Why do biologists need math?
Biology is the study of the living world, and in order to understand the principles of life,
we need to be able to interpret the world around us.
Math is the tool that allows biologists to quantify and measure all the different aspects of life.
Let’s take a brief look at some ways that biologists use math.
Let’s say you manage a forest and want to know how much lumber you can harvest from each tree.
First off you can calculate the height of a tree using trigonometry.
You can then measure the circumference of the tree and calculate its cross sectional area.
From this information you can determine how to have the log milled
so as to maximize the amount of lumber obtained.
You can make these calculations before cutting down the tree so as to make sound decisions.
What if you wanted to know how much a population of individuals varied in weight?
You might be in charge of a population of mice for research which have been fed something like Yummy Chow.
First you could weigh each mouse. Then you could find the average weight (otherwise known as the mean)
by adding up all the weight values and dividing by the number of mice.
Next you could calculate the weight range by finding the difference between the highest and lowest weight values.
And finally, you could calculate what percentage this variation in weight was of the mean.
But what if you wanted to know whether one type of food resulted in bigger mice?
Then, still using math, you could make the same measurements on another group of mice who had been fed Super-Yummy Chow.
You could then find out how much one population varied from another.
Did the mean weight vary or was a larger range of weights realized?
Was the variation the same percentage of mean weight?
If you wanted you could then ask the question about the differences you measured
and use statistical tools of math to determine if the difference was big enough to not have happened by chance.
Are the mice as a group, who were fed different chow really different or did the difference just happen by chance?
Lots of people get the flu and epidemiologists track these cases each season using math.
They want to determine the incidences (new cases occurring)
and the frequency (number of cases that already exist).
Tracking these numbers helps determine the rate of change (# new cases over time).
Do we have an outbreak of flu right now?
To answer this we need to determine if we are experiencing an increased rate of incidences in the area.
Measuring a phenomenon and then determining its rate of appearance or disappearance
over time can help us to answer these questions.
Using linear and nonlinear algebra you can look at how one thing is correlated to another.
For example you might question just how drinking coffee is related to the number of hours you sleep at night.
You could vary the amount of coffee you drink in a day
and measure the number of hours you sleep that night.
After a number of days varying the coffee intake and measuring the hours of sleep,
a graph could be constructed.
Does a linear negative relationship exist in which increasing coffee intake reduces the hours slept?
Maybe there is no correlation between the amount of coffee and the hours of sleep.
but drinking moderate amounts increases the number of hours slept.
You could investigate all of this using math.
If a correlation is established then you could investigate whether one thing is causing another
by conducting experiments with controls.
Maybe you’re interested in how fast something is changing over time
and also want to know if the rate of change is increasing, staying the same, or decreasing.
Calculus can help us with this.
For example you mow your lawn in the summer
and only want to mow when you have to.
How fast is the grass growing?  And will it be growing at an
exponential rate?  Or will that rate vary throughout the season with rainfall
and other environmental factors?
What will the total amount of grass cuttings be that you have to bag and carry off to the compost pile?
Using calculus would allow you to find answers to these questions.
When studying biology it’s helpful to understand the character and dynamics of what we observe.
The many powers of mathematical techniques help us do just that.
In later videos, we will take a deeper look at these principles
and explain how you can use math to study biology.
