SAT Math Tutoring

I have Bachelors degrees in both Mathematics and Physics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Science Tutoring

Science has informed an integral component of my worldview and education. In middle school, I took extra summer courses so that I could take higher level science classes during the school year. I took AP courses in Chemistry, Biology and Physics in high school, receiving scores high enough to receive college credit in each area. I went on to receive a Bachelors of Science degree in Physics and continue to do research in the area of theoretical physics, which furnishes the most fundamental description of Nature afforded by science. Since it has been quite a while since I have taken biology, I would say that my stronger areas are in chemistry and physics, as I have had continual exposure to these subjects over the years. However, if given enough notice and the course syllabus, I would be able to prepare proper biology lessons for high school students.

Writing Tutoring

In high school, I wrote for the newspaper and served as the editor-in-chief for two years in a row. I also took both levels of AP English in high school, for which I received college credit. I have been continually required to write essays to institutions of higher learning, explaining to them why they should invest resources in my education. In addition, I have written scientific papers documenting results I have obtained in my research, publishing an article in the Journal of Physics A and a textbook chapter with the InTech publishing company during my undergraduate studies.

Calculus I Tutoring

I taught myself differential and integral calculus in middle school (reaching a conceptual road block at multi-dimensional integration) and tested out of Algebra II freshman year of high school. I took Calculus BC in high school and received an A in the course and made a 4 on the AP exam. I received a Bachelors of Science degree in Mathematics in 2013, which involved taking courses in real analysis (the mathematically rigorous theory behind how calculus is constructed from the axioms of the real numbers). I have tutored and taught introductory physics (at the University of Colorado - Boulder and Harvard University), which is based on the differential and integral calculus.

I will be starting my doctoral studies in mathematics at MIT this fall semester.

Calculus 2 Tutoring

My Calculus BC course in high school covered topics included in a standard Calculus II course at the university level. I received an A in the course and a 4 on the AP exam. I have a Bachelor's of Science degree in Mathematics and have been using the techniques I learned in Calculus II in my physics research for the last six years. I am currently a teaching assistant at Harvard University for the Physics 15b: Introduction to Electromagnetism course. The material in the course makes frequent use of Calculus II concepts.

Calculus 3 Tutoring

I took Calculus III (multivariable calculus) at Houston Community College during my senior year of high school. I received an A in the course and was later able to transfer the credit for the course to the University of Texas - Austin the following year, where I begun my degrees in physics and mathematics. The introductory electromagnetism course I am teaching at Harvard relies in a fundamental way on multivariable calculus in the sense that the concepts developed within the subject form the natural language of electromagnetism.

Math Advance Tutoring

I took Ordinary Differential Equations at UT-Austin my freshman year of college. I failed my first exam and increased my score on subsequent exams until I made a 98 on the final. I received an A- in the course. The following semester, I took linear algebra and made a B- in the course. The context was that the professor failed over half of the class and I had some personal issues that semester. The following semester, I transferred universities and took Complex Analysis, Abstract Algebra, Classical Mechanics and Scattering Theory.

In Complex Analysis, I learned how to generalize calculus to the case where the domain is the complex plane. I learned Cauchy's integral theorem and residue theory, which turned out to be essential for my ongoing physics research (in particular, in the calculation of Green's functions). I received an A in the course.

In Classical Mechanics, although a physics course, I was introduced to the variational calculus as it shows up in the Lagrangian formulation of Newtonian mechanics. I received an A in the course.

In Abstract Algebra, we studied elementary set theory and ended the semester studying groups, rings, algebras and fields. I received an A in the course.

In Scattering Theory, although a graduate physics course, I learned advanced linear algebra and methods for solving integro-differential equations used to describe the collisions of quantum particles.

In later semesters, I took: real analysis, advanced matrix theory, advanced partial differential equations, statistical mechanics, signal analysis, two semesters of graduate quantum mechanics and graduate-level wave propagation theory. In these courses, I learned about the rigorous formulation of calculus, functional analysis, number theory, methods of solution and existence and uniqueness proofs for partial differential equations, statistics, probability theory, wavelet analysis, Fourier analysis, linear algebra and Hilbert space theory. I received an A in all of these courses except graduate Quantum Mechanics II (I received a B+).

I have a Bachelors of Science degree in Mathematics (magna cum laude). I will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Physics Advance Tutoring

(see Math Advance qualifications).

In my research, I have been studying quantum mechanics, quantum chemistry, numerical algorithm construction, diffusion phenomena, non-equilibrium statistical mechanics, quantum field theory and stochastic field theory. I wrote a paper on how to construct non-orthogonal bases for bound state systems such that overlap between the basis vectors contains information about the physics of the system (i.e. the Hamiltonian responsible for keeping the system bound).

I have taken graduate physics courses in quantum mechanics and scattering theory, making As in all courses except quantum mechanics II where I made a B+.

I have a Bachelors of Science degree in Physics (magna cum laude).

Physics I Tutoring

I took Introductory Mechanics my first semester at UT-Austin and made an A. I tutored the subject over last summer and taught the subject at both the University of Colorado - Boulder and Harvard University within the last year.

Physics II Tutoring

I took Introductory Electromagnetism my second semester at UT-Austin and received an A- in the course. I am currently teaching the subject at Harvard University. I have a Bachelors of Science degree in Physics.

Trigonometry Tutoring

I taught myself trigonometry in middle school but finally took the course in high school and received an A. I have to used trigonometry every day in my own physics research and in teaching my students at Harvard for their introductory electromagnetism course.

I have a Bachelors of Science degree in Mathematics (magna cum laude) and will be starting my doctoral studies in mathematics at MIT this fall semester.

Algebra Tutoring

I taught myself algebra in fifth grade out of my grandfathers algebra textbook. I finally took the course in seventh grade and received an A in the course. I have been using algebra in my own studies and teaching for the last 12 years.

I have a Bachelors of Science degree in Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Algebra II Tutoring

I studied abroad, in Venezuela, my first semester of high school and so had to test out of the first semester of Algebra II. I then took the second semester upon my return to the United States. I received an A in the course. I have been using Algebra II techniques in my research and teaching for the past 10 years.

I have a Bachelors of Science degree in Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

AP Physics Tutoring

I took AP Physics my senior year of high school and received an A in the course and a 4 on the AP exam. I have continued studying what I had learned in AP Physics for the past 6 years.

I have a Bachelors of Science degree in Physics and Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Calculus Tutoring

I taught myself differential and integral calculus in middle school (reaching a conceptual road block at multi-dimensional integration) and tested out of Algebra II freshman year of high school. I took Calculus BC in high school and received an A in the course and made a 4 on the AP exam. I received a Bachelors of Science degree in Mathematics in 2013, which involved taking courses in real analysis (the mathematically rigorous theory behind how calculus is constructed from the axioms of the real numbers). I have tutored and taught introductory physics (at the University of Colorado - Boulder and Harvard University), which is based on the differential and integral calculus.

I have a Bachelors of Science degree in Physics and Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Calculus AP Tutoring

I taught myself differential and integral calculus in middle school (reaching a conceptual road block at multi-dimensional integration) and tested out of Algebra II freshman year of high school. I took Calculus BC in high school and received an A in the course and made a 4 on the AP exam. I received a Bachelors of Science degree in Mathematics in 2013, which involved taking courses in real analysis (the mathematically rigorous theory behind how calculus is constructed from the axioms of the real numbers). I have tutored and taught introductory physics (at the University of Colorado - Boulder and Harvard University), which is based on the differential and integral calculus.

I have a Bachelors of Science degree in Physics and Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Geometry Tutoring

I was bused to the high school and took geometry in 8th grade. I received an A in the course.

I have a Bachelors of Science degree in Physics and Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Math Tutoring

I have a Bachelors of Science degree in Physics and Mathematics (magna cum laude) and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Physics Tutoring

I have a Bachelors of Science degree in Physics and Mathematics and will be starting my doctoral studies in mathematics at MIT this upcoming fall semester.

Pre Calculus Tutoring

I studied pre-calculus in my free time during middle school and learned about trigonometric functions and the concept of limits as applied to functions. I then taught myself differential calculus and learned the importance of a solid foundation in pre-calculus in order to appreciate the beauty and power of calculus. I took the course my sophomore year of high school and received an A.

I have since used techniques from pre-calculus/calculus in my coursework and my own personal research for the past 10 years.