James’s current tutoring subjects are listed at the left. You
can read more about
James’s qualifications in specific subjects below.
Through years of experience as a tutor, in addition to studying traditional mathematics in college, I have a very thorough understanding of basic Algebra and its applications.
Areas of proficiency within Algebra I include (but are not limited to): the real number line, inequalities, linear functions (lines) and their graphs, slope (rise over run), polynomials, fractions, probability, algebraic properties, area & perimeter of basic geometric shapes, exponents, radicals, simple factorization, and order of operations.
I took a course in Modern Algebra while at Virginia Tech. This course taught the theory behind relationships such as domain, range, functions, composite functions, inverses functions, associativity, commutativity, identities and the inverses that relate to them. These topics are necessary to build on with more applied or advanced Algebra. Later Algebras also deal with simultaneous equations, which would require a more basic understanding of lines and how to graph them. Algebra II also deals with more advanced techniques to solving problems, such as completing a square to find a general form.
I also had several courses in Linear Algebra which deals with the algebra of simultaneous equations. Calculus is mostly a lot of algebra, including factorization, simplification and methods to solve for some variable. It might not be obvious, but Algebra plays a very big role in Calculus, which is why there is so much emphasis on Algebra throughout middle and high school.
I've taken several Calculus based courses including Derivative Calculus, Integral Calculus, Vector Geometry, Multivariable Calculus, Vector Calculus, and Advanced Calculus while at Virginia Tech. I received a 5/5 on my AP exam for Calculus AB in 1999. The bulk of my experience tutoring has been with Calculus for the past two years.
Subjects I teach to master Calculus I & II include (but are not limited to): Functions and their graphs, slope, limits, the tangent line problem, derivatives, different methods to produce the derivative (power rule, product rule, quotient rule, chain rule), sequences and series, approximating area under a curve, anti-derivatives, definite and indefinite integrals, applications of integration (area under a curve, volume bound by rotation of curve, center of mass, length of curve), parametric equations, and polar equations.
I have taken several courses in relation to discrete math. This field of math deals with theory instead of computation and applications. Discrete math relies heavily on number theory. For example, discrete math offers the knowledge on how to prove that the sum of any two even integers is also even, in a way that is "acceptable" to the math community. Many of these concepts may not seem obvious at first, but when you learn how to approach problems in this fashion, it can be very fun and rewarding. Computer programmers are required to take many classes in this field, and its applications for programming are very relevant.
Discrete math begins with "truth tables", which studies "if-then" statements and logical equivalences. Set theory is another big topic, which talks about the intersection or union of two or more sets. The subject matter expands concepts you may already be familiar with (e.g. greatest common multiples) to a topic called "modulo" which deals mostly with remainders. Mathematical induction is another popular topic which is typically used to establish that a given statement is true of all natural numbers. The biggest reward from a discrete math class is the ability to write solid mathematical proofs. I can help teach this topic because I have a lot of experience writing proofs, and have many resources to help with this topic. This is one of my favorite topics!
Classes that I've taken related to discrete math (proof writing) include:
Introduction to Proofs, Vector Calculus, Modern Algebra, Advanced Calculus, Introduction to Numerical Analysis
My field of study is traditional mathematics but I also studied some economics while at Virginia Tech. Economics is extremely math oriented as it deals with supply and demand right from Econ 101. In my first economics class at VT, I was a note-taker and learned the information very thoroughly because of that. I went on to take some Calculus based Economics courses which were very insightful. I have been studying relationships between supply, demand, and pricing for years with my small business and with the stock market. While it is not always necessary, I tend to show economics examples to students whom I tutor Calculus.
My first geometry class was sometime in the early 90s, some 20 years ago. This was my introduction to proof writing and abbreviated arguments such as "side-angle-side" when attempting to show two triangles are similar. In college geometry, the concept was similar, but the approach was with functions, using the sides of the triangles as independent variables for these functions, to obtain a consistent ratio between each function. The latter part is much less intuitive, however learning the advanced method has made high school level geometry somewhat trivial.
Additionally, I have extensive experience with the types of geometry problems that appear on exams such as the SAT, AP Calculus, and ACT.
Furthermore, trigonometry is a topic that immediately follows geometry as a natural progression in mathematics. I have a thorough understanding in this field of mathematics, which aids to my understanding of geometry as a whole.
While at Virginia Tech, I took several Linear Algebra based courses. Linear Algebra, Intermediate Linear Algebra, Modern Algebra, Differential Equations, and Intro to Numerical Analysis were all classes which dealt heavily with matrix theory and the algebra of simultaneous equations. These classes ranged from topics of basic understanding of matrices, to matrix operations, to solutions to systems, and applying these concepts in classes like Differential Equations with eigenvectors and eigenvalues. I have some experience tutoring in row reduction, matrix multiplication, and solving for inverse matrices.
Pre-Algebra is an introduction to equations and expands beyond basic arithmetic. It provides a mastery for arithmetic while preparing the student for equation writing.
Subjects that I teach in Pre-Algebra include (but are not limited to): the real number line, integers, negative numbers, order of operations, exponents, factorization of numbers, fractions, decimals, arithmetic properties, and basic geometric formulas.
Pre-Calculus is a course that requires a student to have a knowledge of Geometry, Trigonometry and advanced Algebra, all in order to be prepared for Calculus. The majority of my experience with students has been with Pre-Calculus and Calculus, and I have a very thorough understanding of what is needed to succeed.
Subjects I teach to master Pre-Calculus include (but are not limited to): Functions and their graphs, domain and range, slope of lines, equations of lines, completing the square, division of functions (also called synthetic division), roots/zeroes of polynomials, rational functions, logarithms, inverse functions, reflections/symmetries/translations of graphs, summations, sequences, series, permutations, combinations, and mathematical induction.
Trigonometry is an extension of Geometry and primarily deals with angles and sides of triangles. There are many exams with questions related to this topic, including the SAT, ACT and AP Calculus exams, all of which I have experience with.
Subjects I teach to master Trigonometry include (but are not limited to): Basic trigonometric sine, cosine and tangent functions, inverse functions (cosecant, secant and cotangent), the unit circle, pi, graphs of trigonometric functions, trigonometric identities, complex numbers, triangle and circle ratios, and common trigonometric values (multiples of 30 degrees and 45 degrees).