March 11, 2012

How Do I Memorize Mathematical Formulas?

Mathematical Formulas are like linking pins that serve as the path routes of mathematics. Just like when you supposed to move from one city to another you require a map, so in case of mathematics when you work yourself from one step of a question to another, you require the help of mathematical formulas. These formulas are like the governing bodies of the subject of mathematics and are responsible for the web structure of mathematics.
Such is the beauty of mathematical formulas, that if you can understand them and memorize them, your memory can replace scores of helping books and bulky mathematical solutions.

The following are a few basic techniques that can be used to memorize the governing bodies of mathematics, called the 'mathematical formulas'. There is no doubt in my mind that if you can following these steps, your grasp on the subject of maths will be enhanced.

1. Formulas should be written by hand instead of just going through them orally. Vast majority of the students just unconsciously overlook the easier formulas while solving a problem. They never give a reference to these formulas in the solutions and just consider that these easy formulas are nothing more than mere 'understood by all' trivial facts. But here lies a major problem. When a student keeps overlooking such formulas, he is unable to repeat them and thus with the inclusion of more and more complex formulas, he starts to forget the basic ones. This a major flaw in the learning curve of majority of the students. If we can just bear the extra efforts of  a few seconds and make a reference to these formulas, by writing them besides our solutions, we can indeed benefit from it in the long run.

2. Student should design a time-table wherein they can include a formula revision session. Such a session can either be at the start of a fresh lecture or at the end of it. The perfect scenario will be to include these sessions both at the beginning of their mathematical practice and at the end of it as well. If you have just overlooked a previously learned maths formula, a revision session will ensure that you can memorize it again and again.

3. In mathematics, there are scores and scores of formulas for every discipline. For example algebra has many formulas and so does trigonometry. But for every discipline of mathematics there is a set of primary formulas and the rest of the complex formulas and sub-formulas are more or less derivatives of these basic formulas.
And the basic mistake that most of the students make while preparing formulas is that they emphasize on every single formula separately. This puts a major stress on their memory, since there as many formulas in a particular discipline of mathematics. Assume the case of Trigonometry. If you try to learn every primary and tertiary (derived from primary) formula separately it will be a time consuming and attention diverting exercise.
But there is a more effective technique to memorize these various formulas.
Just try to learn the primary formulas and try to work out the tertiary formulas by using the primary (basic) formulas.

The below example will help you understand the importance of just memorizing the basic formulas and just working out the more complex formulas by using these basic formulas.

Here is a formula ..............     (a + b)^2 + (a - b) ^2 = 2 (a^2 + b^2)

Now if you can memorize the two basic algebraic formulas of (a + b)^2 and (a - b)^ 2 you can easily work out the above mentioned formula, without wasting the extra energy of learning the third one as well.
This requires practice - But remember our motto is practice. Nothing in maths can be achieved without PRACTICE.

4. Always pay attention to the mathematical symbols while learning a formula. Never overlook and make a mistake by using + instead of - or the other way round. If you get confused by the symbols used in two different formulas try to revise these formulas together and pay attention to the different symbols used in each of them. For example the difference between (a + b)^2 and (a - b)^2 is that in the first formula there is a +2ab and in the second formula there is -2ab.
Always be attentive to such differences to avoid errors.

5. If you have any confusion regarding any two formulas, always practice them together. This will enable your mind to develop an understanding regarding their use.
For example if you have a confusion regarding the formulas of the circumference, diameter and area of a circle, try to revise them together.

Circumference = 2∏r
Area = ∏r^2
Diameter = 2r