...I have a deep passion for teaching and traveling, and I began my teaching career in Russia, working with gifted high school students. I've also prepared students for the highly competitive Russian Math Olympiads. My teaching experience extends to Thailand and Denmark, where I've adapted to various curricula, including local standards, IGCSE, IB, and Common Core. (read more)
...Suppose R n R-1 ? {(a, a): a ? A}. Let R = {(x, y): x, y ? A}. By definition of inverse relation, R-1 = {(y, x): x, y ? A}. By definition of subset, if (x, y) ? R n R-1, (x, y) ? {(a, a): a ? A}. Hence, x = y, and so (x, y) ? R implies (y, x) ? R. Since x = y, ? (xRy ? yRx), x = y. Thus, by definition of antisymmetric, R on A is antisymmetric. (read more)
...I have tutored online, but I much prefer teaching in person. I have two children now in college, at Ivy League schools. I was their primary caregiver throughout their childhood, and helped them with their schoolwork whenever they needed it. (read more)
I started tutoring mathematics when I was in college. The tutoring experience shifted my career goal to become a teacher. I taught middle and high school mathematics for 5 years and decided to pursue a graduate degree. (read more)