...And the hilarity continues!

368 went off pretty well. It turns out we'll have a 13th member of the class who hasn't registered yet, but who will be signing on soon. The more, the merrier, but unfortunately 13 is has a much smaller number of divisors than does 12 (in fact, here's a note to 368 students: 12 is actually abundant. What does this mean?), a fact which makes 12 a class size much more amenable to fair and equitable group work. Nevertheless, we'll prevail!

We spent most of the class period today just jawing about various sorts of numbers, focusing on prime numbers and their importance in the realm of cryptography. The difficulty of factorization came up in our conversation, as did the AKS algorithm for primality testing, theoretical considerations involved in counting primes without explicit testing, and subtleties dealing with the Prime Number Theorem. Karl (continuing in the use of pseudonyms) asked a fantastic question regarding the estimate provided by the function x/ln(x), as to whether one could tell if it were an underestimate or an overestimate. We wrapped up by checking the accuracy of this approximation for 10¹⁶ and 10²¹, and neither gave substantial error (Deidre, I fear you might have made a calculator error in class...). Cool beans. We'll start off class on Friday with brief presentations on different sorts of natural numbers, and questions that can be asked about them.

Meanwhile, in my one section of Calc I, I had a great time today. The first 15 minutes or so were ho-hum as I was busy yammering away about functions and how they're defined, but once I turned the class over to them, I had a lot more fun. We spent 15 minutes or so coming up with and graphing some real-valued functions, breaking out Mathematica for the first of what will be many times this semester. Afterward, I let them take a crack at designing plausible functions to describe several phenomena occurring in geoscience, chemistry, physics, and the humanities. (As always, you can check out the prompts for this exercise on my website.) Boy, who'da thought that you could get folks in a Calc I course to come to fisticuffs over a hypothetical reader's interest in Northanger Abbey?

Ah, and soon Friday comes...