Michael’s current tutoring subjects are listed at the left. You
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Michael’s qualifications in specific subjects below.
I got a perfect score on the math portion of the ACT, and of course I have learned much since then. I also know a thing or two about standardized tests so can give you some strategic pointers.
Algebra is the basis of all symbolic variable mathematics, in which the exact value of one or more unknown quantities is obtained by logical, methodical manipulation of known relationships. Algebra 1 introduces the rules governing this manipulation, as well as other mathematical ideas you may not have seen yet. (Turns out you CAN take the square root of a negative number!)
On a personal note: believe it or not, I didn't think I was very good at math until I took algebra in the eighth grade. Perhaps you, too, have found math up to this point pointless and boring--how many times must one regurgitate 5 x 6 = 30? Trust me, it gets a lot more exciting. And ironically enough, it was in taking algebra that basic arithmetic became easy. (Such is the general pattern--one doesn't really master algebra until calculus.)
Algebra 2 picks up where the first installment leaves off. Think of it as one of those movie sequels that are actually as good or better than the original (like Toy Story). For example, here we deal with solving systems of equations with multiple unknowns--turns out there are actually several ways of doing this.
I took and aced "Algebra 2: Return of the X" my freshman year in high school. Loved it.
Astronomy is the study of objects in the sky, mostly the night sky, and bumps up against the physics of the entire universe. It includes the planets and moons of our own solar system, the stars and constellations, the structure of our galaxy and others, and of the universe as a whole.
The ASVAB consists of a number of tests in subjects ranging from general science, to math knowledge and arithmetic, to vocabulary, to mechanical comprehension. I have not taken it, but was asked a few months ago to work with somebody who was preparing for it, and (in his words), he "learned more than [he] ever did in school." I can refresh your algebra skills and show you tricks to speed up your calculations, especially in the context of a multiple-choice test. I can explain most of the science and mechanical knowledge questions too, as well as the word knowledge and paragraph comprehension.
How do you find the slope at any point on a curve that is constantly changing direction? How can you find the area of a region not bounded by the nice straight lines that make up rectangles, triangles, and trapezoids? Calculus! Calculus slices the mathematical world into itty bitty pieces called differentials. Comparing differentials gives you slopes. Adding them up gives you areas. And that's just scratching the surface. All of your math studies to this point have been laying the foundation for calculus.
I was exposed to calculus in my first algebra class just as a lark or random tangent by the teacher, and was immediately hooked. After completing Algebra 2, I taught myself calculus over the summer, pausing only when I encountered trig, which I didn't yet understand.
I took a chemistry course in high school and again in college. Much of chemistry overlaps with physics, and that's where I'm most comfortable. I also really love stoichiometry (both doing it and saying its fun name).
Differential equations are equations involving one or more derivatives of an unknown function. A variety of slick techniques exist to solve for the unknown function, depending on the exact type of differential equation presented.
As a Master of physics, I have significant exposure and experience in dealing with ordinary and partial differential equations. Alas, opportunities to practice are few and far between, so I would love to keep that sword sharp by helping you with your ODE or PDE problems.
Geometry, from the Greek for earth-measure, is one of the oldest branches of mathematics. It deals with the properties of lines, angles, and shapes, often deriving rigorous proofs from relatively few self-evident axioms. Analytical geometry puts the ideas from geometry into the context of algebra, specifically the x-y plane.
I took a geometry class my sophomore year in high school and excelled.
Matrices, determinants, and eigenvalues, oh my! Linear algebra explores the world opened to view when in Algebra 2 you extracted the coefficients of systems of linear equations, put them in a matrix, and shook out a solution.
As part of my coursework in college I took a semester of linear algebra (in which, as usual, I earned an A). Additional studies of physics drove home the key points of this type of math, moving it from the abstract to the "real world."
I am self-educated in the use of Excel, picking up my skills in the course of performing incidental job functions. As such, I know most of the basic features and rules, plus a few neat tricks.
In two words or less, physics boils down to "things move."
I have been a physics guy since my freshman year of high school, when I took an eagerly-awaited Conceptual Physics class. After getting a 5 on the AP my senior year, I dived right into physics as my university major, completing a BS and an MS in the subject. Currently I teach physics at a community college and derive much joy and satisfaction therefrom.
Prealgebra, true to its name, prepares you for algebra. Math begins to move beyond the basic arithmetic skills to the powerful thinking tool it will become as you move forward.
As prealgebra is to algebra, so precalculus is to calculus. Here the acquired disciplines of algebra, geometry, and trigonometry come together to prepare the student for the rigors of calculus. There even tantalizing sneak peeks into calculus itself.
Now, true confession: I did not take a "precalculus" class as such (my school didn't offer it, and I didn't need it anyway). However, since living in Las Vegas I have had many opportunities to successfully tutor students struggling with one aspect or another of precalc.
Probability is really cool, as it manages to take something as strict and predictable as math and apply it to things that follow no defined rule (or else rules far too complex to be dealt with directly). Probability tells us what will generally happen if we repeat the same experiment over and over, such as drawing cards from a deck, or rolling dice, without specifying the outcome of any particular instance.
As a stand-alone class, probability was never part of my curriculum. However, the principles thereof have been part of courses I have taken, from prealgebra to thermal physics to quantum mechanics.
I scored very well on the math portion of the SAT. The SAT, like the ACT, samples the math courses you have taken from the beginning of your education. You will need to read graphs, think logically, and have a variety of mathematical tools at the ready.
Trigonometry (affectionately known as "trig") begins as an intense look at right triangles but quickly becomes about much more, from general triangles to complex numbers to waves.
I taught myself trigonometry when I encountered trig on my way to learning calculus. I also took a trig class in high school. And naturally the classes I took in my major kept my skills sharp.