Some teamwork

Math Journal: Post assignment reflections

We encountered many obstacles through this assignment, the first being the lack of teamwork our group had. We started off as three members, but we took in another one. That person had little sense of responsibility and understanding. Finding the formula for the harmonic number was a great problem we needed to solve, thus we assigned that to him as his first role. I would not have minded if he had tried early, but he cropped up with many excuses, like it was still such a long time before the deadline, and that he was busy (Relatively free compared to some of us though who takes three times more languages and do not have the privilege of little travelling time from school to home), despite constant reminders. When he claimed to have reaped some results, it turned out to be a recurring function, which required input of the previous result to find the next result(not particularly useful). By the time sense struck us that we should have given up on depending on that person long ago, it was too late. Fortunately the deadline was extended. Sometimes, despite how capable other people are, it still takes just one person to bring the rest down. A balance between compassion and selectivity of team elements would always be helpful. Being too kind at times, does not mean being kind to the person in the long term.

From past experience, I realised that nothing beats face to face discussion; otherwise, and the possibility of horrendous results surface. Some people think that with leaps and bounds in technology, digital communication is a huge improvement from the tiresome times where we have to find a place to meet and discuss work. I beg to differ, because only with physical discussion, will we be able to better communicate, with more than just words. Expressions play an important part too, when wanting to know how each other feels about an idea, and to know who is following and who is not. Doing work face to face, is also physically easier, compared to having to use those computer peripheral to transmit thoughts. Besides, not everyone checks their email all of the time.

On my experience, usually online discussion only leads to two things, a rough idea and the division of work. Many people love to divide work, and they claim that that lightens each person’s burden. However, when we divide work over the internet, most of the time everyone is doing their own stuff, and there is a lack of conformity in thoughts. Despite their work being wonderfully done, the different parts of a report might not necessarily fit properly, both in structure and content. Each jigsaw piece can be beautifully and intricately created, with a melodious blend of colours, but it turns out to be not much use should they not fit with each other. This is not teamwork, this is just well-done individual work neatly compiled together.

That is why, from the start I have suggested us coming together to brainstorm and discuss, and finish the math journal in front of each other, such that we all know what each other is doing. However, due to the lack of time we had because of the extreme delays we suffered from waiting for someone, we could not find a time to do so. It turned out that my postulate had proved itself right once again, because, not meaning to bring myself higher, but it turns out that I was doing a lot of the work in the end because some people did not have the initiative to do so.

The second obstacle was the boundaries of mathematical knowledge we had. As it turned out, the Harmonic Series was not easy topic to write much about with our elementary knowledge of series. We, or at least, I, had to do a lot of research and digestion before being able to start writing the report to ensure I understood what I was writing, instead of mere copying from sources. This research includes reading up on topics in calculus, such as infinite series like the Mercator series and a little integration, understanding it; and also trying to formulate my own equation to make sure that my understanding matches the understanding of books and internet.

Despite the research, the formula for the Harmonic numbers was still a huge problem. The moment I found that there was no straight formula found on the internet about a formula regarding the Harmonic number, I had a feeling that we were in trouble. It finally turns out that it requires understanding the digamma function, the logarithmic derivative of the gamma function, which is equivalent to the factorial operation for positive integers. However, the full equation defining it was way beyond our understanding.

When we found Euler’s result, we thought that our problems have vanished; the Harmonic number is equal to the integral of (1-x^n)/(1-x) from 0 to 1. However, by evaluating the integral we realised that we got back the harmonic series. That was no use. Finally, we made do with a close approximation of the Harmonic number.

The result might not had been as ideal as we had hoped for, but I felt that I have learnt a lot through the constant probing for answers, which lead from one question to another. Although, our goal of finding and understanding the formula for the exact value of harmonic numbers was not clearly achieved, I have learnt many other things, like understanding the proves for alternating series after very long times of pondering and having a slightly better understanding of elementary calculus. I cannot help but to agree that over here, the journey means more than the finish.

I must say that by having done a lot of work, hours of background research, hours of report writing and question solving, I am positive that I enjoyed my work more than anyone else in my group. Now that the journal is done, I found myself learning a lot more than I thought I would be learning. I feel really proud of what we have done, and although it would be ideal that everyone co-operates to their best, it still does not matter who ‘slacks’ and who does not, because diligence and responsibility comes with its own reward. I know that sounds rather cliché.

Wow, the world is fair after all.