Teaching

Geometry from the Ancient Greeks to Einstein

Mondays and Wednesdays, 5:15 - 6:30 p.m.

Professor
Hubert Bray
bray@math.duke.edu

189 Physics Building (919)757-8428 (mobile)

Office Hours: after class, and upon request

189 Physics Building (919)757-8428 (mobile)

Office Hours: after class, and upon request

This is a DISCUSSON BASED class. I ask that you attend class every day. 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.

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" 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 Monday, August 23

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 Wednesday, August 25

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 Monday, August 30

Homework #1

1.1, 1.7, 1.15, 1.17, 1.22, 1.23, 1.28

For Wednesday, September 1

Homework #2

1.29, 1.43, 1.49, 1.52, 1.53, 1.54, 1.57,

For Monday, September 6

Homework #3

1.58, 1.71, 1.79, 1.80, 1.81, 1.100, 1.107

For Wednesday, September 8

Homework #4

1.109, 1.111, 1.112, 1.114, 1.118, 1.125, 1.129

For Monday, September 13

Groups 3 and 4: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)

For Wednesday, September 15

Groups 1 and 2: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)

For Monday, September 20

Homework #5

1.138, 1.151, 1.165, 1.166, 1.167, 1.168, 1.169

For Wednesday, September 22

Homework #6

3.5, 3.16, 3.24, 3.26, 3.33, 3.40, 3.55

For Monday, September 27

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, September 29

Homework #8

5.22, 5.23, 5.25, 5.26, 6.5, 6.7, 6.16

For Wednesday, October 6

Homework #9

6.17, 6.18, 6.23, 6.25, 10.2, 10.3, 10.8

For Monday, October 11

Groups 1 and 2: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)

For Wednesday, October 13

Groups 3 and 4: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)

For Monday, October 18

Homework #10

10.15, 10.16, 10.17, 10.21, 10.26, 10.35, 10.36

For Wednesday, October 20

Watch these videos:

3.07 World Lines and the Twin "Paradox"

3.08 Boosts are Rotations in Space and Time

For Monday, October 25

Watch these videos:

3.09 How Velocities Add

3.10 How Velocities Add, Part 2

For Wednesday, October 27

Watch these videos:

3.11 How Lengths Contract

3.12 The Train in the Tunnel Paradox

For Monday, November 1

Groups 1 and 2: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)

For Wednesday, November 3

Groups 3 and 4: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)

For Monday, November 8

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 10

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 15

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

For Wednesday, November 17

Free discussion.

For Monday, November 22

Free discussion.

For Monday, November 29

Groups 3 and 4: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)

For Wendesday, December 1

Groups 1 and 2: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)