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| Teaching mathematics and physics |
| Analyze all the facts, and find knowledge of that which you wish to know. |
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Dr. Sanford Aranoff
Currently Adjunct Associate Professor of Mathematics and Science at Rider University Things I emailed to students in my classes. Scroll down to see all the files. "What is mathematics?" I ask students. Numbers!" is the usual reply. "No," I respond. "Mathematics is a collection of arbitrary self-consistent statements. These are things I have emailed to my math students. You all may benefit! Click on a file below:
Arrangements.pdf Science is a collection of theories. A theory is a mathematical system verified by observations and experiments. "What is a molecule?" I ask students. "A bunch of atoms joined together," is the usual reply.I then say this: In science, if we ask what is something, the answer is what do we have to do to measure it. How do we get a molecule? Let us look at water, for example. Let us take a drop of water. A tiny drop. A tiny-weenie drop. The tiniest drop we can take. This is a molecule, which is the smallest amount of water one can have. You see, a molecule is a single thing, not a bunch of things. An atom is a molecule of an element. We think molecules are the basis of all matter. We base this upon the ideas of Greek philosopher Leucippus. Aristotle disagreed. Actually, although most scientific work agrees with Leucippus, Aristotle's ideas find expression in liquid helium below 2.17 K. In this case, although the basic physical ideas of energy, entropy, mass, temperature, and volume are valid, we cannot speak about molecules. Instead, we must think of superfluid helium as a single indivisible substance. These are things I have emailed to my Chemical Thermodynamics students: Click on a file below: Summary Chapter 1.pdf Updated 8/27/2011. |
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