Paul’s current tutoring subjects are listed at the left. You
can read more about
Paul’s qualifications in specific subjects below.
Discrete mathematics is an interesting, useful, and unique area of mathematics. Topics discussed in discrete math cover probability, set theory, logic, graph theory, combinatorics, and more. Applications of discrete math are numerous: for example, graph theory can be used to arrive at possible DNA sequences based on the fragments obtained; combinatorics can be used to find the number of isomers of organic compounds. Further examples undoubtedly exist--those that I have mentioned are from my own experience.
Equally important, however, is the analytical thinking that this area offers. While most may be quick to say that discrete math may appear simple, with a little practice and an open mind, it can introduce a different way of looking at problems. In the grand scheme of analytical thinking, this fact alone makes it an important asset for any analytical discipline.
Linear algebra is a very interesting discipline in mathematics. It's not uncommon to use matrices to find quick solutions to large systems of equations. In fact, matrices can be very helpful in various modeling problems, such as the amount of deflection experienced by a board of wood. Linear algebra is essentially the algebra of matrices and systems of equations, and with it comes a unique set of mathematics. For large systems of equations, or systems with quite a few variables, linear algebra is a very powerful tool for finding the needed solutions quickly, without having to necessarily isolate each variable individually, and resubstituting into other equations until each variable is solved for.
I have been using Macintosh computers for about 4 years now. While my knowledge of them is not the "be-all, end-all" of Macintosh computing, they are fairly easy to become acclimated to. In fact, many operations that people are used to using in Windows can be done in Macintosh as well--the only difference is that some keys are named differently. Macintosh also does support Windows in various ways: Microsoft Office programs are commonly tweaked to run nicely on a Macintosh, and for Windows-only programs that have no Macintosh equivalent, there's Boot Camp for running Windows. In this day and age, Macintosh computers are becoming so flexible and versatile that in terms of function, the gap between Windows and Macintosh is narrowing quickly. If anything, the only gap that might remain is the fact that Windows has a program for almost every idea under the sun, while Macintosh is still walking the path to get there.
Organic chemistry is commonly summed up as the chemistry of compounds containing carbon and hydrogen. While it can be true, it's quite an oversimplification. Organic chemistry, in a roundabout way, is what keeps us alive as living beings, gives us some of the most commonly-used materials, and increasingly important in this age, provides new ideas for technology and energy. From pharmaceuticals to materials, organic chemistry is one of the central disciplines in the general field of chemistry; this much I know from my own experiences as a synthetic chemist. From carbon and hydrogen to nitrogen and oxygen; amines and alcohols to ketones and aldehydes, organic chemistry is a detailed discipline in three dimensions. For most, practice makes perfect for this type of class, whether it's about learning concepts or memorizing reactions.
As an apprentice educator and scientist, public speaking is one thing I'm accustomed to from years of weekly presentations and seminars (and I'm an otherwise fairly quiet person myself). Whether shy, nervous, or lacking confidence, public speaking is an important aspect to master in today's world, and should not be left unattended. If I can get used to it, so can you; the key is mostly practice, with a watchful eye or two on the lookout for your best interest.
As a New York State high school student, I have taken and excelled in various Regents exams while simultaneously involved in an Advanced Placement program. While the structure of courses and exams have changed over the years, the material covered remains the same. Exams that I have taken within my listed specialties include: Math I (now Integrated Algebra I), Math II (now Geometry), Math III (now Algebra II and Trigonometry), Chemistry, Physics (2002, the year I took it, was the year of the Physics Exam Controversy, in which grades were curved because of suspected faulty question writing. I received a 91 before the curve.), French and Comprehensive English.
In the realm of teaching and tutoring, assisting students with study skills is more of a diagnostic process. In order to make improvements, students have to describe how they prepare for exams, take notes, attempt solving problems, et cetera. The teacher or tutor, however, has to be able to figure out changes based on the student's approach to academics--there's usually more than one right way to study any given subject. Although it may be more trial-and-error than a straightforward "here's what to do for this problem", this approach can expose students to varying views on studying. These varying perspectives can provide a main plan and even a backup plan for students to follow, which can be very helpful in the long run. In that respect, utile study skills are more like a railway system--a student may have one train of thought, but at a junction, other routes may be equally helpful; it's always good to have options.