All of
Roman’s current tutoring subjects are listed at the left. You
can read more about
Roman’s qualifications in specific subjects below.
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 box of maximum volume and have 10000 sq. cm. of cardboard to use, what should be the dimensions? (Optimization).
etc.
High school calculus covers the topics covered in the first two semesters of college calculus discipline and introduces you to the most fundamental concepts in the subject so you can answer questions such as these two and many more.
I took AP calculus (BC level) when I was a senior in high school and got my perfect 5. Since then I took more advanced courses in the subject and also took Physics all the way up to Quantum Mechanics.
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 put Number theory to practical use very often, but did apply it during my college curriculum in math and computer science.
During my college education, I helped many students in both subjects. For Discrete Math, I sometimes like bringing up some of the areas of recreational mathematics (Games and Puzzles), since this is the most natural way to get the students interested.
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.
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 in electric circuits.
2. Matrix transformations are used extensively by computer graphics systems. For example OpenGL makes extensive use of vectors and matrices to render objects in 2D/3D.
3. In classical Mechanics the principal rotation axes of a body are parallel to the eigenvectors of the moment of inertia tensor (3 by 3 matrix "I" in this case). In a motor, for example, if the axis of rotation is not principal, vibration occurs which can damage the system. That's because the angular momentum (L=Iw) and angular velocity (w) are not alligned with each other.
I took the course as an undergraduate and was one of the best students in the class. Since then, I helped a number of students with this subject during my college studies. In doing so, I emphasized applications of the concepts so that the students are aware of the subject's importance and can grasp the concepts more easily.
I also applied it both in my science classes and outside of school including programming some geometry-based applications including one written in OpenGL.
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 mention that solving many puzzles, which many of us like doing in our spare time, requires logical thought.
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.
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.
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.