My approach includes practicing general standardized testing skills, with a solid foundation grounded in mathematics. Usually, I tutor a student in a high school math course and investigate specific homework problems. During the investigation, I explain how it would be seen on the ACT. I also use practice problems and go over test day expectations.
Algebra 1 is a big leap for many students. It's a departure from the arithmetic that students have been focused on and introduces abstraction for the first time. I have a great deal of experience helping students new to algebra to succeed in their studies. I can help students visualize abstract ideas and I'm very comfortable discussing and explaining math. Best of all, I enjoy algebra and bring that enthusiasm to the table.
From logarithms to conic sections, compound interest to partial fractions, I'm the tutor for you. I've helped many students tackle and succeed with this material and provided insights on how it ties together with trig, calc, and other big picture ideas.
Familiar with AP Calculus test material as well as fundamental theory. Fluent in topics of limits, derivatives, integrals, sequences and series, as well as application of these methods in the sciences and higher mathematics.
I took two years of Differential Equations classes in the course of my math degree and used them in a practical setting for the physics degree. I'm familiar with Ordinary Differential Equations, have a particular knack for power series solutions to differential equations, have a physics intuition for solving partial differential equations, and have written my own simple numerical differential equation solvers in the C programming language. Laplace transforms, Legendre polynomials, and Fourier series (oh my) I know when and where these techniques are useful.
I am great at showing students how to do proofs, constructions, and geometry word problems. I help students change angles, distances, congruences, and symmetries from abstract ideas to practical mathematical tools. I use a wide range of techniques from working proofs backwards, to using colored pencils for diagrams. I also bring a strong background in formal logic which is the foundation of geometry.
I studied linear algebra first in high school, later in a comprehensive manner as part of my degree in mathematics. I actively use linear algebra for business and in graphics programming. I'm comfortable showing students a wide range of subtopics in linear algebra including: solving systems of linear equations, determinants, Cramer's rule, matrix inverses, linear transformations, eigenvalues and eigenvectors, change of basis, rotations, affine transforms, complex-valued matrices, solving systems of ordinary linear differential equations, and much more.
I've taken college courses in critical thinking which used symbolic logic. I'm aware of categorical (the syllogistic), propositional, and predicate logic. I can help students break arguments in to symbolic statements, compute truth tables, and help analyze validity of argument forms. I'm also aware of the connection with logical fallacies, both formal and informal.
I've tutored physics throughout my time as an undergrad as part of the Learning Center peer tutoring program at UCR. I earned a double major in Physics and Mathematics. I'm familiar with mechanics, thermodynamics, electromagnetism, optics, quantum mechanics, and cosmology to name a few fields.
Prealgebra is the beginning of every math student's nightmare: word problems. I show students how to change word problems into pictures and how to organize their information. Most importantly, I provide instant feedback on practice problems, encouragement when discouraged, and praise for good work.
The purpose of this class is to develop the perception a student needs for calculus. Function slopes, asymptotes, end-behavior, translations; the purpose of these topics are to ultimately give a student an intuition into function behavior. I help students visualize, predict, and master these concepts so that functions become tools and plastic, dynamic objects instead of just a line on a piece of paper.
My approach to probability stems from a physics viewpoint. The physics view allows a more intuitive understanding of gaussian, binomial, and other distributions. Weighted probabilities, expectation values, permutations, independent events, and bears oh my! If you are struggling with topics in probability, perhaps a different perspective will give you the edge you need to gain a foothold.
I've had much practical use of trigonometry in college and professional life. Great knowledge of applications in word problems, trig identities, addition and doubling formula, unit circle/special angle practice, Fourier transforms, to name a few topics.