Professor H. L. Bray

Math 190S-01M:
The Mathematics of the Universe

Summer Term 2, June 29 - August 5, 2020
Monday - Wednesday - Friday, 5 p.m. - 7:05 p.m.

Professor Hubert Bray                     
189 Physics Building                             (919)757-8428 (mobile)
Office Hours: after class, and upon request
TA: Sam Lester,

Syllabus and Course Information

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 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. Rough drafts of your papers are due to the TA of the class  (Sam Lester, a former student of this class) 2 days before the due date so that he can give you feedback. You will also meet with students in groups the day before your presentations to practice your presentations with each other. This is all to set you up for success on your presentation day when both your paper and your presentation are due by midnight to both and

For Monday, June 29

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, July 1

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, July 3

No class - University wide holiday.

For Monday, July 6

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

For Wednesday, July 8

Email papers (by midnight) and presentations (by the beginning of class) to and

For Friday, July 10

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

For Monday, July 13

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

For Wednesday, July 15

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, July 17

Email papers (by midnight) and presentations (by the beginning of class) to and

For Monday, July 20
Watch these videos:
3.15 Time Travel and Alien Abduction
4.01 Intro to General Relativity
4.02 The Geometry of Black Holes

For Wedneday, July 22

View these slides:  Presentation on Special and General Relativity

For Friday, July 24

Watch these videos:
2.01 The Kelly Criterion: Triple or Nothing
2.02 The Kelly Criterion: Quadruple or Nothing
2.03 The Kelly Criterion - The 0-1-2-3 Game
2.04 The Gambler's Ruin

For Monday, July 27

Email papers (by midnight) and presentations (by the beginning of class) to and

For Wednesday, July 29

Homework assigned in class is due.

For Friday, July 31

Homework assigned in class is due.

For Monday, August 3

Homework assigned in class is due.

For Wednesday, August 5

Email papers (by midnight) and presentations (by the beginning of class) to and