Many problems in probability are solved by assuming independence of separate experiments. When we toss a coin, it is assumed that the outcome does not depend on the results of previous tosses. Similarly, each cast of a die is assumed to be independent of previous casts. However, this assumption is frequently invalid. Draw a card … Continue reading ToplDice is Markovian
Month: August 2019
The curious behaviour of the Wilberforce Spring.
The Wilberforce Spring (often called the Wilberforce pendulum) is a simple mechanical device that illustrates the conversion of energy between two forms. It comprises a weight attached to a spring that is free to stretch up and down and to twist about its axis. In equilibrium, the spring hangs down with the pull of gravity … Continue reading The curious behaviour of the Wilberforce Spring.
The Brief and Tragic Life of Évariste Galois
On the morning of 30 May 1832 a young man stood twenty-five paces from his friend. Both men fired, but only one pistol was loaded. Évariste Galois, a twenty year old mathematical genius, fell to the ground. The cause of Galois's death is veiled in mystery and speculation. Whether both men loved the same woman … Continue reading The Brief and Tragic Life of Évariste Galois
Stokes’s 200th Birthday Anniversary
Next Tuesday, the 30th of August, is the 200th anniversary of the birth of George Gabriel Stokes. This extended blog post is to mark that occasion. See also an article in The Irish Times. Whether we are designing aircraft, modelling blood flow, studying propulsion, lubrication or the dynamics of swimming, constructing wind turbines or forecasting … Continue reading Stokes’s 200th Birthday Anniversary
Algorithms: Recipes for Success
The impact of computing on society is ever-increasing. Web-based commerce continues to grow and artificial intelligence now pervades our lives. To make wise choices, we need to understand how computers operate and how we can deploy them most constructively. Listen to any computer scientist and soon you will hear the word “algorithm” [TM168 or search for … Continue reading Algorithms: Recipes for Success
ThatsMaths 