Tag: Mathematics

Risk Analysis

Risk Analysis

Risk Analysis

05/15/19

“How can we analyze risk?”

Every engineering, business, or policy action has some sort of risk attached. Whether it be installing a wind turbine or funding a renewable energy startup, something could go wrong. As a result, before institutions will make a Risk Analysis to see if taking such an action is rational. Risk analysis can be performed in a multitude of different ways, both qualitatively and quantitatively.

Climate Change Attribution

Climate Change Attribution

Climate Change Attribution

04/09/19

“How can we attribute what is responsible for climate change?”

One of the biggest debates going on about climate change is what is causing it. Many political pundits will claim that everything can be explained entirely through natural factors such as the Earth’s tilt or volcanoes. However, to prove causation, mathematical analysis will need to be done to isolate each component and observe its effects. Using this Climate Change Attribution, we can see that these effects do not contribute greatly to global warming and that carbon emissions is the primary driver behind climate change.

Hypergeometric Distributions

Hypergeometric Distributions

Hypergeometric Distributions

03/06/19

“How can we measure the probability of drawing something without replacement?”

Sometimes, we would like to know the probability of choosing certain types of cards and that we either choose the right or wrong card. The problem with this is that the probability will change with each card drawn. As a result, this will take on a special Hypergeometric Distribution.

The probability of choosing the desired card can be found with the equation

With N being the total population, n being the number of draws, K being the number of successful members of the population, and k being the amount of the successful members desired.

Image credit: Wikipedia

On Convergence of Infinite Sums

On Convergence of Infinite Sums

On Convergence of Infinite Sums

Matthew Hanna

02/18/19

“What is so special about infinite sums coming to a specific value?”

 

1

We have all seen the classic sum.

2

Which is often represented as…

3

We, in our high school careers, have been taught that this sum is 2. This is
most often done so with an algebraic manipulation of both sides of the sum. We
haven’t been taught how to verify this sum. But how would we go about doing
this?
The basic idea is that if I end my sum at nite point, my result will deviate
from the actual sum by some error (which we will call ε. This error is some
positive real number. To verify that this sum indeed approaches 2, it suffices
to show that for any error, there exists a nite point in the series in which the
difference between 2 and this point is less than the error AND all further points
will also be less than the error.