I conceive of mathematics as a fantastic citrus tree: the three main branches of oranges, limes, and lemons representing the major fields of algebra, geometry, and analysis. Each part of the upper canopy takes advantage of what is below it. Thus, number theory has two great approaches, one algebraic and the other analytic. Topology makes use of all three fields, as does the very different field of mathematical modeling.

All trees have woody parts, foliage, and fruit. The trunk and branches absorb water and nutrients from the soil. The foliage absorbs energy from the sun, using it to convert the nutrients to usable food, and allowing the tree to grow. The fruit allows the tree to reproduce. I have represented the foundations of mathematics as the trunk of the tree, the support and food supply. The foliage and fruit could represent the two aspects of pure and applied mathematics: which is which, do you think?

fall 2007 course description

the mathematical perspective

paper guidelines

homework guidelines

summary of proof techniques

additional resources

truth table forms

back to logic & proof

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