Fourier’s Wonderful Idea – I

Breaking Complex Objects into Simple Pieces ``In a memorable session of the French Academy on the 21st of December 1807, the mathematician and engineer Joseph Fourier announced a thesis which inaugurated a new chapter in the history of mathematics. The claim of Fourier appeared to the older members of the Academy, including the great analyst … Continue reading Fourier’s Wonderful Idea – I →

Cubic Skulduggery & Intrigue

Babylonian mathematicians knew how to solve simple polynomial equations, in which the unknown quantity that we like to call x enters in the form of powers, that is, x multiplied repeatedly by itself. When only x appears, we have a linear equation. If x-squared enters, we have a quadratic. The third power of x yields … Continue reading Cubic Skulduggery & Intrigue →

Subtract 0 and divide by 1

We all know that division by zero is a prohibited operation, and that ratios that reduce to ``zero divided by zero'' are indeterminate. We probably also recall proving in elementary calculus class that $latex \displaystyle \lim_{x\rightarrow 0} \frac{\sin x}{x} = 1 &fg=000000$ This is an essential step in deriving an expression for the derivative of … Continue reading Subtract 0 and divide by 1 →

Reducing R-naught to stem the spread of Epidemics

We are reminded each year to get vaccinated against the influenza virus. The severity of the annual outbreak is not known with certainty in advance, but a major pandemic is bound to occur sooner or later. Mathematical models play an indispensable role in understanding and managing infectious diseases. Models vary in sophistication from the simple … Continue reading Reducing R-naught to stem the spread of Epidemics →