Who are you?
You are a professional who would like to build a mathematical model in your spare time.
Why?
You have spare time, don't you? Yes, the time between arriving at the bus stop and getting on to the bus. And the time between getting to the train station and actually boarding the train. And also the time between getting to the shuttle stop and actually boarding the shuttle. Well, this is your opportunity to use your spare time for practical purposes. This post will outline how you can build a mathematical model in all that spare time that you have. This spare time would otherwise be used up making pointless Facebook posts. Well, now you have options. No, not stock options. You have to do actual work for that.
How?
This post is inspired by Hal Varian's remarkable paper "How to build an economic model in your spare time". Like the author of that paper, we believe that it is the simple lack of the availability of a post such as this one that has made it difficult for people to develop mathematical solutions to hard problems. Please note that, as is obvious, extensive research on mathematical work done in far-flung countries like Russia and Japan has been done as part of background reading for this post.
For those new to building mathematical models, this post will provide you some practical tips and expert guidance on the steps you can follow to build a math model - all in just your spare time. Which, after reading this little piece, you will have none left of. Because you will be so busy either solving mathematical problems - like Prof. Shankar - or resting on your laurels - like Prof. Manikutty - knowing that you don't have to do any more research. But remember that Prof. Manikutty knows that, in Japan, he is already a "prominent person". Prominent because he is the tallest person around for miles and miles.
Detailed Steps
For this, you will need:
1. A sheet of paper
2. A pen
3. A smart phone
The steps to follow are the following:
1. Grab a sheet of paper. Get a pen. (No if's and but's. Just do it).
2. Point your smartphone browser to the research agenda section of any mathematics professor. (You may find this one by Prof. Krishnan Shankar useful for a good start.)
3. Write down the first interesting research problem you see there. (Make sure you capture the punctuation accurately.)
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4. Suppose G is isomorphic to a finite cyclic group of order n. Given an element g in G, is there a fast way (polynomial time) to compute the order of g?
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(Don't worry if you didn't understand what the two above sentences mean. I don't either.)
4. Think about it (in your spare time)
5. ?
6. ?
7. ?
8. Write down the solution on one side of the plain sheet of paper and the mathematical model involved on the other side. In your spare time.
9. You have now built a mathematical model in your spare time.
In summary, if you have this handy-dandy guide, building mathematical and economic models is not that hard. Oh well, actually, that only applies if you are some type of Einstein. Or Ramanujan.
And finally, a true mathematical puzzle to seriously think about : Find the first odd perfect number. Or prove that none exist.
Recall that a perfect number is a number which is equal to the sum of all its positive divisors not including itself. The problem is simple enough to state but has proven incredibly difficult to solve. That's all, folks. Happy puzzling!
Update: updated the post a bit. Fixed typos.
