390 Last
Day Quick Answers 5 May
Most
important thing today - any questions about your exam. But,
I think did most of that last time. Are there questions different
from Friday? Any new topics? Please remember - the next week
is important. Take it seriously. And please oh please
let's not have issues about academic integrity. You may
access _NO_ materials during the exam. If you violate this,
you will fail the _course_ and be reported for an academic
integrity violation. We'll be back here in 192 hours.
Bring computers and plan your time carefully, the exam _will_ end
promptly at 6p.
Yes, we've done a vast amount, please remember that you have no
reason to try to put it all together into one big picture.
That's my job. Find 4-6 focused stories that you want to
talk about. Don't feel bad that you're not talking about
everything. That's not possible and not the goal.
Does anyone have any last questions about their papers?
I have now dropped lowest reactions for everyone (including a zero
for the one before the first class if you didn't do it). My
goal is to get papers processed over the weekend and again have a
more updated current average then. Thank you to those
two who earned full credit for every reaction, and the five who
got to drop a nonzero score (thus completing each reaction), and
the four who were perfect after drops.
If
you miss sending me reactions, then write an email. I will
reply to all, and we can continue it as long as you like. Of
course - the only reason I keep saying it is that I will miss
them.
I
will be available regular office hours and Thursday 1-3p in South
336 and a special office hour finale Thursday evening at 8p in S.
336.
Lecture
Reactions
Arrow's theorem says that there _cannot_ be an ideal voting
system for 3 or more candidates. We must pick the failings
we choose to accept. And - we can do that. We can pick
weaker goals to satisfy. Someone asked how this is
proven. I don't know, but I found .
"how
easily would today’s computing capabilities solve the Enigma
code?" Quite very, I imagine. Also remember this -
the word coding means some very different things. Enigma
is about cryptography, secret codes. Computer programming
is sometimes called coding, that is very different. Gödel
coding is kinda like secret coding, but there's nothing secret
about it - it's a way of representing mathematics by
numbers.
Turing did not create a physical Turing machine. That was
a thought experiment that has since been realised in a physical
form that we saw.
It seems some people were surprised that there is more equality
and less discrimination under communism. That _should_ be
obvious, if you know more about communism than propaganda that
says it is bad.
I was asked to say more about Japanese mathematics. I will do
that.
I asked Jeff about why he didn't include
Japanese mathematics. He replied in a way that helps to
understand his choices throughout:
One of the problems I
struggled with this (in this and other contexts) is the question
of influence: How much influence did a person or culture have on
the overall development of mathematics? So we can trace a pretty
clear line from modern mathematics back to Euclid, etc., and we
can see the influence of Indian mathematics on Islamic
mathematics, which then influences Renaissance Europe. The
challenge is getting beyond India. It seems there was some
influence of Chinese mathematics on Indian mathematics, but the
evidence gets a little conjectural at that point. (For example, al
Kashi's method of roots is similar to Liu Hui's method, but there
are some idiosyncrasies that suggest it was a independent
invention) With Japanese mathematics, you're looking at an even
more tenuous connection to the mainstream. So while there are some
very neat problems and solution, their influence on the
development of mathematics is a lot harder to identify.
Course
Reactions
Why do we not say more about statistics? Ultimately because it
has a separate history, more with that of science than
mathematics. This relates to why statisticians do not think of
themselves as mathematicians.
I am very glad that so many take away the important point that there
is more mathematics happening now than ever in history. This
is very important for you all to know. I am also very pleased
that many take away a large appreciation of all of
mathematics. That is definitely one of my goals. I am
also very proud that this course inspires more interest in
history. It is an interest deep in my family, and I like that
others can see it here.
I am grateful that we can look at the history of women in
mathematics and see what they each contributed to making the study
of mathematics open to women today.
This is a past critique that is worth addressing even if it wasn't
stated this semester:
1. In
the first half of the class, it was nice to see mathematics from a
variety of cultures and places and see how culture impacted
mathematics. However, in the second half of the class, I felt like
we reverted back to the typical eurocentric view of history. Was
there really no math going on anywhere but Europe and the US after
1600?
No,
of course not. Here are the learning outcomes:
Trace the development and interrelation of
topics in mathematics up to the undergraduate level,
Discuss mathematics in historical context with contemporary
non-mathematical events,
Analyze historical mathematical documents - interpret both the
concepts of the text and the methods of mathematics, and
Identify significant contributions in mathematics from women and
from outside of Europe.
The
first one means that I need to focus on the mathematics that you
have learned. I need to give you the history of mathematics
you know. Yes, most of that comes from Western
civilisation. Yes, there is other valuable mathematics
happening elsewhere, but it doesn’t always feed into what you
learn.
There
is more to absolutely everything that we talked about. I
chose to just do the surface of absolutely everything, breadth
over depth. Remember you can learn more about
everything. If you ever want help doing so, please
ask. One takeaway I get from decades of studying math.
history - it is easier to read history than mathematics. So,
if I want to know about some mathematics I would rather read a
historical account than the research mathematics. Remember
this - history is a good safe easy place to read about something
that might otherwise be daunting.
What
do I see big picture: humans take time to figure things out,
and it happens slowly. Greek mathematics is not amazing and
is built on slaves. Islamic mathematics deserves more
attention. There is more mathematics than you think.
Mathematics doesn’t appear from magic or from supernatural
experiences - people struggle to figure this out.