## Connections in Mathematics

Since the theme of this year’s Welcome to Langara Day was “Get Connected”, it seems worthwhile to look at some of the ways in which this applies to Mathematics, and this post amplifies on the three themes identified in the departmental posting linked to above.

Of the many ways in which Mathematics is the glue or common element which connects apparently different subjects, the case of cyclical phenomena is particularly interesting because it recurs at several different levels.

In precalculus we learn about how trigonometric functions are connected with rotation and so describe many phenomena that are based on some kind of rotary motion – such asĀ daily and annual cycles of sunlight and temperature, tides, seasonal variations in crop prices and so on.

But later, in the study of differential equations, we see also that having the same mathematical equation involved also explains the similarities of behaviour between spring systems, water and sound waves, electrical oscillators, and population cycles in a predator-prey ecological system.

In addition to being the connection between different subjects, mathematics is also used in the study of connections when graph theory is used for example for the counting and analysis of connections in a network. And on a more esoteric but extremely practical level the study of random or stochastic networks is an important tool in the analysis of fluid flow in porus media which is important both in hydrology and in the theory and practice of petroleum extraction.

[…] (publishers of the ‘Maple’ computer algebra system) does exactly what I wanted to do in my earlier posting about the “Get Connected” theme of this year’s “Welcome to Langara” […]