# BTC 2019

In 2019 the subject of the camp was Puzzles and games: Mathematical and Computational Modeling, which ran from June 17 to 28 at the Department of Mathematics premises. We had 14 awesome campers, two of them coming back from last year’s camp.

Here is a list of the workshops we had:

• Page rank algorithm. A brief review of the mathematics that search engines use to decide which result to show first. The students coded a function to compute any power of a 2 by 2 matrix and used this to build a simple weather prediction model. They then used this idea to rank websites in a simple web.
• Number theory. The students wrote their own codes to compute the n-th term in the Fibonacci sequence and to count the number of primes less than or equal to N. They also tested Zeckendorfâ€™s theorem and Goldbach conjecture using a library.
• Population models. Using discrete dynamical systems (exponential and logarithmic). They modified existing functions to account for any growth rate.
• Fractals. Students wrote a recursive function to draw a fractal tree.
• Combinatorial game theory. In this series of workshops, students investigated winning strategies by modeling the games with math. The games studied were Nim and Coloring Graphs. For solving Nim, the workshop reviewed the binary numerical system and XOR addition.
• Mathematical modeling of puzzles. In this series of workshops, students investigated the minimum number of moves required for solving a puzzle or counted number of possible configurations. The puzzles studied were Tower of Hanoi, Chinese rings, Triangular Dominoes and tilings with them, and Instant Insanity.

Students worked individually or in pairs to further analyze some of the concepts of the workshops. Instructors suggested a wide range of possible projects and they chose theme and scope. On the last day of the camp, they presented their results.

A big thank you to all the people who made this event possible. The organizers and instructors: Erika Roldan, Debi Stout, Maritza Sirvent, Rachel Karpman, Feride Tiglay, and Monica Delgado.