Although I have given a few seminars and spoken to a large gathering quite a few times, teaching in class for one full hour is a a complete joy. I requested my professor to give me an opportunity to teach the students of electronics branch about algorithms. Algorithms as a core course is not present in the electronics branch and hence, my professor Mrs. Geetha Prakash was also willing to let me teach. Today was the first day of my teaching. A lot of the guys who were in the class seemed disinterested but, I knew that would be the case since I was also completely disinterested in a few classes when I was a student in PESIT. But, I was glad that the mojority of the class was interactive. I knew a monotonous kind of teaching would certainly put people to sleep (as it happens in most of the meetings in the companies). So, I decided to throw in a few puzzles to the class and tell them something interesting so that, they would keep thinking and their attention did not drift towards anything else.
One of the things that I told them was the history of the 'e'. I also told them how did the logarithm table work. It is interesting that most of the students do not know how the logarithms work. When we were in our High School, we were asked to work out everything using logarithms. Calculators were banned in classes and examination. Everyone in today's class knew how to use logarithm table but, interestingly very very few seemed to know how it worked.
A * B / C had to be calculated and A, B and C were large numbers. They know how to get the answer using the log tables. Use the log tables (to base 10 ... Which few seemed to know) and get the 'magic' logarithm values for A, B and C. Add the log values of A and B and subtract the log value of C. Then use the anti-logarithm table and get the final answer back ... ta daaaa ... Magic !!!!
Converting a complex multiplication and division to a very simple addition and subtraction seems to be a magic. But, behind the log tables is a very very simple technique which any High School student if given the task properly can accomplish. Yes ... A high school student can write a log table. It was 6 years ago that I was fascinated by the log tables and thought that the inventor of the log tables was a magician. When I expressed this to a very very good friend and a mentor of mine, he laughed and said, there is nothing great about it.
Any number can be expressed as a power of any other number. When we hear the base of the algorithm being 10, it means that the number A is expressed as another number 10 ^ x.
A = 10 ^ x
B = 10 ^ y
C = 10 ^ z
A * B / C = 10 ^ (x+y-z)
Hence, we add the log values of x,y and subtract z from it. When we have to find anti-log, we just raise 10 to the power of (x+y-z) and there comes the answer. Interestingly, everyone in the class was able to understand (if not appreciate because of its simplicity). Everyone knew what was happening in each step and everyone had done things like this before. Only thing that made the difference was the inability to link it and come up with a conclusion.
Similarly, when I explained insertion sort and asked them to write it in the form of algorithm, they seemed apprehencsive, but, when I started writing the steps they came up with the next step. I began to realize that, inspite of students being very intelligent and very smart, they were a bit apprehensive... May be due to lack of confidence. I am not sure. But, explaining insertion sort was fun. There are a lot of places where insertion sort is explanined with animations, so, I wont be writing about it ... I found the following like very useful and informative
http://www.sorting-algorithms.com/
Most of the students knew that,
e = lim (1 + 1/n) ^ n as n tends to infinity
(value e = 2.71828182845904523536028747135266249775724709369995...)
It seemed to have weird resemblance with compound interest formula.
If the interest is compounded q times a year: A = P(1 + r/q) ^ nq
When I googled a bit for it ... Indeed ... I was correct... It did have it's root in bank. Jacob Bernoulli seems to have come up with this constant when he was calculating compound interest. He came up with the above number.
I will write a few more blogs on algorithms in the subsequent entries. Mathematics has always astonished me. It remains the best subject to study. When I get depressed or the day doesn't go fine ... I deal with them by reading up a few math stuff ... And it always works !!!
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