The tutor brings up a title he read over the weekend. Last weekend, we had some dreary weather that foreshadowed Halloween. My older son thought I might read a ghost story. I got out a book called Victorian Ghost Stories, …
The tutor introduces Fermat’s Theorem with a first example. Fermat’s Theorem states that, for a prime number p and a number b not a multiple of p, bp-1 ≡ 1 (mod p). (See my post here for a working definition …
The tutor discusses the limit, as n goes to infinity, of the nth root of n factorial. It’s probably easy to agree that, for large n, n! > (n/6)^n. limn→∞ ((n/6)^n)^(1/n) = limn→∞n/6 = ∞ Therefore, limn→∞ (n!)^(1/n) = ∞, …
The tutor uses the ratio test to show the infinite series Σ4n/n! converges. Example: Check Σ0∞4n/n! for convergence or divergence. Solution: The ratio test says that, if limn→∞|an+1/an| < 1, then the series converges. In this case, the terms are …
Calculus: ratio test: checking Σ4n/n! for convergence Read more »
The tutor shows how to integrate sec³x. My post here might be a helpful warm-up towards the technique below. For ∫sec³xdx we use integration by parts: ∫uv’ = uv – ∫vu’ With sec³x we imagine v’=sec²xdx, u=secx. Note that if …
The tutor continues about lists on the TI-83 Plus. I began about lists on the TI-83 Plus back in my post from January 24, 2015. Now I want to continue. My favourite way to enter a list is from the …
TI-83 Plus: more about creating and editing lists Read more »
The tutor shows a hypothesis testing example with a p-value. In yesterday’s post I brought up p-values. Today I’ll give an example: A population is believed to have mean μ0=42.5; a sample of 30 is taken with mean x=41.6, standard …
The tutor explains the concept of p-value. A topic in stats is hypothesis testing. The usual premise: the tester believes they know the mean of a population, but aren’t sure. In such a case, a sample is taken from the …
The tutor offers an interpretation of what the asterisk (aka, wildcard) means in an import statement. I’m not trained in Java, but do write experimental programs with it. Here are some ideas about the import statement, as I understand it: …
The tutor recommends Hardy Boys Mystery 45: Mystery of the Spiral Bridge. As I’ve mentioned earlier, I love reading Hardy Boys mysteries to my family. The tradition started, I believe, before my kids joined school. I’ve read dozens aloud during …
English: Hardy Boys Mysteries: Mystery of the Spiral Bridge Read more »