送交者: lll 于 2005-2-16, 21:36:46:
1. You can see water drops roll over and over on a leaf of taro plant (Japanese dasheen) because of the surface tension of water and the innumerable short hairs on the leaf surface. At first, there were two water drops apart on the leaf. Then, they happened to roll over and collided with each other being combined into one drop. A kid who was watching it shouted with surprise, “1 plus 1 made 1!” This event has very important view point that suggests the deep contact between our conception and mathematics. Do you find contradiction or not? Set up plausible hypotheses and verify them logically.
2. When we look into a mirror, we can see right and left sides are reversed. Notwithstanding, why are the up and down sides not reversed? Explain why.
3. Prove your existence right where you are standing. A proposition that the universe could not exist if humans should not have been there is raised. Is this proposition logically true or false?
4. Derive the Gaussian function in one dimensional space that appears in the error distributions.
5. In the historical background of the combination of algebra and geometry, there was the necessity of “expansion of concepts” that can be seen in the Galois theory and the proof of Fermat’s last theorem. Major mathematicians who are too ignorant and authoritative to understand this meaning might cast scorn saying “It’s ridiculous,” however, are not eligible to teach mathematics. You investigate why they should not.
6. This series of lectures have been carried out on the bases of some altruistic action and purpose, and I always tried to return back to these subjects. Which action and what purpose can you infer? Explain also how you reach the conclusion.