Teaching

A study of the basic terminology and methods of elementary statistics including organization of data, measures of central tendency and dispersion, sampling theory, estimation and testing of hypotheses. Also includes an introduction to correlation and linear regression.

An introduction to calculus with primary emphasis on applications to business and economics. Topics include algebra, problem solving, functions including exponential and logarithmic, mathematics of finance, systems of linear equations, differentiation, and applications of differentiation.

A study of functions, limits, continuity, differentiation, applications of differentiation and an introduction to integration.

A study of integration, techniques of integration, applications of integration and an introduction to infinite sequences and series.

A study of vectors, vector algebra, analytic geometry in three-space, partial differentiation, multiple integration, sequences and series.

A study of the algebra of sets, relations, functions, cardinality, selected topics of number theory, prepositional logic and number systems. 

A study of vector spaces, linear transformations, matrices, systems of linear equations and determinants.

An introduction to the basic structures of modern abstract algebra: groups, rings, integral domains and fields.

An introduction to probability including probabilistic experiments and their sample spaces, random variables and their probability distributions, and functions of random variables and their properties. An introduction to the methods of inferential statistics.

A continuation of the methods of inferential statistics. Topics include introductory sampling theory, estimation, confidence intervals and hypothesis testing, experimental design, and analysis of variance. Some nonparametric statistics also introduced.

A study of the foundations of geometry including transformations, deductive and inductive reasoning and an introduction to non-Euclidean geometries. 

A study of topics in point-set and algebraic topology, including topological spaces, continuous functions, connectedness, compactness, the fundamental group, and the Seifert-van Kampen Theorem.

Rates of change, differentiation, applications of derivatives including differential equations and the fundamental theorem of the calculus. Written communication and applications to other sciences and social sciences motivate course content.

Techniques of integration, geometric applications of the integral, differential equations and modeling, infinite series and approximation of functions. Written communication and applications to other sciences and social sciences motivate course content.

Theory and applications of limits, derivatives and integrals of functions of one, two and three variables. Curves in two-and three-dimensional space, vector functions, double and triple integrals, polar, cylindrical, spherical coordinates. Path integration and Green’s Theorem.

Polar coordinates, parametric equations, sequences, infinite series, vector analysis.

Vector calculus; functions of several variables; partial derivatives; gradients, extreme values and differentials of multivariate functions; multiple integrals; line and surface integrals. 

First order ordinary differential equations, linear differential equations with constant coefficients, two-by-two linear systems, Laplace transformations, phase planes and stability.

Systems of linear equations, determinants, finite dimensional vector spaces, linear transformations and matrices, characteristic values and vectors.