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There is a story about the invention of chess which illustrates some interesting facts about exponential growth and large numbers. The story is that the mathematician who invented chess showed it to the king of India who was pleased and said the inventor could ask for any prize he wished. What he asked for seemed small as he asked for just one grain for the first square, two for the second, four for the third and so on. This can be seen to follow a exponential increase where each square has 2(n-1) grains of rice.    Two is raised to the (n-1) because the first square has 1 or 20=2(1-1)=1 grains. At first this seems like quite a small request when he could have asked for chests of gold and diamonds or a large piece of land to live on. However the amount of rice rises exponentially and even just looking at the final square shows the total is going to be a huge amount of rice.   The final square or the 64th square as that is how many are on a chessboard... read more

In math you learn new terminologies and many significant things pop up. Guys, do you ever dream about analytical calculus? No? Well, why not!   As a high school student you learned algebra and pre-calculus and those are great, but you can really figure that there is more to math than just that. I assume you were dazed and confused. That's okay. Perhaps though you enjoyed your subjects. That is pretty good.   There, you must try to learn analysis, because it is the most-funnest part of mathematics! Do you think I'm wrong? Well, begin with a subject like real analysis. During your study of analysis, you learn about continuity, metrics, and integration. I would like to know more about metrics.   The weird thing is that math is everywhere. Sorry, but I like math because of this fact.   It takes a real scholar to learn math. Got me wrong? Gals sometimes support the most advanced mathematical conclusions. You can make their notions... read more

Read. Pick up something and keep the wheels turning. Keeping fresh on news, or just pleasure reading is a skill that needs to be exercised and worked on regularly. Write. Depending on where you are in your academic career, one thing is fairly certain; you will be required to write the deeper you delve into subjects and years of schooling. Writing is learning on a new level. Research. Research something. Take it beyond Google, and do not rely on Wiki. Anyone can publish on Wiki, and some big mistakes happen there. Research and writing work in tandem, get used to it and have fun with it, after all you will learn something this way (and far into the future). Honing your search skill (Booleans, etc.) will pay you back exponentially one day. Learn something or do something new. Find a new hobby or research (see above #3) something new or do something new after looking into it as long as it's safe of course. Set Attainable... read more

Recently I was asked to relate my favorite education quote. Admittedly, I had a hard time choosing. Education is nuanced. Thousands of teaching and learning quotes are relevant and memorable. After re-reading several of my favorite education quotes, I chose this one as my favorite: “Education is light, lack of it darkness.” (Russian proverb.) Teachers, parents, students, and tutors will all find relevance in this quote. Telling you about my favorite teacher will help explain why I think this quote is so appropriate. My favorite teacher was a middle school teacher named Mr. Z; that’s what we all called him anyway. He was an English teacher (now retired) and sponsor of the school’s Chess team. I never had him for English; instead, I was in his homeroom and Chess club. I didn’t have to have him for English to know he was excellent at teaching that, too. I’d known Mr. Z. since my family moved to the city where I grew up. He was the sponsor of the city’s Chess club. We... read more

Families hire tutors for a variety of reasons. In general, though, tutors help students and professionals learn some skill or information. So, how do you know whether you are getting your money’s worth from tutoring? Here are five areas you can use to grade your tutor. 1. Communication. Tutors should communicate a lot! Tutors should conduct a background interview before starting lessons. They should gather information about student strengths and weaknesses, academic background, learning styles, and schedule information at a minimum. You can feel confident that they know what they’re doing if they do this. They understand that you need to know their students before teaching them anything. They may also use the information to write a learning plan listing several long – term goals for the student. Tutors should also talk with parents or adult students after each lesson. They should meet with parents at the end of the session to summarize student progress and preview... read more

The Mutilated Chessboard A chessboard has 64 squares, 8 by 8. If you have 32 dominoes, each the size of 2 side-by-side chessboard squares, you’ll be able to exactly cover the chessboard with the dominoes. (In fact, there are very many ways you could arrange the dominoes to cover the 64 squares of the board!) But suppose you cut off any two diagonally opposite corner squares of the chessboard, leaving 62 squares. What patterns of 31 dominoes will exactly cover the mutilated chessboard? This is another good exercise in creative problem-solving. Try to observe your own thought processes as you try to solve this. Are you methodical or do you make random guesses? Do you visualize solving the problem or analyze it differently? Do you attack the whole problem head-on, or try to solve a similar but smaller and simpler problem first?

Chess is an interesting game and very helpful for kids who want to enhance their memory skills. It allows you to keep your mental abilities in shape. This is very similar to a physical work-out that helps keep your muscles in shape. If you have a brain that you work-out often, tasks such as remembering things, performing mathematical problems get easier.

When I think chess, I think checkmate! However, I would rather be the one saying it, not hearing it. Chess is as much a game of offense as it is one of defense. It is about strategic decision making and thus calls for sacrifices, in order to gain rewards. Chess is about patience, but one is not expected to do nothing. While expecting to capture the opponent’s most valuable pieces, be on the lookout for baits and traps. Above all, be ready to retreat when necessary. This narrative should give any amateur chess player a general idea of what to expect. To hit and run, conquer or be defeated. However, you must also understand that just like in a real battle, not all of your weapons work the same. A King may be more valuable, but he is usually on the run, or being defended by others. Pawns can be expended, Rooks can be used for defense, and Bishops for long range assaults. Your Knights will help you confuse the opponent, but your Queen has the greatest strength. Sacrifice her... read more

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