I am a tutor and mathematician and theoretical physicist. I have a Master's degree in Physics (1978) from the University of Southern California, I made substantial progress towards a Ph.D. in Theoretical Physics (Solid State) and a Ph.D. in Pure Mathematics (Functional Analysis) at the University of Southern California, I have a Baccalaureate Degree in Pure Mathematics (1976) and a Baccalaureate Degree in Applied Mathematics (1977) from the California Institute of Technology. I also co-wrot... [more]

Algebra 1

I taught Algebra 1 online for eight years for Brainfuse, a pre-eminent online site, and I taught Algebra 1 at Chyten Educational Services in Westlake Village, CA for four years. I have a thorough knowledge of Algebra 1 as well as mastery of Abstract Algebra as taught at the California Institute of Technology. I am an expert tutor of the following subjects of Algebra 1: rational and irrational numbers, absolute value operation and function, the completion of square method of solving quadratic equations, quadratic formula, solving linear systems of equations in two variables, direct and inverse and joint variation, solving linear equations in one unknown, solving literal equations, translating English phrases and sentences into mathematical expressions and equations, graphing linear and quadratic and absolute value functions, domain, range, et. al. Working with me on Algebra will prove to be very beneficial to you -- remember that if you have x dollars, and receive another dollar, then the amount you then have is x + 1 dollars.

Algebra 2

Because of my educational background (B.S. in Mathematics, CalTech, and B.S. in Applied Mathematics, CalTech) I am very familiar with the subject matter of Algebra 2. I am familiar with the Quadratic Formula, the Cubic Formula, the Quartic formula, solving simultaneous non linear equations in two or more unknowns, Horner's method of approximating the zeros of functions, Synthetic Division, Group Theory, Ring Theory, Field theory, graphing of non linear functions, Complex Numbers, Field Extensions, Composite Functions, solving absolute value equations and inequalities, the equations of conic sections, Least Squares Fit, inverse functions, et. al. I have tutored all of the above and have enjoyed doing so and I am very tenacious.

Calculus

I have a Baccalaureate degree in Mathematics and a Baccalaureate degree in Applied Mathematics from the California Institute of Technology. I have a Master's Degree in Physics, I have completed significant coursework towards a Ph.D. in theoretical physics, and I have completed significant coursework towards a Ph.D. in Pure Mathematics from the University of Southern California. I am familiar with the concepts of continuity, differentiability, continuously differentiable, integrability of functions, evaluating integrals, the technique of integration by parts and u-substitution and trigonometric substitution, improper integrals, convergence of integrals, First and Second Fundamental Laws of the Calculus, power series, radius of convergence, Cauchy sequences, double integrals, triple integrals, change of order of integration, Cauchy's Equations, Complex Analysis, De Moivre's Theorem, applications of the Calculus, Line Integrals, Stoke's Theorem, Vectors, Vector Analysis, Velocity, Acceleration, et. al.. Working with me on the Calculus will prove to be very beneficial to you.

Geometry

I have extensive knowledge of geometry as well as a long successful history of tutoring it (meaning that my students of geometry did very well in their classes after working with me). For example, you can discuss with me the following concepts and topics: two dimensional geometric figures, like circles, squares, rectangles, hexagons, dodecagons, polygons, regular polygons, perimeters, areas, geometric proofs, parallelograms, rhombii, solid geometry, cubes, rectangular parallelepipeds, spheres, ellipsoids, cylinders, cones, total surface area, surface area, lateral surface area, Euler's Theorem involving number of faces number of edges number of vertices of a polyhedron, polyhedron, Riemann Geometry, Lobachevsky Geometry, Gaussian curvature, differential geometry, curvature, torsion, tangents, parallel lines, perpendicular lines, similar figures, similar triangles, skew lines, congruence, similarity, acute triangles, triangles, obtuse triangles, right triangles, isosceles triangles, equilateral triangles, Pythagorean theorem, tessellations, planes, N-gons, rotations, dilations, etc..

Physics

I am familiar with and tutor Mechanics, Electromagnetism, Gravitational force, differential equations of physics, thermodynamics, gas dynamics, classical physics, quantum physics, photoelectric effect, polarization of light, waves, work, forces, Black Body radiation, Special and General Relativity, statistical physics, et. al.

Prealgebra

7th Grade math covers arithmetic (multiplication, division, addition, subtraction), learning to use a Calculator, word problems, basic geometric figures, lines, linear equations, solving linear equations, exponents (negative exponents), roots, fractional exponents, etc.. I am an expert at teaching these concepts.

Precalculus

Intermediate Algebra and PreCalculus covers solving simultaneous non linear equations, graphing cubic polynomials and quartic polynomials, methods to solve transcendental equations, elements of group theory, limits, rational functions, graphing rational functions, x and y intercepts of rational functions, functions, simultaneous equations in three variables, basic set theory and logic, types of numbers, polynomial division, solving radical equations, complex numbers, complex plane, solving equations with complex numbers, relations, continuity of functions, continuous functions, discontinuity, types of discontinuities, describing functions analytically and graphically, piecewise functions, composite functions, et. al. I am an expert tutor of all of the topics above and more.

Trigonometry

I am familiar with ambiguous triangles, solid geometry, areas of triangles, Heron's formula, trigonometric identities, trigonometry on the unit circle, double angle formulas, law of cosines, law of sines, half angle formulas, identity for sin(A+B), identity for cos(A+B), identity for tan(A+B), trigonometry for triangles on a sphere, circumcenter, incenter, orthocenter, etc.

Statistics

I am an Associate of the Society of Actuaries (I have the A.S.A. professional degree), which makes me an expert in Statistics (the Society of Actuaries is a group of Statisticians expert in applying Statistics to the effective functioning of Insurance Companies. They are also consulted by Insurance Companies and they design a curriculum of examinations to train and qualify persons to become actuaries). I also studied Statistics for 1 year at the California Institute of Technology and I studied Continuous and Discrete Probability for 1 year at the California Institute of Technology, where we covered Continuous Probability Theory, Statistical Testing Methods, Normal Distribution and its derivation, Student's t Distribution, Fisher's F Distribution, Type I Error, Type II Error, Linear Regression, Multiple Regression, Bayes Probability and Statistical Analysis, Markov Processes, et. al.. I also studied Quantum Mechanics (statistical modeling of atomic and subatomic particles) and Statistical Physics at the University of Southern California.

SAT Math

The main topics in SAT Math are algebra, arithmetic, word problems, basic statistics (interpreting and finding least square lines), graphing, quadratic equations, linear equations, functions, composite functions, two dimensional coordinate systems, circles, solving simultaneous linear and quadratic systems of equations, et. al. I can help my students in SAT Math do all of the above.

Physical Science

I am familiar with and tutor: Classical Mechanics, Thermodynamics, Quantum Physics, Gas Dynamics, Electricity and Magnetism, Statistical Mechanics, Mechanics, Vector Analysis, Matrix Theory, Statistics, Basic Chemistry, Periodic Table, Basic Nuclear Physics, Chemical Equations, basic Earth Science, Tectonics, Basic Meteorology, Tornadoes, Clouds, General Relativity, Special Relativity, Solid State Physics, et. al..

Probability

ACT Math

ACT Math covers arithmetic, pre-algebra, algebra, word problems, complex numbers, volumes of solids, areas of geometric figures, sequences of numbers (arithmetic, geometric), pre-calculus, computations, geometry, properties of triangles, Trigonometry, Law of Sines, Law of Cosines, ambiguous triangles, properties of squares and rectangles, internal angles, external angles, etc.. I am an expert tutor in all of the aforementioned ACT math subjects.

ACT Science

I have a Master's Degree in Physics, I have completed significant coursework towards a Ph.D. in Theoretical Physics, and I am a "world class" physicist since theoretical research I did 40 years ago with Professor Anupam Madhukar is presently the theoretical basis of the active field of nanotechnology. I am also familiar with Chemistry which appears on the ACT Science Test and I am able to make taking the ACT Science Test "easy", and my students eventually learn to enjoy taking the ACT Science Test.

Elementary Math

I have BS degree in Math from Caltech.

Discrete Math

I am familiar with the following subjects which are part of discrete mathematics and I have tutored students in these subjects over the past twenty years. They are set theory, Venn diagrams, and tree diagrams; probability theory where the sample space is either finite or countably infinite; permutations and combinations (where an example of a combination problem is computing the number of ways we can select a committee of three if we select from a set of five people -- the answer is C53 = C52 = 5(4)/( (2)(1)) = 10); random variables where the set of realizations of the random variables are finite or countably infinite; solving systems of linear equations; matrix algebra; Markov chains; and financial mathematics. I enjoy tutoring these subjects of discrete mathematics very much. I have a Master's degree in Physics.

Differential Equations

I have tutored the solution of linear differential equations, like f(x, y) dx + g(x, y) dy = 0. I have tutored the solution of 2nd order linear differential equations like, a y'' + b y' + c = 0 and a y'' + b y' + c = f(x). In physics, differential equations (partial differential) equations occur quite often. I have worked with the Navier Stokes equation, Maxwell's equations, the rocket equation, Laplace's equation, Poisson's Equation, Schrodinger's Equation, Bessel's Equation, the DE for Simple Harmonic Motion, and the Heat equation, to name a few.

Actuarial Science

I have the professional designation, A.S.A is an Associate of the Society of Actuaries. I completed the coursework for this designation by passing 10 Exams created by Mathematicians/Statisticians of the Society of Actuaries. These Exams cover the basic statistical foundation of Actuarial Science (the foundation of the mathematical methods used by insurance companies in the United States and Canada).

Biostatistics

I took one year (3 quarters) of statistics at the California Institute of Technology. My grades were A, B+, B+. I also took an entire year of probability theory at the California Institute of Technology. During the course of tutoring many students in statistics (online and 1 to 1) I came across many examples of statistics applied to biology and public health which I adequately explained and taught to my students. I am familiar with the normal distribution, Student's t distribution and Student's t Tests, the F distribution, F tests, and the discrete binomial distribution. I also independently studied probability and statistics from the book "Probability and Statistics" by H Lass and P Gottlieb of the Jet Propulsion Laboratory of the California Institute of Technology. I will have no problem tutoring students in Biostatistics and I will enjoy doing it.

Econometrics

I studied economics for one year at the California Institute of Technology. In my actuarial studies I studied economic trend analysis and statistical analysis and linear programming which are topics in econometrics and I have taught linear programming. I have also studied optimization theory and operations research on my own. I can tutor all of the aforementioned topics in econometrics and I enjoy doing so.

Linear Algebra

I studied Linear Algebra as part of my curriculum at CalTech on partial differential equations. I also studied Linear Algebra as part of my curriculum at CalTech in Introduction to Abstract Algebra and the graduate course Abstract Algebra. Linear Algebra also appeared in my studies of Galois Theory and Ring Theory and Field Theory at both CalTech and U.S.C.. In particular, I am familiar with Vector Spaces, Subspaces, Linear Dependence and Independence, Null Space, Range Space, Matrices, Vectors, Linear Transformations, Rank of a Linear Transformation, eigenvalue, eigenvector, dimension, basis, span of a set of vectors, et. al..

Logic

Logic is the basis of mathematics (physics). So, as part of my mathematics and physics studies I have applied logic continuously. I also have an interest in symbolic logic, so I am familiar with the fundamental rules of logic. I am also familiar with the terms, inductive logic, deductive logic, tautology, syllogism, modus ponens, modus tollens, conditional statement, equivalence, et. al..

Finite Math

The following subjects are part of finite mathematics where I have studied these subjects in college and I have tutored students in these subjects for many years. They are: mathematical modeling, functions, equations, business applications of functions and equations, matrix algebra, organizing data, linear programming, sophisticated counting including permutations and combinations, and probability and statistics involving finite and countably infinite sets. I enjoy tutoring these subjects very much. I made substantial progress towards a Ph.D. in Theoretical Physics (Solid State) and a Ph.D. in Pure Mathematics (Functional Analysis).