ORMC Meetings • 2024-2025 Academic Year

Students learn about iterated functions and one of the hardest unsolved math problems. This worksheet is also an introduction to what kinds of problems professional mathematicians like to think about.

A comprehensive introduction to Python programming using the online compiler "Trinket.io." Further exploration of the drawing board module "Turtle" and the quantitative module "Math".

Students learned about recursive functions in Python and how to apply them to draw fractals.

This week, we reviewed recursive functions and fractals. We looked at several new examples of recursive functions from mathematics. We also took another look at one of the more challenging problems from last week involving the Koch snowflake.

Students learned about properties of exponentiation (powers) and were introduced to logarithms. We also covered applications to carbon dating and to finance.

Students learned more about properties of logarithms. Specifically, students were introduced to the change of base formula.

Probability and Monte-Carlo simulations.

Expected value.

Students will play a board game similar to Monopoly, but requiring some probabilistic computations to play efficiently.

We finished up our fractals unit. We considered what the "dimension" of a shape really means geometrically, and used this to compute the surprisingly non-integral dimension of the Koch curve.

Financial returns.

Today, students learned about standard deviation and volatility of investments. Several real world examples of volatility were discussed.

For the first hour, we discussed random walks and their use in certain probability problems. For the second hour, we used Python to predict investment returns based on historical data.

This week, students studied the mathematics of torque and levers. We applied the principles to some geometry problems.

Students wrote their own Python programs to analyze financial data of major tech companies.

Students reviewed center of masses of 2D, 3D, and even 4D shapes. Students were also introduced to vectors.

Students will continue studying the second Geometry of Masses packet. If time permits, they will start studying the third one.

Students will start studying basics of statistics, namely how to use a sample mean and SD to estimate these for the population.

Today, students studied basic linear algebra, including parameterization of lines. Students also investigated how to recast a few basic "geometry of mass" ideas in terms of vectors and coordinates.