I am a creative and effective tutor with Master's Degree in Physics and years of experience working with students of all ages. I have an excellent understanding of many subjects especially all levels of calculus and physics. My tutoring philosophy is that a student should have a deep and thorough understanding of the material - not merely know how to get the correct answer. That way, they can become self-reliant and use their knowledge to solve new and challenging problems on their own. I hav... [more]
Because of my background in physics, I have a large amount of practical mathematical experience and; therefore, I understand the topics covered in Algebra 1 better than almost anything else. More importantly, I have been tutoring high school algebra for a long time and am capable of breaking down the mathematical ideas into simple, manageable pieces. Algebra 1 is the foundation of every math class that comes after it, and I can help students develop a strong foundation.
Algebra 2 is a fundamental building block for calculus, and I understand this material very well. I have been tutoring high schoolers and college students in Algebra 2 for a long time, so I know how to help students get a firm hold of the subject matter. I am very comfortable with polynomial and rational functions, exponential and logarithmic functions, graphing, inverses and composition, factoring polynomials, sequences and series, matrix algebra, and many other topics.
Because of my Master's Degree in physics, I have a large amount of practical and academic experience with all aspects of calculus through an undergraduate level and beyond. In addition, I have been tutoring AP and college-level calculus for a long time, so I know the material that is covered very well and can help students understand it. I am very comfortable with limits, epsilon-delta proofs, the formal definition of the derivative, Riemann Sums, the Fundamental Theorems of Calculus, Taylor series, vectors, partial derivatives, Jacobians, multiple integrals, and many other topics.
Because of my background in physics, I have a deep understanding of many elements of basic chemistry. I am very familiar with stoichiometry, energy levels and electron configurations, patterns and properties in the periodic table, and the fundamentals of laboratory techniques in chemistry. I am not familiar with or comfortable tutoring high-level chemistry (such as physical chemistry or organic chemistry), but I can be of help in lower-level college and high-school chemistry courses.
Geometry is a fundamental part of physics, so I know it very well and have been helping students learn it for a long time. I am not qualified to tutor undergraduate or graduate level topology or differential geometry. On the other hand, I am qualified to help high schoolers understand Euclidean geometry, and I am secure in my understanding of area, volume, logic, basic proof writing, trigonometry, distance formulae, and the many angle theorems - among other topics.
During the course of study for my Physics Master's Degree, I studied most fields of physics up to and including quantum field theory and relativistic dynamics. I have a very strong understanding of all fields of physics through an undergraduate level (including electricity and magnetism, classical mechanics, statistical mechanics, and quantum mechanics). In addition, I can tutor in nuclear theory, the Standard Model, and condensed matter and solid state physics at an introductory level.
Calculus was invented to solve physics problems, so I understand pre-calculus (the first step on the road towards more advanced topics) very well because I have a Master's in physics. I have tutored high schoolers and college students in pre-calculus for years, so I know how to help students not just learn the information but actually retain it too. I am very comfortable teaching limits, discontinuities, piecewise functions, reading mathematical tables, graphing and graphical interpretations, finding the equations of lines and other polynomials, exponentials, trigonometry, and the formal definition of the derivative.
Trigonometry is an integral part of both geometry and pre-calculus, which together lay the foundation for mathematical physics. As a result, I understand trigonometry very well. I am extremely well-versed in the uses and interpretations of sine, cosine, tangent, secant, cosecant, and cotangent and all of their inverse functions. I have been using trigonometry and tutoring it for a long time, so I can help students develop a firm hold on the material.
My Bachelor's Degree in Classical Studies trained me to critically interpret texts and clearly express myself in writing. I can help students with these same skills by focusing on good writing habits, proper essay structure, and correct grammar and syntax. I believe in helping students understand what they want to achieve with their writing and helping them use their language to reach that goal so that they can write the best version of their paper that is possible.
Because of my master's degree in physics, I have extensive experience with all topics in physics and astronomy. I am knowledgeable about Newtonian gravity, orbits, basic cosmology, the physics of stars, and special and general relativity.
Government & Politics
I have studied American Constitutional Interpretation and have a strong understanding of the political and judicial structure and history of the United States. I believe that history and law go hand-in-hand and that by learning about the fundamental aspects of the American government in its historical contexts you can gain a better understanding of both. In addition, I have studied a lot of comparative politics and have a strong understanding of the political and governmental systems of several other countries - especially Mexico, the United Kingdom, France, Russia, Iran, and China.
Because of my degree in Classical Studies, I have a strong background in textual analysis and paper-writing. I am familiar with most texts that are regularly assigned in high school, but I specialize in Shakespeare and in ancient literature. I am especially familiar with the works of Homer and Horace.
Because of my master's degree in physics, I have a large amount of practical as well as academic experience with the study of probability and statistics. I also have experience tutoring high school- and college-level statistics, so I am familiar with the topics that are usually covered and the common pitfalls.
Because of my background in advanced physics and logic, I have a large amount of experience with set theory, group theory, modular arithmetic, and matrix and other non-Abelian algebras. I have also studied a substantial amount of combinatorics and probability theory. I could tutor in the areas of rings, fields, and graphs but only at a basic or introductory level.
Because of my master's degree in physics, I have a great deal of practical and academic experience solving a large variety of differential equations. I have studied in detail many methods for solving ODEs and PDEs including separation of variables, undetermined coefficients, integrating factors, series solutions, numerical solutions, Wronskians and Cramer's Rule, and Green's Function methods. I have also studied Sturm-Liouville theory as well as solutions to systems of linear ODEs.
I have a Master's degree in physics which focused on quantum mechanics. Most modern branches of physics rely in some way or another on linear algebra, but quantum mechanics especially does since so many problems boil down to finding eigenvalues and eigenvectors or establishing a basis space. I am comfortable with all linear algebra topics including change of basis formulae, diagonalization, Gramm-Schmidt Orthonormalization, quadratic forms, and singular value decomposition.
I have a great love for Boolean and First-Order Predicate Logic. I have studied logic several times in both philosophy and mathematics courses, but most notably, I took a class in college on mathematical logic which concluded with a proof of The Soundness and Completeness Theorem of First-Order Predicate Logic and an in-depth examination of the Incompleteness Theorem of Arithmetic. I can help you understand deductions, argumentation, and model interpretations and extensions. I would need a refresher on model theory, the Compactness Theorem, and LST Theorem before I could tutor graduate-level logic, but I am very comfortable with the material taught in most undergraduate courses.
I have a bachelor's degree in Classical Studies from Centre College where I graduated Phi Beta Kappa. I took 3 semesters of Latin and 2 semesters on Ancient Greek during college but focused primarily on history and literature in translation. I am most comfortable with the Roman Republic, the Punic Wars, and the early Empire and with 5th Century Athenian democracy and the Peloponnesian and Persian Wars; however, I am still knowledgeable about the later Empire, the Roman Kingdom, and the Hellenistic Period as well as will Roman and Greek religion, literature, and art.