Going from words to symbols

One of the important skills that we develop in Engineering mathematics, is the ability to develop mathematical relationships from written (or verbal) descriptions. This translation (or perhaps interpretation ?) from "ideas" into equation form is challenging because its requires both mental dexterity and familiarisation with mathematical language.

It does take some confidence to translate "If you have a room of volume 60 cubic meters, that is one meter higher than it is wide and one meter longer than it is high, what are the dimensions of the room ?"

into

(x+1)(x+ 2) x = 60; w=x, h= (x+1) and L=(x+2), solve for x

This is particularly apparent when first year engineering mathematics students tackle vector problems that start with descriptions like "A ferry is crossing a river ....". I think this dis-comfort reflects a background of solving problems that either already defined in mathematical terms or has a ready made picture representation provided with the problem. Unfortunately, the problems presented to engineers and applied mathematicians are rarely presented so neatly.

My advice to developing this skill can be broken down into the following steps:

a) Try to represent the problem as a picture through a freehand sketch (labelling lines and symbols from the written description of the problem).

b) Try to visualise the problem from this picture representation, forming an image in our mind, identifying what specific problems you are trying to solve.

c) Express the problem in symbolic form, writing down definitions of the symbols you are using or any assumptions you need to make.

d) Solve the equation (or equations) you have formed, showing each step systematically.

e) Look at your answer and your original picture of the problem and ask yourself two important questions:

(i) Have you answered the original question ?

(ii) Does your answer make sense ? (Is it believable ?)

Of course, like any skill, practice will develop your abilities. It must also be admitted that there is an element of "art" to the processes described above that is beyond words or description .... which makes it fun and challenging !