390 Quick
Answers 29 April
All
have draft feedback now, and a more updated current average.
I have included all reactions up to today (there are only 2 left),
and dropped a zero for those who have one. I have _not_ made
any drops for those without zeroes, because I don't know if they
will be the lowest.
Think
of exam topics. Reminder: look back at the questions
on the last exam for creative ideas for the final.
Reminder: you need 2x6 or 3x4 for _both_ post 1600 and
across all history. That is 4, 5, or 6 questions.
For
the reactions due by Sunday, you are also writing 5 course
reactions (in the place of reading reactions, because you will
have *finished the book!* by then). These are reactions to
what you learned in the course. Big picture thoughts on
history of mathematics. Maybe large takeaways.
As
one of your lecture reactions for either day (better for the first
one) you may make a request for what you want me to talk about on
Monday. I’m not promising that I can pull together anything,
but I’ll try what I can. It will be an interesting day,
surely.
And,
if anyone wants to email reactions after Monday … I promise to be
happy for the feedback, and I will reply and respond for as long
as you like.
Truth: I enjoy reading your writing, and I will miss
it.
Our
final is 3:30-6p here 2 weeks from now. It will be a very
familiar day and time. I have fixed the software so that it
will be impossible to submit past 6p. Know that now.
Reminder
to all: we’re in the 20th century. Nothing that is
being discussed now is obvious. One of the big themes this
time is trying understand the foundations deeply. Each time
the answer is “it’s more complicated than you expect.”
More individual than group comments this time, should serve well
for catching up the bit that we're behind.
Lecture
Reactions
What
does it mean to be a model for hyperbolic geometry? Not as
much of a physical object that is touchable (although those models
are great pedagogically), but a mathematically described
object. We know that hyperbolic geometry is consistent
because it applies to the hyperbolic plane which can be described
mathematically. Non-Euclidean geometry proves that the fifth
postulate is independent of the others. It does not disprove
anything.
The 4-colour theorem was first proven in 1976 by Appel and
Haken. It has been reproven a few times since then by other
computers. There is no printed proof.
Perelman
declined all notoriety from his discoveries and has since been
mostly a recluse. "I'm not interested in money or
fame, I don't want to be on display like an animal in a zoo. I'm
not a hero of mathematics. I'm not even that successful; that is
why I don't want to have everybody looking at me.”
Reading
Reactions
The
size of the natural numbers is denoted by Aleph_0. I will
write this. This is not the symbol for the cardinality of an
arbitrary set, but it is the particular cardinality of the
naturals. The question of the continuum hypothesis is if
there is a set of size larger than the naturals and smaller than
the reals. The answer is “could be” - both ways are
consistent with mathematics.
We
do still have international
mathematics olympiads.