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Grant Number: DUE: 9650246
Multimedia software, such as Authorware, allows pictures, photos, paintings, maps, movies and music to be imported into mathematics presentations. Teaching can be enhanced by the addition of historical notes that might not otherwise be possible. These additions enrich the learning experience.
Multimedia software interfaces with symbolic computation systems, such as Mathematica or Maple. Graphs and computations can be carried out in Mathematica and the results presented, interpreted, and discussed with all segments unified under the user-friendly interface of Authorware.
Multimedia permits the development of presentations that can be used with students at different levels. Students only need to visit the portions of the presentations for their particular level. For example, the predator-prey presentation that incorporates shark and food fish data from the Adriatic Sea during World War I can be used in a freshman mathematics seminar or more advanced courses in numerical analysis or differential equations. The freshman seminar introduces first year majors to several different areas of math and statistics. The use of multimedia to include historical background reminds students of the intellectual struggles behind present-day textbook order.
In our presentation on the solution of the cubic equation, we found that the students were strongly motivated by the intriguing lives of the mathematicians who studied the problem and contributed to its solution. How could one's imagination not be captured by the story of a mathematician of the sixteenth century, Cardano, who was the first to publish an algebraic solution of the cubic and who also worked as an astrologer and was imprisoned for heresy because he published a horoscope of Christ's life?
Equally interesting is the story of an Italian biologist, D'Ancona, of the early twentieth century who was studying the competition of species. In attempting to analyze fishing data, he was unable to explain the variation of the ratio of sharks to food fish. Consequently he called upon the expertise of his father-in-law, the famous mathematician Volterra, who then developed a mathematical model which explained the variation of the data. This detail adds life to the study of periodic solutions of nonlinear equations.
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