Mathematics Extended Essay

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Welcome to the world of Mathematics and thank you for considering Mathematics EE!

Please feel free to contact me at liuchangshuo@outlook.com should you have any questions.

Unlike Chemistry or Economics EE, not a lot of students would choose Mathematics EE so you would never fail to have a place in Math EE. Here are some pros and cons for taking Math EE:

Advantages

  1. All “Experiments” will be done in your mind apart from collection of data if you are getting them manually. It saves your time so that you may focus on other parts of IB, given that you can finish Math EE quickly. (Actually many students finished their major portion of Math EE before end of Y5)
  2. Chance for you to learn a new field, be it optimization, discrete mathematics, geometry, modelling or others.
  3. The difficulty can be flexible. You can make difficult results from simple topics or take a difficult field that you had not yet learnt before.
  4. Most importantly, you can lie on the bed and do math. XD
  5. Word count is not a problem. Equation is not counted as words.

Disadvantages

  1. It is hard to find a former template like “heavy metal absorption” or “anti-cancer” in Chemistry.
  2. Luck is important apart from hardwork. New theorem or other discovery does not come easily.

I took Math EE because I would major in Mathematics in Uni. If you have a great certainty in about what you want to do in university, it will be the best chance for you to do an EE about it.

My personal opinion: {Personally I strongly discourage people to take math EE because there is no other subjects to do. Passion and dedication to a thesis is extremely important. Statistically, Math EE students in 2014 Nov batch had score evenly spread out from A to D. Therefore, there is no good reason to think “I may have luck” and randomly choose an EE. It applies to any subject also, I believe. However, if you unfortunately happened to take math involuntarily, don’t worry. Do you best and you will get the reward that is proportional to your put-in. (Then you may end up as a math major, haha) }

What do you wish you’d known about your EE?

Axiom 1. Start early.

 

Definition 1: Mathematics EE have two directions: mathematics modelling and mathematics investigations.

 

Theorem 1.  Do a lot of research before you finalize your Research Question (RQ) on amount of knowledge to learn, past papers on this topic, data available (if needed). It saves your time.

Proof: Using Axiom 1, you have much time before the deadline of finalizing your RQ. In mathematics, especially, a good topic will mean half of EE. Knowing how much to learn will give you expectations of how much you need to work. Consuming an extremely new field is hard and sometimes your mentor may not even be familiar with this field, so please think carefully on whether you have time and ability to learn that far. Past papers on these topics are good, but too much done on this field will make your situation even harder. You are cracking something others are hotly doing but were yet solved! (Not applied to mathematical modelling). Data, if not available, will require you to acquire them manually – time-consuming. Therefore, by considering these three aspects, you can choose a reasonable topic wisely and will not go back and rethink about a new topic (CATASTROPHE! TIME BLACKHOLE!).

Axiom 2: Difficulty is not proportional to the result.

Intuition: Simple math EE gets A as well. The thing about IB is that it evaluates language skills heavily and it is more about how well you express your ideas and equations.

Theorem 2: Listen to your mentor sometimes especially towards the end – paper writing, but not too much at the beginning unless you are extremely sure that your mentor knows what he/she is talking about.

Mathematics covers such a broad area and even our mathematics teachers will not be able to be proficient in all parts of them. If your mentor happened to be unfamiliar with your topic, you have to make decision on your own about “To go or not to go, it is a question” “Think about a new topic?” “Can I really do this”. Or you may ended being misguided. (It happened before.) Consult some of your math geeks around you if they are familiar with your topic.

At the paper writing time, however, listen to your mentor as he/she probably has much more experience than you on writing, such as your mathematical expressions and accurate choice of words. A second person reading your EE can pick out MANY mistakes that you overlooked. I call this Error Theorem (see theorem 3), just joking, XD.

Theorem 3: Let your errors in your EE be a set S defined on real numbers with value of their seriousness, for any  x belong to S, you can always find another error y that belongs to S and x<y.

In layman term, you will have many errors in your EE. The most enriching way to kill them is to scrutinize them out by yourself, which trainings your logic and thinking skill. However, you can also let your schoolmate or your mentor read it and give you feedbacks. You need to learn from these feedbacks and kill the similar mistakes. Please make sure that your mathematics EE is error free! Even a small error will deter the reader from reading on, especially on mathematics.

Theorem 4: Mathematics Modelling is safe, but challenge is risky.

It is safe because there are only a few models that you will be able to touch and there are many examples on each model. Although they look difficult, if you follow the steps, they are in your hands easily. Hence, it is not that difficult to do math modelling. However, be prepared that it is hard to sparkle on such EE to get an A.

On the other hand, if you are doing something that you are not sure if you can churn something out – discovering new things, you are taking a risk. If you ruminate all over the place and have nothing at the end of Y5, you will have trouble. Some people have skill of fathoming creative ideas with reasonably simple mathematics. It is good as well. Read Anthony 2014 Nov’s EE for reference.

So do a weighted evaluation and take your shot!

Personal conjecture 1:  LaTeX is good.

What was the commitment like?

It depends on your ambition and plan. Weekly report is sometimes required by some mathematics mentors. If you have no progress, then your commitment will be longer. Vice versa. I saw some people even changing topic in Y6, which requires much more commitment in a shorter period.

However, you can finish your math EE in one or two weeks in a straight shot. In my experience, I proved my Theorems luckily in the three “EE Days” and slacked all the way till the end of the year during which I just proved some Lemmas supporting my theorems. Then at the end of Y5, I found a step in proof seriously missing and cracked the proof in 2 days fortunately. I typed out my EE in 3 days and slacked all the way till Y6 June and finalized my EE in a week (intense).

Anthony, I believe, finished his EE in a few weeks after the “EE Day”. = =…. So it all depends on your own contribution and luck. I suggest that you shall try to kill EE asap – I am a bad example.

What are some common pitfalls of students who have chosen to take Math EE?

Underestimate and overestimate of self-ability.

Too ambitious or too shallow regarding the broadness of RQ.

What skills would you specifically need for an EE in this subject?

Language skill for mathematics geeks and mathematics fast-learning skill for others.

Do you have any regrets choosing this EE?

No regret. The reward of taking math EE, (much owe to Mr Jin) is ten times of taking Math HL.

I believe that if you work really hard and study beyond the level of math of IB, you will really learn a lot.

There you go, all the best!

Liu Chang Shuo is from the graduating batch of 2014.

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