Professor H. L. Bray

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                     
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 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.