Here's a sample of some citations in an article.
I have been asked for an extension on the draft assignment. Here
are the reasons I think that's unreasonable: You have known these
dates since the opening of the course, and I have emphasised them, so I
don't think it's reasonable that you have forgotten. You should
have written a first start over break or sooner and now be merely
tidying. Aside from all of this, the paper is rather short and
the more than month since last component has been plenty. And the
one reason I think it's impractical - I need time to read them all to
get them back to you to improve to the final versions. To earn
full credit for the draft you must submit by the end of the music in
class on Monday. That all being said, I'm willing to offer the
following sale prices: to get the paper at 10% off you must
submit by the end of the music in class on Wednesday and to get the
paper at 20% off you must submit by the end of the music in class on
Friday. If you do not submit by then, I will record a zero for
your draft. I will return those drafts submitted on Monday first
as a batch, then those on Wednesday as a batch, then those on Friday as
a batch, and any submitted after that when I get around to it (I don't
expect we'll have those. A draft not meeting the minimum
requirement (1250 words) will not earn a passing grade.
I also decided yesterday to start trying out IM office hours. The
account is JohannesOhrs on AOLIM. Please tell me if you have any
questions or thoughts about this idea.
Quick Answers §8.2
An interesting observation that we're seeing a number of familiar
mathematicians. Does it mean that they're the best?
Probably not. I think it's reasonable to say that this is
merely the period of time which you are most familiar with.
We're also in a time of a large amount of mathematics being produced.
There was surely an air of excitement in mathematics - and
results came fast and furious. Sometimes in this intensity some
of the details weren't attended to carefully, but the intuition was
there. Details came later (many in the 19th century).
Series in particular require questions of convergence (as you
know), but most of those weren't addressed at this time.
Jeff Suzuki is a mathematics professor at Brooklyn College with a PhD
in math. history. I know him, think highly of him, and trust his
authority on most subjects. He is also human and hence fallible
and as we well know sometimes he's presenting bold opinions rather than
facts. I like that too.
No debating it - Euler was amazingly prolific in any measure. And
he had 13 children. And he had memorised the Aeneid (about 10,000
lines of epic poetry). And he was blind for part of his life, and
could only see out of one eye for most of it. Anything you read
about Euler sounds amazing - and almost all of it is true. One of
Euler's most important contributions is our modern notion of function.
That in itself probably gives him some claim to being the founder
of modernn mathematics - with all the rest he did - it's difficult to
argue (but not impossible).
I say again, there's much we don't have an opportunity to do. I
would be most pleased if someone took me up on my offer to explore
other - e.g. Euler's work on either Fermat result.
Surely it was well understood at this time what irrational meant.
√2 had been long known to be irrational before this time
(probably even called as much for around 200 years).
The idea of Euler's god story is that he was supposed to be
intimidating enough with the (meaningless) mathematics to silence the
doubters. As Suzuki says, seems unlikely that this oft-repeated
story is true.
Witch of Agnesi
Nicolaus II worked on trajectories, differential equations,
probability, and was heavily invovled in the Newton-Leibniz controversy
- working out details comparing the precise mathematics in their works.
I would say Jakob and Johann are the "most important" Bernoullis, but
htat's probably open to debate. There are 8 listed at the
MacTutor site.
Did l'Hospital to anthing original? Not that I know of.
Neither Lambert nor Saccheri proved the 5th postulate (as we will see,
that is impossible). They basically repeated what was done around
the 11th century by al-Khayyami and al-Haytham. I won't say much
about them because of that. Non-Euclidean Geometry is a BIG DEAL.
When we get to it actually being understood, I'll say more about
it. It definitely was a surprise about 2000 years in the making.
Although they are still rare, we will now start occasionally seeing women at this point.
I don't have information about Daniel B's epidemiology work, but I imagine it could be found with a little effort.
Suzuki isn't saying much about Lagrange here because he'll say much
more about him later. I'll follow his lead on that.
Remember: continental calculus is like Leibniz, English is like
Newton. So, our characters now all on the continent are doing
Leibniz-style calculus.
Russia took a while coming to the world stage, and even at this point,
it's not really Ruessians be W. Europeans in Russia. Although
they have done important mathematics in the 20th century, it takes a
while. As an indicator, we only get to listen to one piece of
Russian music.
We have some dates in Russia - remember they're using the Julian calendar still, so they are "O.S."
Complex numbers are definitely appearing sporadically at this point in history.
"The number of Bernoulli's prominent in mathematics reminds me of the
Bach family in the musical area." I would wager at least one of
each must've known the other.
Last time: Yes, l'Hospital's rule to him looked like y = dp / dq, i.e. derivative of p divided by derivative of q.
Long ago: Rectangles go back to prehistory, probability has been building for about 200 years at this point.