Subjects

I specialize in the following courses. Click on each for more details and a partial list of subtopics.

If you don’t see a particular topic covered, please contact me! I have broad experience with most math topics through the undergraduate level, and I’d be happy to discuss whether I can be an effective tutor for your needs.

  • Expressions, equations, and inequalities of one or more variables; manipulating and factoring polynomials; exponents and radicals; functions including polynomials, quadratic, rational, exponential, and logarithmic functions; transformations of functions; piecewise functions; conic sections.

  • Lines, angles, and their measurement; triangles, including congruences and similarities; quadrilaterals, general polygons, and areas, perimeters, and volumes; transformations and the Euclidean plane; introductory proofs using theorems of geometry.

  • Right triangle trigonometry; sine, cosine, and tangent definitions; the unit circle; trigonometric identities; graphs and transformations of trig functions; Law of Sines and Cosines; word problem solving techniques involving trigonometry

  • Polynomial, rational, exponential, logarithmic, and trig functions; solving equations and inequalities involving these functions; domains and ranges of functions and their inverses; creating equations of variables; optimization problems involving quadratics

  • Limits, derivatives, antiderivatives, integrals, series, parametric equations, and ordinary differential equations; optimization and related rates problems; proofs requiring formal definitions of limits, Intermediate Value Theorem, and similar; power series, Taylor/Maclaurin Series, and their applications; applications of calculus such as areas/volumes, arc length, and domain-specific (e.g., physics, biology, probability)

  • Systems of linear equations; matrices and matrix operations; theory of vector spaces and linear transformations; inverses and determinants; eigenvalues/vectors and diagonalization; coordinate systems and change of bases; inner product spaces, the Cauchy-Schwartz inequality, and the Gram-Schmidt algorithm.

Mathematics

  • Descriptive statistics; histograms and other forms of data visualization; sampling methods and survey design; introductory probability; inferential statistics including confidence intervals and hypothesis tests (z/t tests, chi-squared, and ANOVA); predictive statistics using linear regression. Both traditional (pen and paper/calculator based) and coding-based (using R/RStudio, Python, or Excel), including bootstrap methods.

  • Coding and data analysis in R and RStudio, including data visualization, implementation of all topics from introductory statistics, and writing functions in R; best practices for effective communication with coding and reports; using libraries such as ggplot, dplyr, and the rest of the tidyverse.

  • Fundamentals of probability; discrete and continuous random variables including the classic distributions (e.g., binomial, geometric, Normal, and exponential); expectation, variance, and covariance; joint distributions; conditional random variables and expectations; probability-generating and moment-generating functions; Normal and bivariate Normal theory.

  • Discrete Markov chains, including waiting times, irreducibility, stationary, and reversibility; Poisson processes; continuous-time Markov chains; Brownian motion; martingales; branching processes; renewal processes.

  • Descriptive statistics including maximum likelihood estimation; hypothesis tests and optimality (including likelihood ratios and the Neyman-Pearson lemma); theory behind ANOVA, goodness of fit tests, and least squares regression.

Statistics and Probability