Mathematics

COURSE DESCRIPTIONS

130 Basic Mathematical Concepts
(3 s.h.) This course is a review of basic mathematical concepts. It is not open to any student who has scored 480 or higher on the MATH SAT, scored 19 or higher on the MATH ACT or passed a college level math course. MATH 130 does not fulfill the quantitative reasoning requirement of the Common Curriculum.

150 College Algebra 
(3 s.h.) Students are provided with a background in algebra appropriate for the application of mathematics to disciplines and for further study in mathematics. Topics include equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and systems of equations. Emphasis is on logical analysis, deductive reasoning, and problem solving. This course is open to students who have scored 480 or higher on the MATH SAT, scored 19 or higher on the MATH ACT, have passed the MATH 130 Exemption Exam, or have passed MATH 130.

155 Mathematics in Contemporary Society 
(3 s.h.) Students will investigate mathematical topics in relationship to life in contemporary society. The course will emphasize quantitative reasoning in the context of applications, focusing on mathematical modeling and critical analysis of real-world problems. Topics to be covered may include basic probability and statistics, mathematical modeling, finance, voting and appointment, and logic. Supplemental topics may be introduced depending on the interests of students enrolled in the course.

156 Mathematics for Prospective Elementary School Teachers I 
(3 s.h.) This course is designed for those who wish to become elementary school teachers. Discrete probability, descriptive statistics, geometry, numeration, measurement, algebra, and applications to science are covered. It includes both content and process knowledge. The emphasis is on building diverse mathematical reasoning and problem-solving skills. Virginia mathematics SOL for grades K-6 addressed. *Prerequisite: MSAT 480 or MATH 130, or a Q course. Fall semester.

157 Mathematics for Prospective Elementary School Teachers II 
(3 s.h.) The primary goal of this course is to introduce students to Euclidean geometry, axiomatics, and deductive reasoning. Emphasis will be on open exploration, conjectural inductivism, visualization, analysis, and informal deduction. Educational software like Geometer’s Sketchpad will be used to conduct computer investigations. *Prerequisite: MSAT 480 or MATH 130, or a Q course. Spring semester.

171 Precalculus with Trigonometry 
(3 s.h.) Algebraic, trigonometric, logarithmic and exponential functions are explored. The main emphasis will be on developing trigonometric functions and their properties, since they play an indispensable role in the modeling of physical phenomena and in the study of calculus. Included is a Derive software project on modeling and problem solving. *Prerequisite: MATH 150 or equivalent.

211, 212 Introduction to Calculus and Analytic Geometry I, II 
(4 s.h. each) MATH 211 is required for mathematics majors and recommended for majors in the sciences and economics. We treat the basic concepts of differential calculus and its applications including limits, continuity, differentiation, the chain rule, the mean-value theorem, optimization problems, antiderivatives, and the fundamental theorem of calculus. MATH 212 develops the concept of the definite integral and its applications. Integration of transcendental functions, integration techniques, L’Hopital’s Rule, and improper integrals are covered. *Prerequisite: MATH 171.

221 History of Mathematics
(3 s.h.) This mathematics course reflects the college’s emphasis on global awareness. Mathematics has a fascinating history, interwoven with striking personalities and outstanding achievements and contributions from many different countries throughout the world. We address the development of mathematical ideas from a historical perspective as well as the scientific, humanistic, and global import of the subject. *Prerequisite: MATH 211. Alternate years.

231 Discrete Mathematical Structures 
(3 s.h.) This is an introduction to techniques of theoretical mathematics. We will explore logic, truth tables, deductive proof and the principle of mathematical induction. Algorithms, algebraic structures, discrete probability, counting methods, relations, and graph theory are also covered. Some of the topics have substantial application to computer science. *Prerequisite: MATH 211. Fall semester.

233 Statistical Methods and Theory I
(3 s.h.) An introduction to applied statistics and theory. Topics include measures of central tendency, discrete and continuous random variables, Normal distributions, Binomial distributions, sampling distributions and the Central Limit Theorem, probability, correlation and regression, producing data from sampling and experiments, hypothesis testing using the z, t, chi-square, and F distributions, confidence intervals, and analysis of variance. The statistical software package SPSS will be used to illustrate the material presented. *Prerequisite: a ‘B’ in INT 222, PSYC 250,
or MATH 211. Alternate years.

234 Statistical Methods and Theory II 
(3 s.h.) A second course in applied statistics and theory. Topics include analysis of variance, multiple linear regression, and nonparametric statistical methods. The statistical software package SPSS will be used to illustrate the material presented. *Prerequisite: MATH 233. (Offered as needed.)

252 Problem Solving Seminar 
(3 s.h.) Students are presented with quantitative problems and asked to find methods of solution. They present those methods informally to the seminar group. Some real-world problems from business or industry are considered. Content varies from year to year. *Prerequisites: MATH 212, MATH 231. Offered as needed.

301 Multivariable Calculus I 
(3 s.h.) Indeterminate forms, improper integrals, differential equations, infinite series, polar coordinates, parametric equations, vectors and vector-valued functions are studied. Derive, a symbolic computer algebra system, will be used to explore a variety of nonroutine problems. *Prerequisites: MATH 211 and 212. Fall semester.

302 Multivariable Calculus II 
(3 s.h.) Vector-valued functions, functions of several variables, partial differentiation, chain rules, directional derivative and gradient, applications of extrema, multiple integrals, vector fields, line integrals and Green’s Theorem are studied. Derive, a symbolic computer algebra system, is used. *Prerequisite: MATH 301. Spring semester.

304 Numerical Analysis and Computing 
(3 s.h.) This course surveys the techniques and algorithms of numerical computing, numerical solution of algebraic equations and differential equations, interpolation, approximation, and iteration theory, numerical differentiation and numerical integration, error analysis, stability and convergence of solutions. The computer algebra system Maple is used. *Prerequisite: MATH 301. Alternate years.

306 Ordinary Differential Equations
(3 s.h.) This is the study of the theory and methods of initial value problems of first and second order equations as well as systems of first order linear equations with constant coefficients. Methods such as integrating factors, undetermined coefficients, variation of parameters and the linearization of nonlinear problems will be covered. Uniqueness and existence questions will be discussed. Differential equations is a powerful modeling tool and can be applied to diverse areas of study including environmental and population studies, radioactive decay, fluid flow, epidemiology and much of engineering. Students will be required to make a presentation in their area of interest. *Prerequisite: MATH 212 or equivalent. Spring semester, alternate years.

311 Probability and Distribution Theory 
(3 s.h.) Sample-point and event-composition methods for calculating the probability of an event; Bayes’ rule; the binomial, geometric, hypergeometric and Poisson probability distributions; mathematical expectations; moment-generating functions; Tchebysheff’s theorem; continuous random variables and their probability distributions; multivariate probability distributions; and functions of random variables. This course is recommended for students planning to work in industry. *Prerequisites: MATH 211 and 212. Offered as needed.

312 Mathematical Statistics
(3 s.h.) A combination of theoretical and applied statistics on the following topics is explored. Point and interval estimation; hypothesis testing using the z, t, chi-square and F distributions; regression and correlation; analysis of variance; contingency table analysis; Shewhart control charts, measurement system evaluation, and process capability studies. This course is recommended for students planning to work in industry. *Prerequisite: MATH 311. Offered as needed.

322 Linear Algebra 
(3 s.h.) This class develops the theory of vector spaces and its underlying relevance to matrices and systems of linear equations. Topics include the vector space Rn, abstract vector spaces, elementary operations and systems of linear equations, linear transformations, and eigenvectors and eigenvalues. Emphasis is on providing a bridge from the intuitive developments of lower level courses to the more rigorous abstract courses in mathematics. All students will be required to make a presentation on an application area. *Prerequisites: MATH 211 and 231. Spring semester, alternate years.

341 Modern Geometry
(3 s.h.) Euclidean geometry, non-Euclidean geometry, projective geometry, and the abstract axiomatic method are studied. This course is strongly recommended for students planning to teach mathematics. It also provides an excellent background for graduate study in mathematics. *Prerequisite: MATH 231. Offered as needed.

370 Colloquium in Mathematics 
(3 s.h.) Selected topics in higher-level mathematics are offered which are not among our regular courses. The list below reflects the knowledge and expertise of the current faculty and are typical courses in an undergraduate curriculum. The colloquium is also used to introduce students to potential research areas. Topics include: Abstract Algebra II, Real Analysis II, Topology, Statistical Methods and Theory II, Complex Analysis, Elementary Numerical Analysis, Mathematical Modeling, Partial Differential Equations, Women in Mathematics, Mathematics Pedagogy, Introduction to Functional Analysis, Partially Ordered Groups, Graph Theory, and Engineering Mathematics. Alternate years.

400 Abstract Algebra I or Real Analysis I
(3 s.h. each) MATH 400 alternates between abstract algebra one year and real analysis the next. Both courses develop mathematical maturity through the use of intuition, deductive logic and mathematical analysis. Abstract algebra studies the structures of axiomatic mathematical systems such as groups, rings and fields. Real analysis develops the mathematical techniques necessary to understand the real line as well as functions on the reals. MATH 400 may be repeated for credit and all students who plan to attend graduate school in Mathematics must take both courses. *Prerequisites: MATH 302 and MATH 322. Fall semester.

401 Senior Seminar
(3 s.h.) MATH 401 provides the structure under which students complete their senior research projects. Students must sign up for 1 s.h. of Senior Seminar in the fall and 2 s.h. of Senior Seminar in the spring of their senior year. Each student completes a faculty-approved research project, writes a senior paper based on the results, and presents the results to the mathematics faculty. The student is required to write a paper and pass an oral examination on the theory related to her research area, as well as propose her research project in the fall. She will perform her research in the spring semester, and defend her senior research project paper when done. This requirement applies to Adult Degree Program students as well. *Prerequisite: MATH 400.

Note: Directed inquiries, teaching assistantships, and internships are arranged on an individual basis. Internships and teaching assistantships may include service-oriented work in the community for fulfilling civic engagement requirements.