrently.
35 credits eachThe following and other topics are offered as needed. Repeated credit 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. Applications to middle school mathematics, and high school general mathematics and first-year algebra curriculum. Prerequisite: Mth 212 or 251.
Experimental Probability and Statistics.
Study of probability and statistics through laboratory experiments, simulations, and applications. Applications to middle school and high school general mathematics curriculum. Prerequisites: 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 informal background necessary for appreciation of formal development. Prerequisite: Mth 213 or Mth 251.
2 credits a term for 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; Mth 321 or 361; Mth 331, 341; Wr 123 or 227.