I recently graduated from University of Massachusetts Boston with an M.Ed. in LTET. I have heard many times how many in America are struggling in mathematics, a subject that I consider to be extremely important, and a lot of fun. In late middle school and during high school, I started helping students in mathematics. My cousin Stan was my first client and by the time he entered college, I helped him get an A in first year calculus. I also helped many other students at Brookline High School achieve better grades and helped coach the school mathematics team. My strategy was to guide the students through problems and require students to give it the best shot and not to give up. We all know what it's like when a student simply shows us a math problem and immediately asks for a solution. I also believe that students need a chance to explore concepts as this can not only help them recall concepts that they forgot, but also discover new ones on their own.
I participated in the Brookline High School Math team from 1999 to 2001, attended the HMMT competition three times and was in the ARML team. During my senior year, I scored a 5 (Extremely well qualified) on the AP test in Calculus. I am also an alumnus of PROMYS which is a high school summer program in mathematics at Boston University in which the central subject was Number Theory. When I was an undergraduate student, I took a lot of science courses and participated in the Putnam competition, in which I got a 32, one of the highest scores of any students in my college. Our Putnam coach included one of the Putnam problems as extra credit in his discrete math final exam because of the solution that I came up with and later explained during the break.
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Roman's subjects
Algebra 1
I helped many students in Algebra 1 in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Algebra 2
I helped many students in Algebra 2 in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Calculus
Differential/Integral calculus was co-invented by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, but the ideas leading up to it trace back to the ancients who invented the "Method of Exhaustion". Either way, the goal was always to solve practical problems, especially in physics and other sciences. Examples of questions that can be answered:
How much energy is needed to launch a 1000 ton shuttle into near-earth circular orbit? (Physics)
If you want to make an open rectangular...
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Geometry
I helped many students in Geometry in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Prealgebra
I helped many students in Prealgebra in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Precalculus
I helped many students in Precalculus in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Trigonometry
I helped many students in Trigonometry in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills come from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Probability
I helped many students in Probability in my high school and college years. I always loved studying mathematics and helping others make significant progress in it.
Many of my skills came from my participation in several mathematics Olympiads. I minored in math and physics in college. I also have a Master's degree in Secondary Mathematics Education.
Discrete Math
I have been exposed to Discrete Mathematics since early high school, and have used a lot during my undergraduate studies, most notably in context of computer science. My exposure to it included Combinatorics, Graph Theory, etc. There was also some coverage of cryptography near the end of a college level course.
As for the Number Theory, I was exposed most of the basic concepts from early middle school, and in high school, I attended PROMYS, which covered it at the college level. I haven't...
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Linear Algebra
In Linear Algebra, linear equations, matrices, vector spaces, and linear transformations are studied. Although a few concepts, such as solving linear equations dates back to the ancients, a number of important matrix concepts like determinants and eigenvalues/eigenvectors were developed more recently and gave rise to the modern areas of the subject.
Examples of applications:
1. Systems of linear equations occur when using Kirchhoff's laws in Physics to solve for currents/resistances...
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Logic
I took mathematical logic during my undergraduate education. The topics included boolean algebra, theorem proving via rules of inference, and later, equation logic. Part of the curriculum revolved around proving certain major results, including the completeness theorem for boolean algebra, and the compactness theorem. I helped a number of students with solving logic problems. I emphasize the fact that practicing logic strengthens one's ability to think in many different school disciplines. I also...
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