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Many students ask me what is my study strategy. I usually churn out ‘A’s, with the occasional ‘B’ in my tests and exams, well above the class average. While my friends seem to struggle with studying and tie themselves with last minute revision a day before the exam date, I take a good night sleep and wake up the next morning ready to graciously execute some integration sums. I do better than them and it is no surprise that they want to know how I do what I do. Here’s my answer.

Nothing beats a good study strategy, especially in the subject of mathematics, of consistent practice. Other aspects of studying are also important, reading of theorems, discussing concepts with friends, memorizing derivations, but none of these would prove fruitful if they are not practiced with consistency.

Supposed you are given a new theorem to study, let’s just say it is de Moivre’s theorem. You may fully understand it after an initial reading. Besides what is too difficult of understanding multiplying the argument by its power. Simple this theorem may be but a reading of it does not expose you to its full problem solving capability. During the exam, you are not asked to state out de Moivre’s theorem but to use it to solve the given complex number problem.

So you flip through the exercise section and briskly solve the first three problems and call yourself a master of the theorem. Hmmm, not quite. All you have done is to a simple application of the theorem that you have read five minutes ago. Everyone can do that because the theorem is right in front of them.

Then why is it that when you are asked to answer a rigorous A-level complex numbers question, you fail in using de Moivre’s theorem. Well, the reason is that in the mix of calculus, sequences, mechanics questions, the meaning of the theorem is lost because you have yet internalized it in your mind.

Internalizing a theorem is to have second nature to you, to be able to both state the full theorem, including the conditions attached to it, and identify the variety of problems at first sight which need the theorem to be solved. It does sound attracting to be able to recall any theorem to solve any math problem. It is a skill any student would want but unfortunately there is no short cut in acquiring the skill. It takes consistency to do so.

This is best explained with a graph. We are all familiar with graphs such as ,  and . Suppose if you will that your ‘learning quantity’ takes the form of one of the three graphs. I have plotted the three graphs, along with a  for the interval . Bearing in mind that the  indicates your ‘learning quantity’ which is what you want to maximize, which of the four curves would you want your learning ability to follow?

You should be quick to answer that you want a  curve simply because it has the largest  value for the whole interval. This means that your learning is maximized in that short interval. This is somewhat true as seen by how the typical students, before the exam, rush through thousand of notes in that few days before the exam. You may think at this point of time that the students whose learning follows the other curves lose out. But do they?

Changing the interval to , we see a vast difference between the  curve and the rest. The  curve all increase in a dramatic rate. While they did start slow in their learning, through consistency in learning, their learning capability has shot through the roof. From closer inspection, we see that the  which started out to increase the slowest in the short term interval is now increasing the fastest. Such a student started out slow but with consistency he is able to internalized the theorems and his learning quantity far surpasses the rest.

Now that is how I study, a strategy of consistent learning. Most students, and trust me when I say most of them, think that they can master their subjects by ‘rushing’ through studying in a short time span. This is certainly bound to fail if there is no consistency in the learning. They will tire themselves out and lost interest in the subject while I leisurely absorb and internalize theorems at a slow at steady pace, maintaining enthusiasm in the subject. And when the exam comes, it will be these factors that get me that ‘A’.

Why not you try that? Don’t crap all the studying in two days prior to the exam like the  curve but for now, try to follow the  curve, where your learning starts slow but shoots up after the initial period. Trust me, you would have a mysterious air of confidence when you take the exam. Besides, if you really wanted to maximize your learning in the short, you should be following another curve.