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, NYU, Princeton, Stuyvesant, Hunter, Bronx Science, Staten Island Technical, and more. Wha... [more]
I have tutored Algebra 1 and 2 for more than 20 students, and have not encountered a problem which I couldn't explain.
I have tutored Calculus I, II, III, and IV, that is to say, the full Calculus series, for several students at Columbia, NYU, Harper, and other schools. There is no topic within the Calculus series which I haven't explained at least a few times. I've also tutored students in advanced versions of Calculus, such as vector Calculus and courses that integrate topics from Linear Algebra. I've also tutored a few students in the proof-heavy course titled Real Analysis or Modern 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.
I have tutored introductory Statistics for at least 20 students, including courses that require Calculus, the theory of random variables, and sigma-algebras, Measure Theory, and Probability Theory. These have been courses offered at elite colleges like Columbia, NYU, Cooper Union, and at high schools including Hunter. I'm familiar with the AP Statistics curriculum. I've also tutored for classes that use the statistical programming language R and relevant Python modules like pandas.
I've tutored Computer Science several times. I'm able to explain the Object Oriented Programming paradigm that is essential for Java, as well as algorithms, data structures, and the design of Graphical User Iterfaces (GUIs).
I've prepared students for the SAT countless times. I teach both the content of the test, as well as test-taking techniques such as time-management, guessing strategies, and ways of reasoning that can avoid long calculations whenever possible.
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 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.
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 Differential Equations about a dozen times, for classes that have used Zill's textbook and the more advanced book by Boyce and diPrima. I have helped students with such topics as solutions to linear, homogeneous, exact, and Bernoulli type equations, to name a few. I have also helped with series solutions, matrix methods, and Laplace transforms. I have tutored the course offered at Columbia a number of times, and am familiar with the topics typically encountered in that course.
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 taken MIT's 6.00x course in Computer Science and gained certification.
I've tutored introductory CompSci courses in Python, Java, and C++ for five years. I've also tutored several students in advanced theoretical topics like Algorithms, Computability, and Automata Theory.
I took Linear Algebra at Columbia University while getting my Math degree. I've tutored the subject several times, and taken more advanced courses Abstract Algebra. I've also used knowledge of the subject in fields like Statistics, Machine Learning, Differential Equations, and Computer Science.
I have taken Symbolic Logic, Mathematical Logic, Advanced Logic, Computability, and Modal Logic, each with excellent marks. I've tutored the subject several times for students at Columbia, NYU, City College, and via Skype with students at Penn State, Kings College London, and the University of South Africa, with some of this work at the graduate student level.
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'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.