A Poll at the Forum

Often I see polls saying that Rob Ford has a political base that is either made of concrete or completely at odds with the reality of what it means to be a responsible leader that represents the people. The most recent example is a tweet in #TOpoli today citing an article in the Toronto Star … Read moreA Poll at the Forum

Confirming a New Years resolution

Over the last year I have been taking note of some of the stories in the various science/tech news feeds with of hope of eventually finding the time to expound on them in a format such as this. There is really no perfect time to commence such an activity and over the winter break I … Read moreConfirming a New Years resolution

Least squares and pseudo-inverses

To appreciate the connections between solutions of the system $$Ax=b$$ and least squares, we begin with two illustrative examples. Overdetermined systems: $$A$$ is $$m \times n$$ with $$m > n$$. In this case there are more equations than unknowns, $$A^{\top}A$$ is $$n\times n$$ and $$AA^{\top}$$ is $$m\times m$$. The connection with the pseudo-inverse is that … Read moreLeast squares and pseudo-inverses

Intermediate Value Theorem – Limits and Continuity

Intermediate Value Theorem To begin with, let’s start with the basic statement of the theorem. Theorem If $$f(x)$$ is continuous on a closed interval $$[a,b]$$ and $$N$$ is any number $$f(a) < N < f(b)$$ then there exists a value $$c \in (a,b)$$ such $$f(c) = N$$. The illustration corresponding to the theorem is to … Read moreIntermediate Value Theorem – Limits and Continuity