I collect the applications from our Research Experiences for Undergraduates program.
The most recent starts out, “Dear Madam.” I am annoyed. I made sure that my title, Dr., and name was given clearly on the web page with application instructions. Send to Dr. So-and-so at this address.
Use my proper academic title. Why is this so hard?
One of my students was falling asleep in class today. Fortunately, we were discussing a mathematical model for a rabbit population, and so I could truthfully say, “We are now going to talk about sex.” That did the trick.
Can you guess who formulated this model? Here are the assumptions:
- We start with one pair of baby rabbits, 1 male, 1 female.
- Rabbits take 1 month to reach sexual maturity.
(We were discussing the previous step as the student’s eyes closed.)
- As soon as rabbits reach sexual maturity they mate. The female gives birth to a male, female pair the next month, and every month thereafter.
- Rabbits never die. At least not for the duration of this modeling scenario.
So how many rabbits are there?
- The first month, there is one pair of rabbits.
- The second month, the rabbits reach maturity and mate. There is still one pair of rabbits.
- The third month, the rabbits give birth to another pair and get pregnant again. There are two pairs of rabbits.
- The fourth month, the first pair gives birth again, and the first two pairs get pregnant. There are three pairs of rabbits.
- The fifth month, the first two pairs give birth, and the third pair gets pregnant for the first time. There are five pairs of rabbits.
- As you can see, each month the number of births we get equals the number of rabbits 2 months back. We add that to the rabbits we had in the previous month. So the number of rabbits equals the sum of the preceding two numbers.