### School of Natural Science and Mathematics

## Mathematics Course Descriptions

**MATH 105 Elementary Statistics** (3)

This is an introduction to the fundamental concepts of statistics. Topics include data collecting, displaying, summarizing, drawing inferences, probability, expectation, normal distribution, sampling distributions, point and interval estimation, significance testing and simple linear regression. Appropriate application software utilized.

**MATH 108, 109 Concepts of Mathematics for Teachers I/II** (3, 3)

This two-part sequence is designed for the elementary education major as an introduction to selected topics in mathematics. Topics include sets and set operations, number and numeration systems and their operations, algorithms, measurement, reasoning and problem solving, patterns and relations, geometry, probability and statistics. Open only to and required for students preparing to teach at the elementary school level.

**VTMA 111 Mathematical Thought and Problem-Solving** (3)

This course provides students with a mathematical approach to solving problems as well as an introduction to the nature of mathematics. The course seeks to improve facility with computations, mathematical notation, logical reasoning, and verbal expression of mathematical concepts. Content is selected from classical and modern areas of mathematics such as geometry, number theory, algebra, graph theory, fractals, and probability. The delivery of the content takes on a variety of forms including in-class activities, projects, discovery learning, and lecture.

**MATH 114 Precalculus Mathematics** (3)

This course prepares students for the calculus sequence. Topics include polynominal and rational functions and their graphs, exponents and logarithms, trigonometric functions and identities, and applications.

**MAWI 228 Discrete Mathematics** (3)

This course introduces the basic techniques and methods of reasoning for discrete problem solving. Topics include induction, set theory, elementary combinatorics, and graph theory. Applications to computer science are emphasized. This course satisfies the writing intensive *Veritas* program requirement. Same as CMSWI 228.

**MATH 247 Calculus I** (4)

This is an introduction to the fundamental concepts of differential and integral calculus with an emphasis on limits, continuity, derivatives and integrals of elementary functions. Applications to curve sketching, max-min values, related rates and areas will be given. Derivatives and integrals of elementary transcendental functions are developed. Prerequisite: MATH 114 or its equivalent.

**MATH 248 Calculus II** (4)

Techniques and applications of integration are studied. Topics include improper integrals, polar coordinates, parametric equations, plane analytic geometry, sequences, series and Taylor’s theorem. Prerequisite: MATH 247 or permission of instructor.

**MATH 249 Calculus III** (4)

This course presents the calculus of vector-valued functions and functions of several variables. Topics include directional derivatives, Lagrange multipliers, multiple integration and line and surface integrals. Prerequisite: MATH 248 or permission of instructor.

**MATH 285 Applied Statistics** (3)

This course is an introduction to the principles and techniques of data analysis and statistical models. Topics include the methods of exploratory data analysis, the design of experiments, sampling, hypothesis testing, simple and multiple regression, and the analysis of variance. Prerequisite: MATH 247 or permission of instructor.

**MATH 332 Graph Theory** (3)

The theory and practical applications of graph theory are studied. Topics include paths and cycles, bipartite graphs, digraphs, spanning trees, connectivity, matchings, coloring, planarity, Hamiltonian cycles, and graph classes. Prerequisite: MATH 228 or permission of the instructor.

**MATH 364 Linear Algebra** (3)

This course examines the mathematics of matrices and determinants with applications to systems of linear equations, vector spaces, linear transformation, eigenvalues and eigenvectors, and canonical forms. Prerequisite: MATH 247 or permission of instructor.

**MATH 368 Algebraic Structures** (3)

This is an introduction to the fundamental concepts of abstract algebra. Topics include Abelian groups, permutation groups, cyclic groups, isomorphisms and Cayley’s Theorem. Additional topics covered (as time permits) are rings, ideals, integral domains, and fields. Prerequisite: MATH 228 and MATH 248 or permission of instructor.

**MATH 377 Foundations of Geometry** (3)

This is a survey of geometries, both classical and modern. Topics include finite geometries, fundamental concepts of Euclidean geometry in the plane and higher dimensions, theorems leading to the modern synthetic approach, constructions and transformations, history of the parallel postulate and non-Euclidean geometries. Understanding and writing clear and consistent proofs are major course objectives. Prerequisite: MATH 228 or permission of instructor.

**MATH 384 Differential Equations** (3)

This is a study of the solution methods for first order lineard,nonlinear, and higher order linear differential equations. Laplace Transforms, power series solutions, Picard’s method and systems of linear differential equations are examined. Prerequisite: MATH 248 or permission of instructor.

**MATH 387 Probability** (3)

This is an introduction to the theory of elementary probability. Topics include Kolmogorov’s axioms of probability, conditional probability and independence, finite combinatorics, discrete and continuous distributions, moments, jointly distributed random variables, limit theorems, generating functions, Markov chains and random walks. Prerequisites: MATH 228 and MATH 248 or permission of instructor.

**MATH 390 Mathematical Statistics** (3)

The course provides the mathematical foundations of statistics. Topics include functions of random variables, transformations of random variables, order statistics, sampling theory and distributions, introduction to the theory of point estimation and statistical inference, confidence intervals, hypothesis testing, likelihood ratio tests, regression, correlation, analysis of variance and analysis of enumerative data. Prerequisite: MATH 387 or permission of instructor.

**MATH 398 Independent Study** (1-3)

This course allows for the independent study in an area of mathematics. Topics are selected to meet a student's interest or need. Permission of the instructor, department chair, dean and associate provost is required.

**MATH 436 Elementary Number Theory**

Elementary number theory with a focus on both history and theory is studied. Topics include the Euclidean Algorithm, Diophantine equations, the Fundamental Theorem of Arithmetic, congruences, number-theoretic functions, primitive roots, continued fractions, and the theorems of Fermat, Wilson, and Euler. Prerequisites: MATH 228 and MATH 247 or permission of instructor.

**MATH 447 Introduction to Real Analysis** (3)

This is a rigorous development of the fundamental concepts of analysis, including the real number system, functions, sequences, limits, continuity, convergence, differentiation, integration and series. Prerequisite: MATH 248 or permission of instructor.

**MATH 457 to Complex Analysis** (3)

This course develops the theory of complex analysis. Topics include the complex number systems, limits, sequences, analytic functions, the Laplace equation, contour integrals, Cauchy integral theorems, power series, singularities and conformal mapping. Prerequisite: MATH 248 or permission of instructor.

**MATH 472 Topology** (3)

This is an introduction to point-set topology or algebraic topology. Possible topics include metric spaces, normal and regular spaces, compactness, connectedness, continuity of mappings, homotopy and homology groups, fixed-point theorems and knot theory. Prerequisite: MATH 248 or permission of instructor.

**MATH 484 Numerical Methods** (3)

This course examines a variety of numerical methods for applications of mathematics. Topics include the numerical solution to nonlinear equations, interpolation, numerical differentiation and integration, and the numerical solution to differential equations. Prerequisites: MATH 248 or permission of instructor. Same as CMSCI 484.

**MATH 488 Operations Research** (3)

This is an introductory course in operations research. Topics are selected from linear programming, network models, project scheduling, stochastic processes, game theory, queuing theory, decision analysis, non-linear programming, dynamic programming, simulation, and forecasting. Prerequisite: MATH 248 or permission of instructor.

**MATH 489 Modeling and Simulation** (3)

This course develops mathematical models and techniques for constructing mathematical models. Topics may include population growth, epidemics, scheduling problems, predator-prey interaction, transportation, economic and stochastic models. Prerequisite: MATH 248 or permission of instructor. Same as CMSCI 489.

**MATH 492, 493 Practicum** (1-3)

Practicum presents an opportunity to gain practical experience through a one semester internship. The nature of the work experience and the number of credits must be approved in advance by the department chair.

**MATH 495, 496 Seminar I, II** (1, 1)

Each of these courses is designed to enhance the comprehension of the fundamental concepts of higher mathematics and to develop an understanding of their organization. Each course may involve applying ideas and techniques learned in earlier classes to solve mathematical and applied problems, and they may also involve directed reading and study in contemporary publications.

**MATH 497 Undergraduate Research in Mathematics** (1-3)

Under the supervision of a faculty instructor, students conduct research on mathematical questions posed by the student or the instructor. Work may be done individually or in teams as determined by the instructor. The course prerequisites and enrollment limitation vary with the instructor and topic. Prerequisites: permission of instructor.

**MATH 499 Special Topics in Mathematics** (3)

Students work on advanced projects or study in some area of mathematics. Examples include partial differential equations, advanced complex number theory, or harmonic analysis. This course is offered at the discretion of the department with regard to the needs and aptitudes of the students.