MA4235: Graph Theory I

This is my last paper for the semester. That's right, I only took 4 modules! Of which, one was non-examinable. So only 3 papers this exam season; of which, 2 have already passed. The last paper is on Thursday night, so that gives almost 3 more days to study for just one paper. Shouldn't be too difficult, or so I thought!

Today, I tried to do some of the tutorial questions, and man... they were killer! Going to take a different approach tomorrow and do the pass year papers! Much easier, and more morale boosting!

Anyway, this module is a sub-branch of combinatorics and discrete math. Combinatorics is what is known to most of you as "permutations and combinations". Well, that's at lower level. But graph theory is more than just that, graph theory is a branch of math that has very powerful and immediate applications in real life. Some simple applications include timetable scheduling and transportation-route problems. The more complicated ones involve the best route a postman should travel to how computer networks work.

And of course, some of you were stumped by the following problem at last year's leadership retreat:

Mr and Mrs Tan attended a party at which there were 2 other couples. Various handshakes took place. No one shook hands with his or her spouse, no one shook hands with the same person more than once, and of course no one shook his or her own hand. After all the hanshaking was done, Mr Tan asked each person, including his wife, how many hands he or she had shaken. To his suprise, each gave a different answer. How many hands did Mrs Tan shake?

Well, those of you who know the answer, don't tell! Let those who don't know use their brains a little! Especially, this is the holiday season, not good to let the brain waste away! I was actually quite suprised at last year's leadership retreat, Faith (Tan) was able to give me the correct answer, and she actually used graph theory to solve it!

I enjoyed graph theory, or MA3233 rather. Had perhaps the best math lecturer in NUS for that module! MA4235 on the other hand... was too discrete for me! The proofs are okay. I understand them. But that kind of proofing involves skills that are very much different from analysis! And that is the main problem for me!

Anyway, Graph Theory is fun. And I am glad that they are introducing it at JC level. As a H3 subject. (H3 replaces what we once called S-papers.) It will be good for everyone to learn graph theory in fact; even in E-math!

And they should remove relative velocity from A-math and replace it with APGP again! Relative velocity is just too tough for secondary school and it's a physics topic not a math one! On the other hand, APGP is so important that it's taught at primary 3 level in China! It's so essential to calculus. I feel that teaching calculus without APGP is like teaching someone how to count to 100 when he doesn't even know what numbers are!

One good (or perhaps bad) thing is that this module is full open book. So no helpsheets! (Thank God!) But that means the problems can be a lot more difficult and unseen in nature!