Ideas for Modules

• Magnetic Pendulum -- numerical simulation (described in the Math Exploration Quilt overview page.
• Swim-and-Walk -- a river-crossing problem explored step-by-step by several modules that span a very wide range of mathematics. Starts with time=distance/rate and progresses through the Pythagorean Theorem, graphing, numerical optimization, curve-fitting, and calculus.
• Population growth -- exponential increase, effects of resource limits & competing populations, cyclic behavior, phase plane graphs, chaos.
• Integers -- GCD, LCM, graphs of cyclic (and noncyclic!) behavior, explore computational cost vs solution method, optimization by continuous approximation, and how all this relates to the Golden Ratio.
• Graphing -- linear and logarithmic axes; "accurate" and misleading representations; chartjunk.
• Polynomials -- graphs vs coefficients.
• Complex numbers -- graphical interpretation.
• Trigonometry -- basic trig functions (for right triangles)
• Curve fitting -- via polynomials, exponentials, rational functions; effects of noise on fit.
• Calculus -- finite differences to derivatives; sums to integrals.
• Probability & random numbers -- dice games, card games, election polls, Monte Carlo simulation.
• Iterative numerical solution of nonlinear equations.
• Optimization: numerical vs analytic.
• Money exchange & budgeting -- take a trip, but don't spend too many dollars!
• Chemistry
  • titration -- change of pH vs amount of reagent added
  • mixtures -- change of boiling/freezing temperature as function of concentration. Change of concentration over time as a result of freezing (also models heat transfer and phase change).
• Physics
  • Simple mechanics -- bouncing ball, damped pendulum (1D).
  • DC circuits -- network voltage/current for simple resistor (linear) and semiconductor (nonlinear) circuits.
  • AC circuits -- network voltage/current over time for simple RLC and semiconductor circuits.
• Economic models -- profit versus advertising budget, ...

To date, reasonably robust Excel workbooks have been generated only for the first two ideas. Those workbooks can be accessed through the hyperlinks in the above list.

However, several other Excel workbooks have been done as quick-and-dirty prototypes designed to check out ideas. They include:

• 3-D Surface graphics with a simple GUI (Graphical User Interface) to control viewing angle.
• Solves an integer problem using brute force. The problem is "How many sheep, pigs, and chickens can you buy, given that sheep, pigs, and chickens cost so much each, and you have to spend exactly so many dollars?" This workbook is interesting because it lets you easily explore what happens as you change the prices. (Caution: such exploration can easily lead you to conclude that these "exactly equal" problems are insanely unrelated to anything that matters.)
• A potpourri of spreadsheets (several in one workbook) addressing compound interest, calculation of pi via inscribed/circumscribed polygons, and calculation of pi via solution of a trigonometric equation using a series expansion and successive refinement.