Skip to main content

Mathematical Models

In every physical science, we rely heavily on mathematical models to accomplish further scientific research.  (Yes, even you biologists and organic chemists; you just have the mathematical models hidden.)  Mathematical models are the key to all scientific research.  (And for those reading this from outside of the United States, I will use the word "sciences" in place of the term "physical sciences" from here on out; be prepared for that.)

This brings up a key question; what exactly is a mathematical model?

It would be good to have an equation fall under a mathematical model.  This can be the case, but more often than not, one equation is insufficient.  It also doesn't have to contain equations; there can also be inequalities, where a value is either less than or greater than a certain quantity.

Mathematical models are descriptions of a system with mathematical language, which can be one or many equations or inequalities.  This is more of a functional tool than it is a precision tool.  They are used to solve real world problems, where the entire system doesn't have to be precisely defined mathematically, but the problem area is mathematically approximated to high enough of a precision to be solvable in all cases.

An example of mathematical modeling is the population of a species in response to what is called "forcing factors", factors which force the behavior of a species population.  This is also called "population dynamics".  This may seem like a relatively heartless application of mathematical models, but there are many times where one needs to use these models to do the greatest good in the world.  For instance, there are people who are working on population dynamics models as applied to humans to try to locate problems with our growth to try to fix those problems.  I hope these problems can be located soon enough, for everyone's sake.

And as always, don't forget to be awesome.
Take that as you will, 
-K. “Alan” Eister Δαβ

Labels

Labels:
Location: Paradise, NV, USA

Comments

Post a Comment

Popular posts from this blog

Multiple Regression: Basic Statistics Lecture Series Lecture #14

As promised from last time , I am going to cover multiple regression analysis this time.  As mentioned last time, correlation may not imply causation, causation does imply correlation, so correlation is a necessary but insufficient (but still necessary) first step in determining causation.  Since this is a basic statistic lecture series, there is an assumption that matrix algebra is not known to students who take this course, so this section will only be working with the solutions obtained through a program such as Excel , R , SPSS , or MatLab . This is the regression case where there is more than one independent variable, or multiple independent variables, for a single dependent variable.  For example, I mentioned last time that there is a causal correlation between the number of wins a team in the MLB has and the ratio of the runs that team score to the runs that team allowed.  The more runs they scored per run they allowed, the more wins they are likely to hav...
Post a Comment
Read more

Confidence Interval: Basic Statistics Lecture Series Lecture #11

You'll remember last time , I covered hypothesis testing of proportions and the time before that , hypothesis testing of a sample with a mean and standard deviation.  This time, I'll cover the concept of confidence intervals. Confidence intervals are of the form μ 1-α ∈ (a, b) 1-α , where a and b are two numbers such that a<b, α is the significance level as covered in hypothesis testing, and μ is the actual population mean (not the sample mean). This is a the statement of there being a [(1-α)*100]% probability that the true population mean will be somewhere between a and b.  The obvious question is "How do we find a and b?".  Here, I will describe the process. Step 1. Find the Fundamental Statistics The first thing we need to find the fundamental statistics , the mean, standard deviation, and the sample size.  The sample mean is typically referred to as the point estimate by most statistics text books.  This is because the point estimate of the po...
1 comment
Read more

Basics of Statistics Lecture #10: Hypothesis Testing of Proportions

As promised last time , I am going to cover hypothesis testing of proportions.  This is conceptually similar to hypothesis testing from the mean and standard deviation , but the calculations are going to be different. A proportion is the percentage of success in a sample or population, reported in decimal form.  This means that if heads comes up 50% of the time, then it is reported as p=0.50.  Because of this, the calculations are different than that of the mean and standard deviation case from last time.  For instance, when we have proportion data, we don't know the standard deviation of either the sample or the population.  This means that the standard error calculation cannot be performed as typical.  We must instead use a proportion-specific version, which is given by $\sigma_{E}=\sqrt{\frac{p*(1-p)}{n}}$, where p is the proportion and n is the sample size.  If we have the sample size and the number of successes, we can calculate the proporti...
Post a Comment
Read more