# “Introduction to Groups” by Johann Thiel

This week Dr. Thiel spoke about “Introduction to Groups”:
Title: “Introduction to Groups”
Speaker: Johann Thiel (NYCCT)
Date/Room: Thursday Oct. 26, 2017, 12:45-2:00pm, Namm N719
Abstract:

A group is an important mathematical structure in abstract algebra. In this talk we will introduce some of the definitions needed to understand basic group theory (with lots of examples) and talk about some important applications.

Below is an image of the symmetries of an equilateral triangle. What is the group structure here? # October 12, 2017: “The Coin Change Problem” by Johann Thiel

This week Dr. Thiel spoke about “The Coin Change Problem”:
Title: “The Coin Change Problem”
Speaker: Johann Thiel (NYCCT)
Date/Room: Thursday Oct. 12, 2017, 12:45-2:00pm, Namm N719

Abstract:
What is the minimum number of coins needed to give someone 82 cents in change? There is a simple algorithm that solves this question for our current coin system using pennies, nickels, dimes, and quarters. (Can you figure out the algorithm?)
The more general form of this question is called the Coin Change Problem: given a list of coin denominations and a change amount, what is the minimum number of coins needed to make the change amount?
In this talk we will apply dynamic programming techniques to this problem. In particular, this talk will feature some Python programming.
Here is a link to an introduction to dynamic programming and below you can see some of the graphs that were generated during the talk.
The graph below shows the minimum number of coins needed to make n cents from 1 to 100 with pennies, nickels, dimes, and quarters.
The histogram below shows the distribution of the above values.
The graph below shows how the average number of coins needed to make n cents (from 1 to 100) if we add a new coin denomination to our system. The lowest average is produced by adding a 32 cent coin.
Here is a link to a math research paper about a “better” coin system.

# September 28, 2017: “A look at the radical side of trigonometry” by Dr. Satyanand Singh

On Thursday September 28, 2017, Dr. Singh spoke to us about “A look at the radical side of geometry”:

Dr. Singh’s abstract can be found below. Further details can be found in the journal article “The Sine of a Single Degree” by Travis Kowalski, which appeared in the November 2016 issue of The College Mathematics Journal; the pdf is available for download on JSTOR here.

September 28, 2017: Dr. Satyanand Singh: “A look at the radical side of trigonometry”
Abstract: In this presentation we will illustrate by geometric and algebraic means how one can calculate the exact values of sin(3n◦), where n takes on integral values in the interval 0 ≤ n ≤ 9. In this journey we will encounter different shapes such as
and travel along a complex path to derive a multitude of ways to represent sin(1◦). These notions readily extends to other trigonometric functions.