Jeffrey’s current tutoring subjects are listed at the left. You
can read more about
Jeffrey’s qualifications in specific subjects below.
Algebra I focuses on the real number system, the study of polynomials, the solving and graphing of linear equations and linear inequalities, the Cartesian Coordinate System, slope, equations of lines, factoring polynomials, solving polynomial equations, rational expressions, integer exponents, and problem solving.
Algebra II (with Trigonometry) focuses on functional notation, linear functions, absolute value functions, quadratic functions and equations, and other basic algebraic functions - with the graphs and translations thereof also being taken under consideration. Moreover, linear equations and inequalities are examined, as are the methods of solving polynomial equations, the basics of radicals and rational exponents, exponential and logarithmic functions, geometry, and right triangle trigonometry.
The study of Calculus of a Single Variable includes, but is not limited to, the following topics: limits, continuity, differentiation of algebraic functions, applications of differentiation, anti-derivatives, the definite integral, transcendental functions, techniques of integration, applications of the definite integral, conic sections, polar coordinates, improper integrals, and infinite series.
In contrast, the study of Calculus of Several Variables includes the following topics: curves and vectors in the plane, the geometry of three-dimensional space, vector functions in three-space, partial derivatives, multiple integrals, and line and surface integrals.
I first undertook the examination, in earnest, of differential equations while completing a program of study at Syracuse University. One course, in particular, included an analysis of first order differential equations, second order linear differential equations, power series solutions, Bessel's equations, and Laplace transforms. Systems of differential equations and applications were also examined.
I went on to graduate from Syracuse University with a Bachelor of Arts degree in Mathematics (Magna cum Laude), and I have since returned to my studies, at the graduate level, at the University at Albany. It is here that I have further studied differential equations, and the coursework that I have completed includes a careful examination of partial differential equations, wherein the properties of solutions of both first order and classical second order equations have been reviewed. Furthermore, several of the techniques of solution, including the separation of variables and Fourier series, were discussed in detail.
It might be of further interest to note that I have functioned as a professional academic tutor and/or an adjunct faculty member, for a period spanning more than fourteen years, for institutions such as Onondaga Community College, Mohawk Valley Community College, Schenectady County Community College, Morrisville State College, Fulton-Montgomery Community College, the State University of New York Institute of Technology, and Colgate University. As such, I have had ample opportunity to continue my examination of differential equations in a variety of settings and under varying sets of circumstances.
An Introduction to Theory of Statistics provides a mathematical treatment of the principles of statistical inference. Topics of study include, but are not limited to, the following: probability, random variables - both discrete and continuous - and random vectors, univariate and multivariate distributions, and an introduction to estimation.