Professor H. L. Bray
Teaching
Math 190S-01M:
The Mathematics of the Universe
Summer Term 1, May 13 - June 6, 2020
Monday - Tuesday - Wednesday - Thursday - Friday, 10:00 a.m. - 12:05 p.m.
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: after class, and upon request
TA: Sam Lester, samuel.lester@duke.edu
Welcome to the class! We're going to have a lot of fun together. Unlike
most math classes, these classes are discussion based. Furthermore, the
topics we cover will have a lot to do with the questions you ask in
class, so bring your favorite questions!
Before many of the classes, I'm going to ask you to watch videos, as
you can see below. Listen and learn with these videos as well as you
can. Don't worry if you don't understand everything - that is not
expected the first time. Just do your best and come to class with your
questions!
However, make sure you do watch the videos. The daily quizzes are OPEN
NOTES and will be easy for those who watched the videos, rewarding
those who understood the simplest ideas. We'll pursue the deeper ideas
in class. The whole point is to get the discussion going with the
videos, so that we can cover some cool topics in class. Enjoy!
You will write 3 papers in the class, each 5-10 pages, on a topic of
your choice relating to the class, broadly interpretted. You will also
present each topic to the class with a PowerPoint style presentation
that lasts no more than 5 minutes.
We'll discuss your topic ideas in class each Thursday, so come to class
with some ideas. You'll then have Fridays and Saturdays to write your
paper (roughly), with a rough draft due by midnight each Saturday. On
Sundays you'll create your 5 minute presentations which you can
practice in group meetings on Sundays with the TA (Sam Lester, a former
student of this class). You will then give your official 5 minute
presentation in class on Mondays, with the final version of the paper
due on Mondays by midnight (except Memorial day - which is a Monday, so
everything is due Tuesday).
For Wednesday, May 13
Watch these videos:
3.01 The Rule of Pythagoras
3.02 Rotations and the Dot Product
3.03 Gauss's Geometry and Special Relativity
For Thursday, May 14
Watch these videos:
3.04 Special Relativity is a Minus Sign in the Rule of Pythagoras
3.05 The Light Cone
3.06 The Universality of the Speed of Light
For Friday, May 15
Watch these videos:
3.07 World Lines and the Twin "Paradox"
3.08 Boosts are Rotations in Space and Time
For Monday, May 18
Papers and presentations due.
For Tuesday, May 19
Watch these videos:
3.09 How Velocities Add
3.10 How Velocities Add, Part 2
For Wednesday, May 20
Watch these videos:
3.11 How Lengths Contract
3.12 The Train in the Tunnel Paradox
For Thursday, May 21
Watch these videos:
3.13 De Sitter Space: The Spacetime Unit Sphere of Special Relativity
3.14 Hyperbolic Space The Spacelike Unit Sphere of Special Relativity
For Friday, May 22
Watch these videos:
3.15 Time Travel and Alien Abduction
4.01 Intro to General Relativity
4.02 The Geometry of Black Holes
For Monday, May 25
Memorial Day Holiday - no class
For Tuesday, May 26:
Papers and presentations due.
For Wednesday, May 27:
View these slides: Presentation on Special and General Relativity
For Monday, June 1
Papers and presentations due.
Saturday, June 6, 2020
FINAL EXAM from 9 a.m. to 12 p.m.