I have tutored Algebra 1 and 2 for more than 20 students, and have not encountered a problem which I couldn't explain.
In high school, I obtained exceptional marks in the Word Knowledge, Arithmetic Reasoning, Paragraph Comprehension, Verbal Expression, and Mathematical Knowledge sections of the ASVAB. I have an advanced degree in Philosophy, which has made me proficient in the English language sections of the ASVAB; and I've completed a Bachelors program in mathematics, which qualifies me to teach the mathematical sections. I cannot offer tutoring for any of the other sections.
I have tutored Calculus I, II, III, and IV, that is to say, the full Calculus series, for several students. There is no topic within the Calculus series which I haven't explained at least a few times.
I have been playing chess since high school, and in high school I was the co-president of the chess club. My chess rating is 1370 in the Elo rating system, which is by no means a professional chess rating. I am qualified to teach an introduction to chess only.
I have taken MIT's 6.00x course in Computer Science and gained certification.
I've read both Zill's introduction to differential equations, and Tennenbaum's more rigorous and proof-based Ordinary Differential Equations. I have also tutored one UCF student for the introductory course, from the beginning of the course until its end, and the student ultimately earned an A. I am thus proficient in ordinary differential equations, though I am not competent to tutor partial differential equations.
Discrete Math is a collection of various other Math subjects including Logic, Combinatorics, Graph Theory, Algorithms, and more. I have studied each of these, either in a class devoted to the (like a course in Symbolic Logic alone) or in classes which contained them as special topics (for instance I learned Graph Theory through studying Probability, Abstract Algebra, and other subjects). So I am familiar with all of the usual topics covered in such a course.
I've tutored finite Math several times, where courses included sequences, series, algorithms, sets, functions, logic, proofs, combinatorics, linear algebra, graph theory, probability, number theory, and game theory.
I have tutored Geometry for at least ten students in the past, and have not encountered any problem which I was not able to explain.
I have tutored the GRE at least 20 times. I am able to tutor students of all skill levels, from the most elementary students who need to dramatically improve a low score, to those who are already performing well and want to reach for a perfect score.
I often emphasize solution techniques that avoid doing real Math, but instead are test-taking tricks that solve problems much more quickly than a direct mathematical solution; however, sometimes the only solution available is a direct and mathematical one. In all cases, I have not encountered a problem I was not able to solve.
I took Linear Algebra and received an A, then took Modern Algebra I and II, receiving a B+ and A respectively. I also obtained an A- average over four Calculus courses and two Modern Analysis courses.
I have taken Symbolic Logic, Mathematical Logic, Advanced Logic, Computability, and Modal Logic, each with excellent marks. While taking Symbolic Logic the professor requested to refer students in the class to me for questions with the material, and after taking the class, asked me to serve as a tutor for the following classes, which I did for one year. I also served as a reference for students, by request of the professor, in Advanced Logic and Computability. In Modal Logic, I assisted two classmates. I am currently tutoring a high school student in Symbolic Logic. My research in Philosophy and Mathematics is in the field of Logic.
I've tutored the LSAT logical and analytical reasoning sections several times. I'm able to provide direct and clear explanations for which choice is the correct one, and why each of the others are false. I am also able to advise techniques for drawing diagrams on the logic games section, and well as general logical rules to help understand the arguments and constraints in each problem.
I have served as a teaching assistant and tutor for a general introduction to Philosophy, a course in Early Modern philosophers, Logic, and a course titled Truth, Value, and Reason. I'm able to tutor any undergraduate subject except Eastern and continental Philosophy subjects.
I have tutored students in basic Probability as well as Calculus-based courses working out of the texts from Sheldon Ross and Robert Hogg.
I am able to tutor students in courses which cover such topics as discrete probabilities, conditional probabilities, random variables, marginal probabilities, order statistics, and maximum likelihood estimators. I am not able to tutor topics such as Measure Theory and sigma-algebras.
I've tutored Python twice, emphasizing concepts of basic syntax, debugging, computational complexity, object-oriented programming, modeling physical and financial systems, and producing graphical output and Graphical User Interfaces.
I am proficient in the material tested in the SAT Math subject tests, both 1 and 2.
I have tutored introductory Statistics and well as Calculus-based courses working from texts by Sheldon Ross and Robert Hogg.
I am able to tutor such topics as standard deviation, Central Limit Theorem, marginal probabilities, order statistics, and maximum likelihood estimators. I am not able to tutor topics such as Measure Theory and sigma-algebras.