Professor H. L. Bray
Teaching
Math 323s:
Geometry from the Ancient Greeks to Einstein
Fall Semester, August 28 - December 6, 2023
Mondays and Wednesdays, 4:40-5:55 p.m., Physics 205
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: after class, and upon request
Welcome
to the class! We're going to have a lot of fun together!
This is a DISCUSSON BASED class. I ask that you attend class every day. If you
cannot attend a particular class, simply email me in advance of the class letting me know
so that we may work out other arrangements.
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!
There are also homework problems assigned before many classes. Some of
those problems may also end up on quizzes, so work as many of the
problems as you can.
Make sure you do the homework and watch the videos. The daily quizzes are OPEN
NOTES and will be easy for those who did the homework and 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
homework and videos, so that we can cover some cool topics in class.
All quizzes, homeworks, papers, presentations, and other assignments will be turned in using GRADESCOPE.
You will write 4 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, so come to class
with some ideas.
Everyone will be assigned to a group of around 4 students to meet with
outside of class. Groups will meet both 2 days before your official
presentation day and 1 day before your official presentation day, on a
schedule that you work out with each other.
Rough drafts of your papers are due to your student group (email each
other) 2 days before your official presentation day so that you may
give each other feedback (over Zoom). You will practice your
presentations with your student group (over Zoom) 1 day before your
official presentation day.
On your official presentation day, use gradescope to turn in your paper (by midnight) and your presentation (by the beginning of class).
I encourage you to make your papers even better after class by taking
the class discussion centered on your paper into account.
Homeworks will be assigned out of our textbook, "A Survey of Classical
and Modern Geometries," version 1.5, by Arthur Baragar. (The author generously posted the book, free to use, on the AMS website.) On all homework assignments,
be ready to present any of your solutions to the class. Also, read the
book up to the pages where the homework is assigned.
For Monday, August 28
Watch these videos:
3.01 The Rule of Pythagoras
3.02 Rotations and the Dot Product
3.03 Gauss's Geometry and Special Relativity
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 Wednesday, August 30
Homework #1
1.1, 1.7, 1.15, 1.17, 1.22, 1.23, 1.28
For Monday, September 4
LABOR DAY HOLIDAY
For Wednesday, September 6
Homework #2
1.29, 1.43, 1.49, 1.52, 1.53, 1.54, 1.57,
For Monday, September 11
Groups 3 and 4: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)
For Wednesday, September 13
Groups 1 and 2: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)
For Monday, September 18
Homework #3
1.58, 1.71, 1.79, 1.80, 1.81, 1.100, 1.107
For Wednesday, September 20
Homework #4
1.109, 1.111, 1.112, 1.114, 1.118, 1.125, 1.129
For Monday, September 25
Homework #5
1.138, 1.151, 1.165, 1.166, 1.167, 1.168, 1.169
For Wednesday, September 27
Homework #6
3.5, 3.16, 3.24, 3.26, 3.33, 3.40, 3.55
For Monday, October 2
Groups 1 and 2: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)
For Wednesday, October 4
Groups 3 and 4: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)
For Monday, October 9
Homework #7
3.60, 5.3, 5.4 (include photo in HW), 5.5 (include photo in HW), 5.17, 5.18, 5.19
For Wednesday, October 11
Homework #8
5.22, 5.23, 5.25, 5.26, 6.5, 6.7, 6.16
For Wednesday, October 18
Homework #9
6.17, 6.18, 6.23, 6.25, 10.2, 10.3, 10.8
For Monday, October 23
Homework #10
10.15, 10.16, 10.17, 10.21, 10.26, 10.35, 10.36
For Wednesday, October 25
Watch these videos:
3.07 World Lines and the Twin "Paradox"
3.08 Boosts are Rotations in Space and Time
For Monday, October 30
Groups 1 and 2: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)
For Wednesday, November 1
Groups 3 and 4: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)
For Monday, November 6
Watch these videos:
3.09 How Velocities Add
3.10 How Velocities Add, Part 2
For Wednesday, November 8
Watch these videos:
3.11 How Lengths Contract
3.12 The Train in the Tunnel Paradox
For Monday, November 13
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 Wednesday, November 15
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, November 20
No homework. In class, we'll discuss Presentation on Special and General Relativity, which you are welcome (but not required) to preview beforehand.
For Monday, November 27
Groups 3 and 4: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)
For Wednesday, November 29
Groups 1 and 2: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)
For Monday, December 4
Free discussion.
For Wendesday, December 6
Free discussion.