Averett University Undergraduate Catalog


Courses of Instruction in Mathematics

Number Title Credits Description
100 Fundamentals of Mathematics 3 A course designed to review and develop mathematical skills needed for college algebra.  Topics include properties of the real number system, graphing, word problems, and selected topics in beginning algebra.  Credits are not computed in the grade point average and are not counted toward the 120 semester hour graduation requirement. Offered each semester.
103 Principles of Mathematics 3 A first course in college mathematics focusing on functions and their applications.  Topics include equations, graphing, relations, and functions with an emphasis on polynomial, logarithmic, and exponential functions. The TI-89 graphing calculator is required.   Prerequisite:  MTH 100 or placement. Offered each semester.
111, 112 Theory of Modern Mathematics I, II 3,3 A course designed to develop a basic understanding of mathematical systems (including a development of the natural number system, the integers, and the rational, real, and complex number systems), number theory, probability and statistics, geometry, technology, and the role of deductive and inductive reasoning.  Prerequisite:  MTH 100 or placement in MTH 103. Offered fall, spring semester, respectively.
151 Precalculus Mathematics 3 A course designed for those students requiring a knowledge of precalculus mathematics with an emphasis on functions and their applications.  Topics include advanced algebra, trigonometry, and analytical geometry.  This course is intended for those students planning to take MTH 201.  The TI-89 graphing calculator is required.  Prerequisite:  MTH 103 or placement. Offered spring semester.
160 Introduction to Statistics 3 A first course in statistics.  Topics include permutations, combinations, distributions, (binomial, normal, Student's t, chi-square, and F), sampling, hypothesis testing, significance levels, confidence intervals, regression and correlation.  Does not count toward minor in Computer Science.  Prerequisite:  MTH 103 or equivalent. Offered each semester.
171 Applied Calculus 3 A study of the basic principles of calculus and their applications.  Designed especially for the student desiring a one semester exposure to the fundamental concepts of calculus.  Topics include limits, continuity, differentiation of algebraic, logarithmic, and exponential functions.  The TI-89 graphing calculator is required.  Prerequisite: MTH 103.  (NOTE:  Credit will not be awarded for MTH 171 after receiving credit for MTH 201.)
Offered each semester.
201 Calculus I  3 A study of differential calculus of the elementary functions with associated analytical geometry.  Prerequisite:  MTH 104 or placement. Offered fall semester.
202 Calculus II 3 An introduction to integral calculus and a continued study of calculus as applied to the elementary and transcendental functions. Prerequisite:  MTH 201. Offered spring semester.
211 Foundations of Higher Mathematics 3 A course designed to introduce students to basic techniques of writing mathematical proofs as well as fundamental ideas used throughout mathematics.  Students will be introduced to the logic needed for deductive reasoning and will use direct and indirect arguments to construct proofs of some elementary theorems.  Topics include logic operators and quantifiers, relations, functions, equivalence relations, and Mathematical Induction.  Prerequisite:  MTH 171 or MTH 201. Offered spring semester.
301 Calculus III 3 A continued study of calculus.  Topics include improper integrals, infinite series, power series functions, and differential equations.  Prerequisite:  MTH 202. Offered fall semester.
302 Linear Algebra 3 An introduction to linear algebra.  Topics include systems of linear equations, vector spaces, bases, dimension, linear transformations, matrices, determinants, the Gram-Schmidt process, eigenvalues, eigenvectors, and geometric applications.  The TI-89 graphing calculator is required.  Prerequisite:  MTH 202.  Alternate years: spring semester, odd years. 
311, 312 Abstract Algebra I, II 3,3 An introduction to a systematic study of abstract algebra from a theoretical viewpoint.  Topics include the theory of groups, rings, integral domains, and fields.  Applications include the construction and description of certain characteristics of the natural numbers, integers, rational, real, and complex numbers.  Prerequisite:  MTH 202.  Alternate years: fall semester, even years and spring semester, odd years, respectively.
315, 316 Theory of Real Variables I, II 3,3 An introduction to a systematic study of analysis from a theoretical viewpoint with an emphasis on real variable theory.  Topics include the Archimedean property, set terminology, topology and limits in metric spaces, continuity, uniform continuity, compact and connected sets, differentiation, Riemann-Stieltjes integrals, and the Weierstrass-approximation theorem.  Prerequisite:  MTH 202.  Alternate years: fall semester, odd years and spring semester, even years, respectively.
321 History of Mathematics 2 A course designed to develop an understanding of the historical and current relationships of mathematics to society and the sciences.  Junior status.
322 Multivariable Calculus 3 A study of the calculus of real-valued functions of several variables, vector calculus, solid analytical geometry, and differential equations.  The TI-89 graphing calculator is required.  Prerequisite:  MTH 301.  Alternate years:  spring semester, even years.
332 Numerical Analysis 3 An introduction to computer methods for differentiation, numerical integration, roots of polynomials, interpolation, systems of equations, and solutions of ordinary differential equations.  Prerequisites:  CSS 212 or 231; MTH 301.  On demand.
401 Geometry 3 An introduction to geometry theories from a modern axiomatic viewpoint.  Basically concerned with Euclidean geometry with an introduction to non-Euclidean geometry.  Alternate years: fall semester, even years.
402 Point Set Topology 3 An introduction to point-set topology.  Topics include general theory, connected and compact spaces, the separation axioms, and properties which remain invariant under certain mappings.  On demand.
403 Probability and Statistics 3 A study of the theory of probability and statistics based on a knowledge of calculus.  Topics include combinatorial analysis, the axioms of probability, expectation, moment generating functions, random variables, sampling, parameter estimation, hypothesis testing, and regression.  Alternate years: fall semester, odd years.
405 Set Theory 3 An introduction to the theory of sets.  Topics include the algebra of sets, relations, Peano axioms, order and well ordering, axiom of choice, Zorn's lemma, ordinal and cardinal numbers with their respective arithmetics, Schroder-Bernstein theorem, and the continuum hypothesis.  On demand.
432 Ordinary Differential Equations 3 An introduction to ordinary differential equations, and the associated methods, theory, and applications. Topics include first-order equations, second- and higher-order linear equations, and systems of first-order linear equations. Prerequisite: MTH 301. Spring semester, even years.
441 Senior Project 3 A primary emphasis of this course is to provide an opportunity for seniors to demonstrate their knowledge of and abilities in mathematics or a mathematics-related area by completing a senior project. In particular, students will demonstrate that they can: communicate in writingclearly and effectively, deal effectively with basic concepts, deal effectively with theoretical concepts as they arise, and apply their mathematical knowledge to develop and understand concepts outside their normal course of study. Prerequisite: Senior Status. Offered fall semester.