Nested Recurrence Relations

Nested recurrence relations are any recurrence relation where at least one of the arguments is dependenton a previous term. For example, the most famous nested recurrence relation is Hofstadter’s Q-recurrence,which is defined by Q(n) = Q(n − Q(n − 1)) + Q(n − Q(n −...

N Queens on an N x N chess board

Have you ever played chess? If you’ve played for any length of time, you most likely know of the dream that many chess players share: to amass an army of queens, the most powerful piece on the board. But with this puzzle, that dream is about to turn into a...

Counting Cards

Next week my talk will be about counting cards in black jack. The pairs and stats related to a certain number of decks used while playing one game will be showed. Also some real instances where people have done very well counting cards in casinos.

Permittivity and Capacitance

My talk is on Permittivity, but before we even get to that we have to define both electrical flux and capacitance, both of which can be done purely mathematically and in physics terms.

Hilbert and Hankel Matrices

Hello everybody! For my 10 minute talk next week I will be discussing the properties and significance of Hankel and Hilbert Matrices. These are famous symmetric matrices that have certain characteristics that cause them to be problematic. Hankel matrices consist of a...

How to Recognize a Parabola

Hello, guys! In my 45-minute talk, I’ll discuss certain theorems and corollaries and proofs that can help us determine whether or not a curve is a parabola. But my main focus is on working with higher degree 2 and 3 equations. For example, if $y = x^2$ is our...

Lights Out and Variants

Hello all! For my 45 minute talk I will be talking about the game, Lights Out, and different forms of the game. Lights Out is usually played on a 5×5 grid, with 25 buttons. And pressing a button, will toggle nearby lights. The goal of the game is simple, right?...

Music, Ternary Continued Fractions, and Jacobi

Ternary Continued Fractions are fractions that can be expanded by special eqns; known as Jacobian Ternary Continued Fractional Eqns. These eqns were developed by Jacobi bc he was very interested in the concept of the continued fraction. and using these eqns was how he...

Envy-free Cake Division Protocols

Have you ever had to split something evenly between a group of people? Chances are that you have, and chances are that when you did, you didn’t use the laws of mathematics to ensure everyone’s complete and mathematically certain satisfaction. Because y’know, that’d be...

Inflation and Stock Returns

Hey everyone! For my talk, we will be exploring the impact on monetary policies on inflation which then results into an impact on stock return and asset prices. This may sound more like an economic or finance talk, but let me assure you, a lot of math can be found...