All of
Dave’s current tutoring subjects are listed at the left. You
can read more about
Dave’s qualifications in specific subjects below.
Algebra 1
Common topics in this subject which I have tutored include: real numbers, solving linear equations, graphing relations and functions, analyzing linear equations, solving linear equalities, solving systems of linear equations and inequalities, polynomials, factoring quadratic and exponential functions, radical expressions and triangles, radical expressions and equations, basic statistics and probability. I am over-qualified to tutor this subject because I was a New York state certified high school math teacher for 10 years (1995-2005) during which time I privately tutored countless students and taught Regents level Course 1 (algebra 1) amongst other high school level math courses for two different schools and a private tutoring agency. I have also tutored several clients in algebra 1 here in Massachusetts with WyzAnt in recent years.
Algebra 2
Topics which I have tutored for algebra 2 include: first degree equations and inequalities, linear relations and functions, systems of equations and inequalities, matrices, polynomials, quadratic functions and inequalities, polynomial functions, conic sections, rational expressions and equations, exponential and logarithmic relations, sequences and series, probability and statistics, trigonometry functions, trigonometric graphs and identities. I am overqualified to tutor this subject area because I was a New York state certified high-school math teacher for 10 years (1995-2005) and tutored countless Regents course 2 level (algebra 2) students during this time. I also taught this level (algebra 2) in 2 different schools during this time and have had multiple clients in recent years whom I've tutored this level to while working with WyzAnt in Massachusetts.
Biology
Subject area includes: acids and bases, pH scale, cell structure, photosynthesis, respiration, chromosomes, cell reproduction, meiosis, sexual reproduction, heredity, DNA, protein synthesis, gene technology, history of life on Earth, evolutionary theory, human evolution, populations, ecosystems, biological cummunities, human impact on the environment, kingdoms, viruses, bacteria, protists, fungi, plants, invertebrates, vertebrates, human body structure and systems and more...
Calculus
Subject area includes: Cartesian plane, graphs of equations, functions, limits, techniques for evaluating limits, continuity, infinite limits, delta-epsilon definition of limits, derivative and tangent line problem, velocity, acceleration and other rates of change, differentiation rules for constant multiples, sums and powers, differentiation rules for products and quotients, extrema on an interval, the Mean Value Theorem, increasing and decreasing functions and first derivative test, concavity and second derivative test, optimization problems, business and economic applications, Newton's Method, Differentials, antiderivatives, integration by substitution, riemann sums and the definite integral, The Fundamental Theorem of Calculus, numerical integration, area of a region between two curves, volume: disc method, volume: shell method, work, fluid pressure and force, arc length, differentiation of log functions, differentiation of exponential functions, differentiation of trig functions, integration techniques, L'hopital's Rule, Integration by parts, trigonometric substitution, partial fractions, improper integrals, Taylor polynomials, sequences, comparisons of series, ratio and root test, power series, Taylor and Maclaurin Series, dot product, cross product, cylindrical and spherical coordinates, vectors, chain rule, double integrals, change of variables, , Jacobians, surface area, vector fields, line integrals, Green's Theorem, Stoke's Theorem, first order linear differential equations, separation of variables in first order equations, homogeneous linear differential equations, non homogeneous linear differential equations, second order differential equations and more
Chemistry
Topics that could be covered would include matter and measurement, atoms, molecules and ions, periodic properties of the elements, basic concepts of chemical bonding, stoichiometry, electronic structure of atoms, ideal gases and gas laws, acids and bases, electrochemistry, nuclear chemistry, and properties of solutions.
Differential Equations
Topics include solving first order equations that don't involve terns in y, and first order equations that do involve terms in y, using integrating factors,second order differentials, homogeneous higher order differential equations, nonhomogeneous linear higher order differential equations, using power series to solve ordinary differential equations, solving diffequations with series solutions near singular points, Laplace Transforms, and solving systems of linear first order equations.
I took differential equations as a sophomore in a Mechanical Engineering degree. I also have taken a class which uses differential equations with Boundary Value Problems as part of a Bachelor of Science in math (Math Major) at Stonybrook University. I also taught a unit on differential equation applications when I was a TA for a Section of a Calculus 2 class at SUNY Albany. I believe this gives me an adequate background for tutoring the subject.
Discrete Math
I majored in math in college and have experience with linear algebra, number theory and logic and could help a perspective student taking courses in this realm who might be involved with writing proofs of this nature.
Discrete math involves the study any form of analytical math outside of the realm of continuous variables as one would see with function theory and the calculus. It is basically a subcategory which concerns logic, set theory, number theory, linear algebra, combinatorics, and sometimes discrete geometry. Courses in this subcategory of math are usually taken by computer science majors, math majors, automata majors etc.
Electrical Engineering
As a mechanical engineering student, and as a straight physics student, I have had some experience solving problems concerning electricity, electric potential energy, electrical circuits, electromagnetic induction, alternating current circuits and electromagnetic waves. I have experience solving circuit problems for series, parallel and combination circuits using Kirchoff's Rules and with calculation of capacitor discharges, resistivity, impedance, inductance...you name it. I can help you with magnetic and electrical field problems concerning emf, flux and all of the different right-hand rules as well.
Finite Math
As I was a math major in college, I am very fluent in multiple mathematics subject areas of which are covered in a finite mathematics course. I have previous experience in both teaching and tutoring this material at both the high school and college level and can very confidently help you with any subject in combinatorics and/or finite math which is taught. Any sub-topic in logic or probability, or set theory as they pertain to a finite math course is right up my alley.
Genetics
As a high school science teacher, I annually teach full units on genetics, heredity, protein synthesis and genetic technology to my biology students. Recently, (2012) I had the privilege of becoming trained in the most up to date information concerning this field by a summer Amherst College seminar for Massachusetts science teachers and also at that time, obtained various genetics lab equipment as well for teaching genetics to biology students at the high school level.
Geometry
Subject areas include: inductive reasoning, biconditionals, deductive reasoning, methods of direct and indirect proof, postulates and proofs, equivalence relations, simple angle theorems, congruent polygons and corresponding parts, proving triangles congruent using two pairs of sides and included angle (SAS), proving triangles congruent using two pairs of angles and included side (ASA), proving triangles congruent using three pairs of congruent sides (SSS), isosceles triangles, equilateral triangles, basic inequality postulates, proving lines perpendicular and parallel, sums of the measures of the angles of a triangle, quadrilaterals, parallelograms, rectangles, rhombuses, squares, trapezoids, simlar triangles and similar triangle theorems, coordinate plane and coordinate geometry, slope, graphing linear equations, areas, locus in coordinate geometry, parabolas, transformation geometry, translations, reflections, rotations, dilations, basic constructions, line and point symmetry and more
Linear Algebra
I have taken a few upper division level college Linear Algebra courses at SUNY at Stonybrook. I received a a B and B+ in the classes which I took. Seeing as though I majored in mathematics, I was required to take Linear Algebra, Abstract Algebra and Number theory courses there which exclusively use matrices and linear dependence and show how these subjects are used in vector calculus and differential equations.
Logic
Basic Logic Skills are crucial for understanding Euclidean Geometry proofs and for understanding Venn Diagrams in Probability and in Computer Science. I have taught and tutored logic at the high school level as it is part of the standard math curriculum in both NY state and CT. As a math major in college (Although as a course for math majors, it was an elective which I did not take.), I was required to know logic for the first chapter in multiple upper division mathematics classes such as Abstract Algebra, Linear Algebra, and/or Non-Euclidean Geometry. Topics we could cover would include: connectives, truth tables, tautologies, the Law of detachment, the Law of Contrapositive, the Law of Modus Tollens, Chain Rule, Law of Excluded Middle, Law of Simplification, Law of Disjunctive Addition, universal and existential quantifiers, conditionals, biconditionals, sets, relations and equivalence classes.
Mechanical Engineering
Before I chose my original college route of becoming a math major for my first degree at SUNY at Stonybrook, I originally completed the first two years of undergraduate Mechanical Engineering Classes at a community college and was accepted into Stonybrook University as a 3rd year Mechanical Engineer. Once I became enrolled there, I switched my interest to a straight mathematics degree. I originally liked math much more than physics. It wasn't until I went back to school many years later at Boston University did I pursue my interest in Physics. All the same, because of this I have taken and done sufficiently well in all of the first two years of Mechanical Engineering School. Topics I studied were: materials, mechanics 1, mechanics 2, physics 1, physics 2, physics 3, calculus 1, calculus 2, calculus 3, differential equations, thermodynamics, freshman chemistry 1, freshman chemistry 2, and Fortran 1 and 2 (a now dead computer language). I still have basic expertise in these areas that can be of use to first and second year engineering students.
Microsoft Excel
Microsoft Excel is perfect for making spreadsheets of all different sorts. I have experience from while I was completing my master's degree in education AND from my current occupation as a teacher. For example, I currently use a Microsoft Excel Spreadsheet to keep data for a point "levels" system which assesses students' behavior during classtime. This Excel Spreadsheet is updated by me weekly. Many countless uses for spreadsheets come up on the job for recording and keeping data.
Physical Science
This subject entails the science of basic physics and chemistry at the middle school and early high school level. The math level needed involves basic algebra formulas and arithmetic used to solve appropriate word problems. Topics include: the properties, classification and structure of matter, the use of the periodic table and the laws and facts for using it as a reference, chemical bonding, chemical reactions, forces and motion, forces in fluids, Bernoulli's Principle, work, power and simple machines, energy, conservation of energy, temperature and heat, electricity and magnetism, sound and light waves, and various types of technologies.
Physics
Subject areas include: Kinematics in one and two dimensions, forces and Newton's Laws of Motion, dynamics of uniform circular motion, work and energy, impulse and momentum, rotational kinematics, rotational dynamics, simple harmonic motion and elasticity, fluids, temperature and heat, heat transfer, ideal gas laws and kinetic theory, thermodynamics, waves and sound, principle of linear superposition and interference phenomena, electric forces and electric fields, electric potential energy and electric potential, electric circuits, magnetic forces and magnetic fields, electromagnetic induction, alternating current circuits, electromagnetic waves, the reflection of light: mirrors, the refraction of light: lenses and optical instruments, interference and the wave nature of light, special relativity, particles and waves, the nature of the atom, quantum mechanics, nuclear physics and radioactivity, ionizing radiation, nuclear energy and elementary particles
Praxis
As a requirement during grad school toward getting my MA, I had to take the math Praxis and passed it the first time I took it and scored fairly well without ever cracking open a book. I have an extensive background in mathematics and am proficient in test taking strategies of government tests such as SAT, ACT math and the Praxis. If I tutored you, we would use a Praxis review book and do a host of problems together from a variety of math subject areas which are covered on the Praxis test.
Prealgebra
Topics in this subject area which I have tutored include: integers, equations, factors and fractions, rational numbers, ratio, proportion and percent, equations and inequalities, functions and graphing, real numbers and right triangles, two dimensional figures, three dimensional figures, basic statistics and probability, polynomials and nonlinear functions. I am overqualified to teach this level (prealgebra) as I have tutored many 8th grade level students during my time as a tutor when I was a New York state certified 7th -12th grade secondary education - math teacher and have had multiple clients which I've tutored this level to here, in Massachusetts, (working with WyzAnt Inc.) as a tutor.
Precalculus
Topics which I have tutored concerning the subject of pre-calculus include: functions, equation theory, matrices, vectors, trig. functions, inverses of trig. functions, applications of trig. functions, sequences, series, polar coordinates, complex numbers, exponential and log functions, conics, probability, limits, derivatives and epsilon delta proofs. I am plenty qualified in tutoring precalculus in that I was a certified New York state high school math teacher for 10 years (1995-2005) and as part of my student teaching, I taught a precalculus class for several months. During these years, I tutored several different clients in precalculus and, in recent years, I have tutored several MORE different clients in this subject working with WyzAnt here in Massachusetts.
Regents
For 10 years (1995-2005) before I moved to Massachusetts, I was a NY state certified high school mathematics teacher with the regents program. During this time period, I also privately tutored many dozens of students in preparation for the annual NY state regents math tests and am very familiar with their means of testing as well as the testing practice materials which are available to test preparers. I could be very helpful to a NY state math student who was interested in meeting weekly to go over regents material from test practicing companies such as Barron's which prep for the regents.
Statistics
Subject area includes: the summation symbol, measures of central tendency, range, mean, absolute deviation, standard deviation, normal distribution, grouped data, measures of location, measures of variability, random variables, probability distributions for discrete random variables, expected values of discrete random variables, binomial probability distribution, hypergeometric and negative probability distributions, Poisson Probability Distribution, Gamma Distribution and its relatives, other continuous distributions, hypotheses and test procedures, z tests and confidence intervals, two sample t test and confidence intervals, analysis of variance, ANOVA, two factor ANOVA, linear regression and correlation, non linear and multiple regression, polynomial regression, regression analysis, Goodness of Fit tests, Wilcoxon Signed-Rank Test, Wilcoxon Rank-Sum Test and more
Trigonometry
Subject area includes: arcs, angles, chords, inscribed angles and their measures, angles formed by tangents, secants and chords, absolute value equations, absolute value inequalities, roots and radicals, simplifying a radical, arithmetic of radicals, rationalizing a denominator containing a radical, quadratic formula, quadratic equations with real roots, line reflections, point reflections, translations, rotations, dilations, relations, functions, composition of functions, compositions with transformations, sine and cosine as coordinates, sine functions, cosine functions, tangent functions, finding reference angles of trig functions, radian measure, reciprocal trig functions, graph of y = sin x, graph of y = cos x, inverse trig functions, exponent laws, exponential equations, graph of y = tanx, logarithms, the law of sines, the law of cosines, the ambiguous case, half and double angle formulas, quadratic inequalities and more.