Student's circle (BMC)
The Boise Math Students' Circle is for Treasure Valley young people with some experience with algebra who want to experience creative mathematics.
Teacher's circle (BMTC)
The Boise Math Teachers' Circle is a community for Treasure Valley K–12 math educators.
The Al-Jabar game
In this session we played the Al-Jabar game of color-mixing algebra. First we learned how to perform addition and subtraction with colors.
Graphs and cycles
One of the most widely used structures in mathematics and applications is a graph. Here we don’t mean the graph of a function, but rather a diagram that you can draw with points (vertices) and segments (edges). Graphs can be used to model networks such as a transit system or even social media Friends. Many of the most important algorithms used in computing operate on data stored in a graph structure. We introduced graphs and some key terminology we use to talk about them.
Functions and Pairing
The concept of a function is one of the most important in mathematics. Most participants were familiar with the idea of a function as something that has inputs and outputs. We took some time to restate this idea, describe some terminology surrounding functions, and extend the idea to multivariate functions. One of the key uses of functions in mathematics is in defining the cardinality of sets: Two sets are said to be of the same size if there is a function that determines a one-to-one correspondence between their elements.
Binomial coefficients and Catalan numbers
In the first part of this session, we gave a brief introduction and reminder about binomial coefficients. These help answer questions like How many ways are there to choose a team of 9 starters from a roster of 25 players? The answer can be found by calculating a “falling factorial” that is, multiplying all the numbers from 10 through 25 together, and then dividing by 9!. The full set of binomial coefficients appears in the familiar diagram known as Pascal’s triangle.
Modular counting and the table setting problem
We began this session with a big reminder about modular thinking. In math, this means saying two numbers are the same when they really differ by a fixed amount. For example, 26 o’clock is really 2 o’clock because they differ by 24 hours. Using this reasoning again and agin, we can answer questions such as: what time of day will it be in a million hours?
Recursion and the four numbers game
Recursion means doing a process again and again.