I am currently offering my services and expertise as a tutor for high school students studying for Advanced Placement Exams and Standardized tests such as the SAT and the ACT. I also tutor college students in the following subjects.
Mathematics
Algebra (College Algebra I-II, Matrix Algebra, and Modern Algebra)- Algebraic manipulation and mathematical reasoning, quadratic formulas, systems of linear equations, and basic functions.
- Trigonometric functions, exponential and logarithmic functions, graphing and polar coordinates, and conic sections.
- Algebra of matrices, elementary theory of vector space and inner product spaces, solutions of linear equations with Gaussian elimination, and triangular factorization. Orthogonal projection, singular value decomposition, least-squares approximation. Determinants, eigenvalues and eigenvectors, and diagonalization.
- Euclid’s algorithm, unique factorization and modular arithmetic, Fermat’s theorems, Euler’s theorems, Chinese remainder theorem, RSA encryption, Pollard rho factoring, error-correcting codes, and Hamming codes.
- Single variable calculus including derivatives and integrals of elementary functions and analytic geometry.
- Techniques and applications of integration, the convergence of sequences and series, Taylor series, and calculus in polar coordinates.
- Multi-variable calculus including vector geometry and three-dimensional vector calculus, partial derivatives and double/triple integrals, integration across surfaces, Green’s theorem, Stokes’s theorem, and Gauss’s divergence theorem.
- Ordinary Differential equations in both first and second-order equations and their applications including series solutions of second-order equations and Laplace transformation methods.
- Elementary complex variable theory and applications, complex fields, and analytic functions. Cauchy’s theorem, power series with complex variables, and residue theory.
- Fibonacci numbers Stirling numbers of the first and second kind, Bell numbers, inclusion and exclusion. Eulerian and Hamiltonian cycles, Matrix tree theorem, planar graphs and the 4-color theorem, Hall’s marriage theorem, and the stable marriage theorem.
- Fundamental principles of set theory, induction, relations, and functions. Counting techniques including permutations, cycle structures of permutations, combinations, and recurrences including the algorithms that generate them.
Physics
General Physics (College Physics I-II and Laboratory and AP Physics 1, 2, and C)- Algebra and calculus applications to the principles of physical mechanics concepts, analysis, and problem-solving. Including the motion of solids and fluids using Newton’s Laws, the conservation of energy, momentum, and angular momentum.
- Algebra and calculus applications to the principles of electricity and magnetism, electromagnetic waves, and physical optics. Including basic circuits, Ohm’s Law, Kirchoff’s Laws, Maxwell’s equations, and electromagnetic radiation.
Computer Science
Introductory Programming (College Introductory Programming and AP Computer Science A)- Object-Oriented problem solving, design, and programming engineering in C/C++. Fundamentals of data structures and algorithm design. Class structures, linked lists, pointers, arrays, and multi-dimension arrays
- Life cycles of programs, programming metrics, requirements specifications, design methodologies, validation and verification, program testing, reliability, and project planning.
- Asymptotic analysis of time complexity with proofs of correctness. Algorithms and advanced data structures for searching and sorting lists, numeric, graph, and string algorithms.
- Theory and techniques of data analysis and error propagation. An emphasis on using computational methods utilizing procedural programming languages in their applications to data analysis in the physical sciences. Treatment of statistical errors, maximum likelihood, chi-square distributions, and curve fitting.
Statistics
Probability (College Probability and AP Statistics)- One and two-variable data, data collection, probability and sampling distributions and their applications, random variables, sampling distributions. Means, chi-squared distributions, and R-squared values. Hypothesis testing and confidence interval estimation. Limit