Tag: Mathematics

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.

# On Writing Semantic Proofs

Hello all! For the 4th Math Monday, I have decided to do two quick proofs to show you how to write a proof.

# 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

# The Coordination Problem

Hello! This 2nd post in Matt’s Math Mondays is concerns a problem in first order logic. I reckon many of you have not taken an in depth course so this might be a little bit difficult. However, there is without a doubt in my mind with some elbow grease, you will be to understand and appreciate the problem!

# 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?”

We have all seen the classic sum.

Which is often represented as…

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.

# Plant Capacity Factor

Plant Capacity Factor

12/26/18

“How can we determine the potential used by a power-plant during a given period of time?”

Power plants are capable of generating a certain amount of energy. But only so much of it actually gets used. The ratio of energy used/potential energy is known as the Plant Capacity Factor. A simple way to conceive of the plant capacity factor is to think about the amount you can study in an hour compared to how much you study. Although you might be able to study a lot in an hour, the amount you actually study determines your efficiency!

Image credit Wikipedia.org

# How Heat Transfer is Used to Model Climate Change

How Heat Transfer is Used to Model Climate Change

12/16/18

“How is Heat Transfer Used to Model Climate Change?”

Heat Transfer is one of the foundational course for a Mechanical Engineer. But internal combustion engines and HVAC are not the only things that the theory can be applied to. Climate Scientists will use many of the same Heat Transfer equations when designing climate models. In this way, Heat Transfer is Used to Model Climate Change.

Image credit singularityhub.com

# Column Space

Column Space

12/11/18

“What is the space spanned by the linearly independent columns of a matrix?”

Matrices are likely to have at least a few linearly independent columns. The span of this space will result in a vector space known as a Column Space. The dimension of the column space is equivalent to the number of linearly independent vectors.

Image credit d2vlcm61l7u1fs.cloudfront.net