Joyful Math

In attempting to evaluate endgames in Go, John H. Conway ran smack into some limitations in game theory. Upon delving into it, it turned out that the problem was the dependence of game theory on real numbers. Conway invented the Surreal Numbers to overcome this roadblock.

In this session, we're going to look at some simple games that Conway, Berlekamp, and Guy use in their book Winning Ways for Your Mathematical Plays to demonstrate valuing games as a sum of their component games. We will talk about how this leads to one formulation of Surreal Numbers. We will look at adding, subtracting, multiplying, and dividing Surreal Numbers. We will also examine some infinitesimal numbers that illustrate why the real numbers are not sufficient for valuing two-player games. We will also look at how the Surreal Numbers handle infinite numbers.

Hey everyone!

We're starting: a Loop Quantum Gravity (LQG) study group to work through the mathematics behind LQG using these two textbooks:

• Rovelli, C., & Vidotto, F. (2015). Covariant loop quantum gravity: An elementary introduction to quantum gravity and spinfoam theory. Cambridge University Press.
• Gambini, R., & Pullin, J. (2011). A first course in loop quantum gravity. Oxford University Press.

Ground-level material: The opening chapters assume some prior mathematical knowledge. To make sure we're all on the same page, I'd like to start by reviewing:

• high-school algebra
• trigonometry
• derivatives
• path integrals
• vector spaces
• change-of-basis transforms

I'm comfortable with these topics, so if you don't remember them or never learned some of them, we should be able to get you up to speed. I don't expect us to get through all of that in one night.

Once we have a solid foundation with the topics listed above, I think we should tackle any further prerequisites as side quests when we encounter them. The books will guide us toward the mathematical tools we actually need.

Come prepared to: ask questions, share insights, and work through some mathematical challenges together. Looking forward to seeing everyone there.

We're continuing our preparation: for our Loop Quantum Gravity (LQG) study group to work through the mathematics behind LQG using these two textbooks:

• Rovelli, C., & Vidotto, F. (2015). Covariant loop quantum gravity: An elementary introduction to quantum gravity and spinfoam theory. Cambridge University Press.
• Gambini, R., & Pullin, J. (2011). A first course in loop quantum gravity. Oxford University Press.

Continuing where we left off: we will continue (and maybe finish?) reviewing the topics we started in the previous session S1E1:

• high-school algebra
• trigonometry
• derivatives
• path integrals
• vector spaces
• change-of-basis transforms

Once we have a solid foundation with the topics listed above, I think we should tackle any further prerequisites as side quests when we encounter them. The books will guide us toward the mathematical tools we actually need.

Come prepared to: ask questions, share insights, and work through some mathematical challenges together. Looking forward to seeing everyone there.