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Math and Reality: an Investigative Approach

This seminar began with a stimulating, intensive, yet entertaining way of looking at problem solving. The participants acquired a broad based background of techniques and mental exercises that enhanced their problem solving capabilities.

Each session began with time spent on a group problem pertaining to that particular session. The group learned to work together, brainstorm, and develop strategies for problem solving. During that time, participants were free to guess, free to be creative, and to experiment with possible solutions.

Fun and games were used to encourage and foster rigorous thought.

After laying a strong foundation for problem solving, we covered the following topics:

• A history of mathematics with an emphasis on the ancient numeration systems. Hands-on activities as well as some of the amazing developments and colorful people of the world of mathematics were explored.
• An in-depth look at the Fibonacci numbers and their occurrence in nature. Pinecones, pineapples, sunflowers and other objects from nature were studies in terms of their Fibonacci paterns.
• Fractals and the exploration of intricate detail. Self-similarity and patterns in nature and their relationship with Chaos were analyzed.
• The science of cryptography. Fellows participated in activities involving the use of secret codes and analyzed the importance of cryptography in daily life.
• Topology and contortions of space. Participants studied differences between solid geometry and topology.
• Mathematics and its relationship to the world of art. Modular math and transformational geometry were used to create Math Art.
• Probability. Games of chance were evaluated in probabilistic terms.
• Part of each session was spent viewing and analyzing the video "Life by the Numbers".
• Field trip to Sandia Labs. Participants were invited to observe the extensive impact of mathematics in the real world.