Exam comments: I was pleased with the results. Here are the
10 | 0000
9 | 988877765433332211
8 | 9765432110
7 | 6332
6 | 3310
Usually I'd be uncomfortable with so many As, but I'm fine with that in
this case. The mean was 87 and median 91.5 modes at 100 and 93.
I wanted people to succeed, and they mostly did.
Now focus most of your attention on writing excellent complete papers.
Something to start planning for - those presenting on GREAT day
will need to do at least one (ideally more) trial presentation with me.
Start planning it into your schedules. Here are some
(60) tips for pp presentations.
The most important are 4, 14, 16, 22, 28, 10, 12, 24, 27 (you
will understand my numbering) - do not violate those.
Quick Answers -§7.2.3
No mathematician should ever make the "try and" mistake (Suzuki p.
196). It's just blatantly illogical. If he was going to
"try and justify it" the trying part is redundant. Doesn't matter
that he tried if he justified.
Stevin marked all his decimal places, even those that had zeroes.
I couldn't quickly find a video or diagram of countermarch.
The tulip story is entirely true. Why? Why do people want anything that's popular?
Stevin's tuning: if you want 12 equally spaced notes within an
octave, which is a 2:1 ratio, the ratio for each of the notes needs to
be 2^1/12 so that (2^1/12)^12 = 2. This is instead of using
small number ratios - which are easily understood and measured.
Stevin's work with limits - finding a way to make numbers closer - that
we can always find a closer number, and that two numbers closer
than any difference (e.g. .9... and 1) must be equal. The
infinitesimal rectangle is probably the rectangle used in so-called
Here's an idea on one as a number - "I have some ideas" does that
include one? That's the best I can think of. Note:
naming issues like this are actually of no consequence.
Our modern system of coordinates is a combination of the historical
ones, but Descartes's work was best known, so probably had the most
influence. Note how Descartes is spelled.
We are quite close to modern algebra now - look at the original sources
as we explore them this week.