Hi, I am a graduate from Columbia University with a B.A. in Mathematics as well as an M.A. in Philosophy. I have eight years of experience including one year as a tutor for the Brandeis University Philosophy department, and two years as a teaching assistant at Columbia. For the past six years I've been self-employed as a tutor and consultant, working with students at elite schools including Columbia, Cooper Union, NYU, Princeton, Stuyvesant, Hunter, Bronx Science, Staten Island Technical, an... [more]
I'm a tutor for advanced mathematics, but I still really enjoy tutoring students in high school subjects because I get to show them different perspectives on what can otherwise be a pretty dull subject. From the interesting tricks and number facts, to applications of Math to business and Science, I get to teach kids what I wish I had seen as a high schooler, including Algebra 1.
Although I'm a tutor for advanced college-level Math, I still really enjoy teaching high school subjects. I get to show students what I wish I had seen when I studied the topic, from interesting tricks, to different perspectives, to applications to Science. I've also tutored Algebra 2 more than any other subject I tutor, and I've been doing it for eight years. I've seen all the common mistakes that students make, and I can explain any given concept in at least a couple different ways.
I've tutored the full Calculus sequence, advanced Calculus, and Real Analysis, for about 30 different students. These courses are sometimes, at different universities, called Calc I through IV, Vector Calculus, Vector Analysis, Honors Calculus, or Modern Analysis. I've used the Stewart text extensively, cover to cover several times, as well as Rudin's Principles of Mathematical Analysis.
I have tutored Geometry more times than I can count! I have helped students become comfortable with proofs and constructions, which are often the topics which they find most challenging. I've also tutored college Math majors in Euclidean Geometry, as well as high school students working from concept-focused texts like those from Kay, Stillwell, and Kiselev.
I've tutored pre-Calculus several times. Whether it covers manipulation of functions, limits, trigonometry, combinatorics, matrices, probability, or any other strange topic, I've seen it all!
I've tutored Trigonometry several times. I like to teach students both the straight-forward computation of solutions, but also different perspectives like the relationship between right triangles and circles, and the application of Trig to Physics.
I have tutored introductory Statistics for at least 30 students, both at both high schools and colleges. These have included courses with and without Calculus, and some courses that required using the statistical programming language R. I've also tutored Mathematical Statistics courses which contain the theory of random variables as well as Probability Theory, Measure Theory, and Stochastic Processes.
I've tutored introductory programming, the Advanced Placement (AP) course, and a course in Algorithms, using the Java language. The courses I've tutored have focused on object-oriented, contract-styled design patterns. One one such was taught with Ocaml in conjunction with Java to demonstrate the difference between object-oriented design and functional design.
I've helped several students prepare for the SAT, both verbal and quantitative sections, although always with focus on the quantitative section. I typically work with a student to identify topics on which the student is weak and produce practice problems for that topic until the student is comfortably able to solve those problems. We also work on improving speed and strategically skipping questions for time management.
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 tutored the GRE at least 40 times with students of wide ranging skill levels, from those who need refreshers on adding fractions, to those who need to push their score from good to great. I tend to make lessons with students that follow a pattern: Teach a few concepts, give simple exercises, give GRE-style exercises, move to the next concept. We set up a schedule and, between meetings, I send exercises, you send solutions, I send feedback. We keep covering more material and reviewing old material. When we reach the end of the material we start covering test-taking techniques and really emphasize GRE-style questions--we get your time-per-question down, pick numbers efficiently, and know what to look out for with tricky graph questions.
I have tutored students in basic Probability and Statistics, as well as more advanced topics. I've worked from books by Tanis and Hogg, Casella and Berger, Ross, all covering what is basically the theory of random variables and Mathematical Statistics. This covers topics like regression, hypothesis testing, transformations, multivariable distributions, conditional distributions, likelihood estimators, and a little bit of robust statistics, non-parametric statistics, bayesian statistics, etc. I've also tutored more theoretical probability in a course that made use of Measure Theory.
I've tutored courses that cover discrete structures several times. Courses have included Graph Theory, Symbolic Logic, Combinatorics, Algorithms, Probability, and similar topics. I've worked from the popular Epp book as well as advanced texts from Tucker and one from Lovasz.
I've tutored introductory Differential Equations about a dozen times, often using Boyce and DiPrima's text but also having used Zill and the Tenenbaum text. These courses have included matrix methods, series solutions, complex functions, and the heat equation in PDEs. Note that I'm not qualified to tutor a full course devoted to PDEs.
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've tutored Linear Algebra several times, both for courses focused on computation as well as proof-based and theoretical courses. I've also studied more advanced topics that helped to give me perspective on the meaning and use of Linear Algebra, including Combinatorics, Abstract Algebra, Differential Equations, and more.
I concentrated on Logic while studying Philosophy and Math at Columbia University. I was a teaching assistant for the Symbolic Logic course, and am proficient with Mathematical Logic, Modal Logic, Non-classical Logic, Computability Theory, Orders and Lattices, and Model Theory.
I've tutored Python a dozen or more times for high school and college students, as well as for employees at firms that use MongoDB and Pandas. I'm familiar with the numpy, matplotlib, sympy, Tkinter and beautifulsoup modules. I usually use the Anaconda package manager with the Spyder scientific IDE, and for pedagogy I make IPython notebooks with Jupyter.
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.