Day 33 in Mat229

• I used your first exam grade to predict your grades on your future exams as well. If your grade on that exam was low, hopefully you'll do better going forward!
• I used only one of your two drops for the quizzes (unless you have extra "GOQF" cards, which I applied right away).

"And yet it moves!" These words, supposedly whispered by Galileo Galilei at the end of his 1633 trial -- held because he supported the Copernican 'heresy' that Earth moves around the Sun -- have long been a byword for how scientists should behave in the face of ignorance, intolerance and ideological inerrancy. They come to mind now, during the all-out war on diversity, equity and inclusion (DEI) happening in the United States.

At the end of his trial, Galileo was made to swear that he did not believe in Earth's motion. He was confined to house arrest and forbidden to write any more about the movement of the planet. If he had had grant funding and a website, I am sure that the Roman Catholic Church would have suspended the former and scrubbed the latter.

....

These are dangerous times. Scientists globally must stand together for sound science and resist bigotry, bias and hate. If science is to honour one of its core values -- a commitment to the truth wherever it might lead -- scientists must stand up when DEI matters. Galileo's story should remind us all: the only way forward is speaking truth to power.

(After 350 Years, Vatican Says Galileo Was Right: It Moves)

Because Eunice was a woman, she was not allowed by her patriarchal society to read her paper before the society. It had to be read by a man.

Imagine what Eunice Foote might have done, had she not been hog-tied by her society. Eunice Foote knew a lot about climate change -- more than the administration of our government, evidently.

• Diversity: maybe we should even allow women to participate in science and society, too.
• Equity: Maybe we should even allow equal treatment for women -- equal pay for equal work, say.
• Inclusion: maybe our society should invite the participation of women!

Radical. And it's not just women, of course....

Once again you'll be allowed a cheat sheet (one page, front and back).

Bring a calculator.

• In terms of numerical schemes, I may give you data values and have you "assemble them" using the various schemes.
• Remember that Simpson's \(2n\)-rule is based on midpoint and trapezoidal \(n\)-rules.
• Remember your error estimates for each method. I may give you a graph of a second or fourth derivative to use to create a bound for the error.

  I may rely on you to produce a "least bound" -- i.e. to find the smallest value of \(M\) that serves.

• Don't forget your old integration rules! (e.g. 347-350 require you to use arc functions, logs, etc.).

• It's sometimes a little tricky to deduce a rule (e.g. #5). This is actually a topic that some of you (CS types) will encounter in Discrete math (e.g. MAT385): recurrence relations, and how to solve them in closed form.

• Notation may be a problem. Any questions about sigma notation?
• The harmonic series is used in at least one problem: \[ \sum_{n=1}^\infty \frac{1}{n} = 1 + \frac{1}{2}+\frac{1}{3}+\frac{1}{4} + \ldots \] The proof that this is divergent is interesting (and shouldn't surprise you, after yesterday): we can think of the \(n\)^th term as being a sample from the function \(f(x)=\frac{1}{x}\): \[ a_n = \frac{1}{n} = f(n) \] So we can think of the harmonic series as a rectangle rule approximation for \[ \int_{n=1}^\infty \frac{1}{x} d x \] which is divergent....