What I Teach
The following are the subjects I teach, by topic, along with descriptions of those subjects. Note that I only offer instruction in math and physics courses, whether as a supplement to a traditional school class or as the primary deliverer of homeschool instruction. I do not offer any instruction in test preparation for standardized tests (AP exams, SAT/ACT, GRE, etc.).
Mathematics Subjects
- Arithmetic
- Counting; basic operations; fractions and decimals
- Algebra
- Expressions of one or more variables, including linear, quadratic, and other polynomial equations, functions, and systems of equations. Rational numbers, real numbers, and complex numbers.
- Geometry
- Shapes, lines, and angles in 2 and 3 dimensions, along with discussion of formal proof strategies.
- Statistics
- Collection and interpretation of data in one or more variables; probability and counting.
- Trigonometry
- Right triangle geometry, with applications to vectors and periodic motion.
- Precalculus
- The extension of algebra to non-polynomial or infinite-degree functions, especially exponential and logarithmic functions; limits and continuity
- Differential Calculus
- Finding instantaneous change in a function of one or more variable; maximum and minimum values; optimization.
- Integral Calculus
- Recovering a function from its derivative; area under curves.
- Multivariable Calculus
- Extending calculus to functions of multiple variables.
- Differential Equations
- Equations whose solutions are functions whose derivatives satisfy certain relationships; initial value and boundary conditions.
- Linear Algebra
- Linear transformations and vector spaces; eigenvalues and eigenvectors; diagonalization and spectral theory; singular value decomposition.
- Number Theory
- The underlying theoretical structure of arithmetic; primes; Diophantine equations; quadratic reciprocity.
Physics Subjects
- Kinematics and Mechanics
- Motion of objects in 1-3 dimensions; energy; momentum; forces; conservation laws.
- Electricity and Magnetism
- Electric charges; voltage and current; electric circuits; electromagnetic waves; Maxwell's equations.
- Thermodynamics
- The application of conservation laws to heat; entropy.
- Optics
- The behavior of light and other electromagnetic waves as they travel through a medium.
- 20th-Century Physics
- Special relativity; blackbody radiation; introductory quantum mechanics.