Professor H. L. Bray
        Teaching

Math 323s:
Geometry from the Ancient Greeks to Einstein

Fall Semester, August 17 - November 24, 2020
Tuesdays and Thursdays, 5:15 - 6:30 p.m.


Professor Hubert Bray                               bray@math.duke.edu
189 Physics Building                             (919)757-8428 (mobile)
Office Hours: after class, upon request

Syllabus and Course Information

Welcome to the class! We're going to have a lot of fun together!

This is a DISCUSSON BASED class. Even though this is an online class, I ask that everyone attend class every day with their cameras on. If you cannot attend, 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.

All homeworks, papers, presentations, and other assignments will be turned in by email to bray@math.duke.edu with subject containing "ModernGeometry" (no space) so that I know this is work you are turning in.

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.

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, email your paper (by midnight) and your presentation (by the beginning of class) to bray@math.duke.edu. 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" by Arthur Baragar. 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 Tuesday, August 18

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, August 20

 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 Tuesday, August 25

Homework #1
1.1, 1.7, 1.15, 1.17, 1.22, 1.23, 1.28

For Thursday, August 27

Homework #2
1.29, 1.43, 1.49, 1.52, 1.53, 1.54, 1.57,

For Tuesday, September 1

Homework #3
1.58, 1.71, 1.79, 1.80, 1.81, 1.100, 1.107

For Thursday, September 3

Homework #4
1.109, 1.111, 1.112, 1.114, 1.118, 1.125, 1.129


For Tuesday, September 8

Groups 3 and 4: Email your paper #1 (by midnight) and your presentation #1 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, September 10

Groups 1 and 2: Email your paper #1 (by midnight) and your presentation #1 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, September 15

Homework #5
1.138, 1.151, 1.165, 1.166, 1.167, 1.168, 1.169

For Thursday, September 17

Homework #6
3.5, 3.16, 3.24, 3.26, 3.33, 3.40, 3.55

For Tuesday, September 22

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 Thursday, September 24

Homework #8
5.22, 5.23, 5.25, 5.26, 6.5, 6.7, 6.16

For Tuesday, September 29

 Homework #9
6.17, 6.18,  6.23, 6.25, 10.2, 10.3, 10.8

For Thursday, October 1

Homework #10
10.15, 10.16, 10.17, 10.21, 10.26, 10.35, 10.36

 For Tuesday, October 6

Groups 1 and 2: Email your paper #2 (by midnight) and your presentation #2 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, October 8

Groups 3 and 4: Email your paper #2 (by midnight) and your presentation #2 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, October 13

Groups 1 and 2: Email your paper #3 (by midnight) and your presentation #3 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, October 15

Groups 3 and 4: Email your paper #3 (by midnight) and your presentation #3 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Tuesday, October 20

Watch these videos:
3.07 World Lines and the Twin "Paradox"
3.08 Boosts are Rotations in Space and Time

For Thursday, October 22

Watch these videos:
3.09 How Velocities Add
3.10 How Velocities Add, Part 2

For Tuesday, October 27

Watch these videos:
3.11 How Lengths Contract
3.12 The Train in the Tunnel Paradox

For Thursday, October 29

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 Tuesday, November 3

 Watch these videos:
3.15 Time Travel and Alien Abduction
4.01 Intro to General Relativity
4.02 The Geometry of Black Holes

For Thursday, November 5

No homework. In class, we'll discuss Presentation on Special and General Relativity, which you are welcome (but not required) to preview beforehand.

For Tuesday, November 10

Groups 3 and 4: Email your paper #4 (by midnight) and your presentation #4 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.

For Thursday, November 12

Groups 1 and 2: Email your paper #4 (by midnight) and your presentation #4 (by the beginning of class) to bray@math.duke.edu. Make sure you have "GTD" in the subject headline, as with any assignments you turn in to me.