Finding Vintage Concentrations in a Sherry Solera (UMAP)

This module models the solera method of making sherry and demonstrates that the method results in a mixture whose composition changes slowly with time and in which no single vintage constitutes a substantial fraction of the whole. The module is appropriate for a variety of courses. For example, it could serve as an introduction to mathematical modeling, or as enrichment material for a second-semester or third-quarter calculus course. To derive full value from the module, students should work as many exercises as they can without looking at the solutions. The exercises are designed to be challenging and to show the power and utility of calculus. It may be appropriate in certain situations for the instructor to provide hints for some of them. The more elaborate exercises could be the basis for oral presentations by students in an undergraduate seminar on mathematical modeling.

Table of Contents:

THE SOLERA METHOD

A SIMPLE MODEL

A MORE REALISTIC MODEL

BEHAVIOR OF THE RESIDUAL TERMS

AN EQUIVALENT STOCHASTIC PROCESS

CONCLUDING OBSERVATIONS

EXERCISES

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHORS