Capstone Project

An outline of project ideas:

  • Evaluate a 2-player game of Risk, with the objective of uncovering methods for accurately predicting the locations of your opponents pieces and their strategy under the following conditions:
    • You can only “see” your pieces
    • You know the number of turns that have occurred, and their order
    • You know where your enemy has attacked you, and with how many pieces you were attacked by
  • The Modeling of Emotions thru their effect on decision making
    • The general idea:
      • Like the old adage, “you can’t measure the wind but you can measure its effect on things.” It is my thought that, while yes you can not measure emotions, you might be able to measure their effect on strategies. And also like the wind, after having measured their effect it may be possible to arrive at some conclusions about the nature of emotions. For example, perhaps we find that the effect an emotion has on strategy decays with time; and we find that this is somehow proportional to how an emotion decays with time. It is not crazy to assume it may be possible to find a decay function for emotions, which may then lend us new insight.
  • An approximation for the Zeta-Function
    • A question that has long consumed my mind is that of the Riemann’s Hypothesis. This question has led me to ponder, “might it be possible to approximate Zeta; and, with that approximation, write a proof showing that if the approximation zeros lie on the critical strip then the same is true for Zeta does too(show Zeta is bounded by an alternating convergent series)?”
      • Clearly, I recognize as an undergrad it is MORE than ambitious to try and solve Riemann’s. That said, it’s not crazy to think I could find several approximations for Zeta.


I have decided on a project:
The proposal of a new path predictive algorithm and its analysis compared to known/existing algorithms. The project incorporates data from GIS software and GPS; which, will be analyzed to derive relevant constants(example: time at a stop light) for a series of linear differential equations and then applied to a graph, in order, to derive an algorithm to predict the path an individual is likely to take. Next, I will build a program to compare the results of the algorithm, other known algorithms, and the actual path taken.


I’ll be back to post my work, as well as an early presentation, and a copy of the draft paper…

I should note, the project has changed since I last wrote. I decided to investigate what I’m calling an emotive game. In particular, I decided to focus on a single case of the “emotive traveling salesman problem.” To briefly explain my meaning, consider you want to go to the hospital. There are, in general, 3 cases which might draw you there:

A routine checkup, an emergency, or because you are sick.

Another way to think of these three cases is “emotively”:

The base case(non-emotive), the high arousal case, or the low arousal case.

Each of these “emotive cases” is, of course, a generalization of many other emotive cases; but, for the purposes of this project, they will suffice. The point here is to suggest a first step towards the development of a cohesive mathematical theory of emotions.



I am finally able to sit down and upload the paper as I presented it for my Capstone, as well as the presentation.

Mathew Paper

Mathew Presentation

An astute observer will note, I only presented one case of the emotive game. I am however working on two other cases. And intend to submit the final paper to be published. This is of course only part one of a much larger project. I recognize that this first part acts only as a suggested model, and needs to be backed by experimentation; which, will be the focus of my second paper.

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