Courses I have taught

Brief descriptions follow; click the titles for more detail and possibly course notes

Material mainly from classical algebra and analytic geometry useful in a wide variety of areas, but especially focused on paving the way for calculus. General notions concerning functions, graphs, transformations, polynomials, polynomial equations, quadratic equations, real roots of polynomials, derivative of a polynomial, rational functions and partial fractions, conic sections. See catalog description.

Material mainly from classical algebra and analytic geometry useful in a wide variety of areas, . Linear equations and inequalities in one and two variables, absolute value and distance and related inequalities, graphs of lines in the plane, distance in the plane, systems of linear equations and inequalities, polynomials and their arithmetic, quadratic equations, graphs of parabolas, rational functions. See catalog description.

Differential and integral calculus with applications. Graphs of polynomial functions and derivatives of polynomials; maxima, minima, points of inflection. Limits of sequences and functions, differentiability and continuity and consequences. Derivatives, Newton's method, Taylor polynomial approximation, elementary transcendental functions, polynomial spline functions. Inverse functions and their derivatives. Implicit functions and differentiation. Integration, Riemann sums, and the logarithm function. Fundamental theorem of the calculus. Integration by substitution, Applications. See catalog description.

Number systems, geometry (area, perimeter), factorization and prime numbers, arithmetic of fractions. Decimal representations of numbers, ratios, proportions. Mathematics for finance (credit card interest, mortgage interest, personal loans, bank accounts and CDs), measurement systems and conversions, triangles and distance in the plane, introduction to algebra.

Review of lines in the plane and their equations. Intersections of lines in the plane. Best-fit lines in the plane via the method of least squares (linear regression). Systems of linear equations. Gaussian and Gauss-Jordan elimination. Underdetermined and overdetermined systems. The method of least squares again. Matrices, linear transformations, and elementary row operations. Computer implementation. Matrix algebra. Systems of linear inequalities and linear programming. Best-fit lines via the method of least absolute deviations. Computer implementation.

Some "paradoxes" involving probability, especially the Monty Hall problem. Gambling. Origins of probability and statistics. Sample spaces, probability measures and densities. Independence. Random variables. Marginal and joint distributions. Conditional probability. Contingency tables. Simpson's paradox. Tests of hypotheses. Markov chains. Expectation. Martingales and fair gambling games. Law of large numbers, central limit theorem and the "bell curve".