All of
Brad’s current tutoring subjects are listed at the left. You
can read more about
Brad’s qualifications in specific subjects below.
Accounting
Accounting, simply stated, is the "language" used in recording business transactions. The simplest transaction is an actual lump-sum transfer of cash on a specific date. Most deals, however, take non-cash forms and are spread out over time -- sometimes over very long, even indeterminate timeframes. This is when accounting gets very interesting, requiring a deep understanding of the principles, assumptions, and estimates used in producing a particular accounting exhibit. It's NOT so much what the numbers ARE, but what the numbers MEAN. And the figures can mean VERY different things in different business situations! It's also helpful to notice when the accounting is sober & conservative and when it's "rosy" and overly-optimistic. I'd be of more practical help in the reading and understanding of accounting statements than in their actual preparation. I've also been requested to perform numerous quarterly audits.
In 1987, Virginia Tech saw fit to award me a Minor in Economics. As a practicing private investor from 1996 through 2006, I examined thousands of accounting exhibits for hundreds of companies and their annual reports describing their financial situations. During that same 10-year period, I wrote 172 pages of essays explaining each of my investments. My favorite investment writers are J.M. Keynes, Ben Graham, Phil Fisher, and Warren Buffett. It was fun to own Berkshire Hathaway shares from February 2000 through 2006.
ACT Math
Students can enjoy simple techniques to "re-frame" many of these ACT Math puzzles using a very different, non-academic approach. Our "toolkit" includes: cutting in half, rescaling, "seeing the offset," "stair-stepping," noting counter-examples, using the "middle-value," "spelling it out" for powers & probability patterns, numer/denom tracking, and system "levelling and cancelling." Our cost-free material contains hundreds of multiple-choice and "grid-in" problems. Typical sessions begin with a tutorial puzzle, followed by a review of test questions, and ending with a timed-test simulation (Goal: 1 answer per minute).
Our ACT sessions will impart a "down-to-earth", visual sense of how any triangles work. Would you like to be able to "see" the three sides and three angles of any triangle without fumbling with equations? This can be performed mentally within a minute. Given two sides and an angle, or two angles and a side, we can specify the three remaining unknowns within 5%. No calculator or tables are needed! We will use two simple approximations often overlooked. This will serve as a handy supplement to the laws of sine and cosine for non-right triangles. We'll see how squares and circles work -- the template for almost all spatial concepts. Geometry areas and volumes can be estimated with no formulas to remember! We will also "see" how most algebra stems from the y=x and y=x^2 relations.
Algebra 2
Picking up where Algebra 1 leaves off, the y=x^2 relation is the starting point for this subject. Learn to "stair-step," "cut in half," and to re-scale systems of equations to "even up" or "cancel." The square, circle, and triangle will form our "template" for all spatial concepts. Students will develop a handy "visual" sense of polynomials, sine waves, and the e^x and ln(x) curves. Algebra 2 overlaps with much of the precalculus description below.
Calculus
Practical training is for science as well as business majors (VT Math 1525 & 1526, RU MATH 126). Calculus is the mathematics of change. Slope (a derivative) is all about observing differences. Integration is simply a "fancy way of adding." Think about your car's dashboard: the speedometer measures velocity. How do you "integrate" the speed? Look at the odometer (an "integrator") -- it adds, or accumulates, the distance traveled. Automatic feedback controls for all kinds of devices and processes use slope detectors or integrators. Say a car's cruise control is set for 60 mph. Heading up a steep hill, the car speed drops quickly. That sudden difference in speed can trigger a differentiator or slope detector to "hit the gas" as well as downshift the "tranny" to bring the speed back up to 60 mph.
In 1987, Virginia Tech saw fit to award me a BSME, magna cum laude. Completing the Cooperative Education program favored me with 2000 hours of power plant performance-testing experience. Graduate school activities included passing on the 1st attempt the ME PhD Qualifying Exam (1987), as well as finishing 70 semester hours of MS & PhD coursework emphasizing real-world measurement and control systems.
Chemistry
It was enjoyable to make the "final four" of the 21 high-school teams competing at the Corning, NY chapter of the American Chemical Society's May 1981 "Chem Bowl". Virginia Tech favored me with a full 1st-year of advanced-placement (AP) chemistry credits. High-school-level chem is likely where I'd be more helpful.
Chemistry is all about the slots in an atom's electronic "outer-shell." We must also attend to concentrations & proportions. Lewis-diagram rules can "size-up" possible compounds, like using Tinker Toys or Legos. We'll also see bond angles and molecular shapes.
GRE
Having been favored with a GRE Quant score in the 97th percentile (770/800 scaling), our GRE math sessions will impart a "down-to-earth", visual sense of how the numbers and formulas work. Students can enjoy simple techniques to "re-frame" many of these GRE Math puzzles using a very different, non-academic approach. Our "toolkit" includes: cutting in half, rescaling, "seeing the offset," "stair-stepping," noting counter-examples, using the "middle-value," "spelling it out" for powers & probability patterns, num/denom tracking, and system "leveling and canceling."
Our cost-free material contains 240 multiple choice problems and over 300 "numeric entries." Typical sessions will begin with a tutorial puzzle, followed by a review of test questions, and ending with a timed-test simulation (Goal: 1 answer per minute). Almost all spatial concepts stem from circles and squares. Geometry areas and volumes can be estimated with no formulas to recall! We'll "see" how algebra comes from the y=x and y=x^2 relations.
Physics
Having been favored with a BS in mechanical engineering, as well as power plant and laboratory experience, our physics sessions will impart a "down-to-earth", visual sense of how matter & energy move and interact. Introductory physics can be boiled down to about two dozen concepts. We will use word-pictures (eating, driving a car, spending money, TV shows and movies, sports) and sketch lots of diagrams to “see” the physics. We will see how the numbers work by “tweaking the knobs” of the formulas. We can draw from the “hands-on” mechanical engineering experience I've been favored with: including 2000 hours in power plants testing equipment, plus 2000 hours in laboratories teaching electronics, vibrations, water-air-heat flow, and building a low-hemolysis, pulsatile blood pump for cardiopulmonary-bypass use.
Precalculus
Our pre-calculus sessions will impart a "down-to-earth", visual sense of how any triangles work. Would you like to be able to "see" the three sides and three angles of any triangle without using a calculator or table of values? This can be done mentally under a minute. Given two sides and an angle, or two angles and a side, we can specify the three remaining unknowns within +/- 5%. No calculator or tables are needed! We will use two simple, overlooked approximations. This will serve as a supplement to the laws of sine and cosine for non-right triangles. Polynomials can be "eyeballed" and factored with simpler methods you may like. "Asymptotes" are simply viewed as "fences" on the x-y grid. Students will also benefit from a "hands-on" look at sine waves, and the e^x and ln(x) functions.
SAT Math
Students can enjoy simple techniques to "re-frame" many of these SAT Math puzzles using a very different, non-academic approach. Our "toolkit" includes: cutting in half, rescaling, "seeing the offset," "stair-stepping," noting counter-examples, using the "middle-value," "spelling it out" for powers & probability patterns, numer/denom tracking, and system "levelling and cancelling." Our cost-free material contains hundreds of multiple-choice and "grid-in" problems. Typical sessions begin with a tutorial puzzle, followed by a review of test questions, and ending with a timed-test simulation (Goal: 1 answer per minute).
Having been favored with a BS in mechanical engineering, as well as power plant and laboratory experience, our SAT Math sessions will impart a "down-to-earth", visual sense of how squares and circles work. Almost all spatial concepts stem from circles and squares. Geometry areas and volumes can be estimated with no fancy formulas to recall! We will also "see" how most of algebra comes from the y=x and y=x^2 templates. I've enjoyed teaching thousands of sessions since the late '80s, both in large classes and in the home on a wide variety of topics. Good teachers care about people, are good examples, know their subject, and are terribly interesting. Students deserve that.