Math Models

Step 1: Formulating

  1. Do a literature review (with proper citation) of the problem. Look for existing research on the matter by (i) using online search tools; (ii) going to the library; or (iii) interviewing someone knowledgeable on the subject (so long as this isn't counted as cheating. No No for IMMC.).

  2. Share with the team the research using google drive and google docs so that everyone is on the same page.

  3. Brainstorm and list the variables associated with this problem.

  4. Make assumptions to reduce the variables to the key essentials for your first iteration of your mathematical model.

5. A good way to decide what assumptions to make is to use a 2 by 2 decision matrix (see example on the left). In this example of modelling projectile motion, we can identify 4 variables: Velocity, gravity, air-resistance and Coriolis effect. We sort them in a decision matrix where the y-axis represents the impactfulness of the variables while the x-axis represents the difficulty of modelling those variables. Variables like Coriolis is low in impact and hard to model so we could make an assumption that there is no spin involved for the projectile nor the Earth hence negating this effect. On the other hand, velocity and gravity is high in impact and easy to model so we should include them in the model.

Step 2: Solving

  1. Deciding on the approach.

  2. Present your solution clearly. Ask yourself: "Will a layman understand your solution?". Write a 1-page summary of your solution.