|10/7/2018| [Show less]
We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.
|10/14/2018| [Show less]
We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.
|10/21/2018| [Show less]
We introduce the Gini index, an economic metric to measure wealth inequality.
|10/28/2018| [Show less]
We introduce Legendre symbols and quadratic reciprocity to study residues modulo primes.
|11/4/2018| [Show less]
We explore applications of quadratic reciprocity.
|11/11/2018| [Show less]
Instead of our typical definition of addition and multiplication, tropical arithmetic looks at minimum and addition operations. We will graph and find roots of tropical polynomials.
|11/18/2018| [Show less]
We will continue our study of tropical arithmetic by proving a version of the Fundamental Theorem of Algebra for tropical quadratic polynomials.
|12/2/2018| [Show less]
Given a ruler, how many inch markings can you remove and still measure each increment between 1 and 12 inches? Is there some way to construct a 12-inch ruler such that each increment from 1 to 12 can be measured in a unique way?
|12/9/2018|| [Show less] |
|1/13/2019| [Show less]
We will introduce continued fractions and learn how to calculate them. We will also investigate the relationship between the irrationality of a number and properties of its continued fraction expansion.
|1/20/2019| [Show less]
We will continue our study of continued fractions with an imporant application in number theory: Given an irrational number, how efficiently can it be approximated by rational numbers? Continued fraction expansions play an important role in solving this problem.
|1/27/2019| [Show less]
In this power-point presentation, we will address the following questions: Why do some musical intervals sound pleasant, while others do not? Why do we have exactly 12 notes in an octave of a piano? Why aren't distances between frets on a flute or a guitar equal to each other? The answers, surprisingly, involve deep mathematical analysis involving continued fractions, the problem of doubling the cube, and rational approximations.
|2/3/2019| [Show less]
We will introduce the formal defnition of a limit of a sequence and develop basic properties.
|2/10/2019| [Show less]
We will continue our practice with formally proving limits of sequences and we will prove some additional properties of sequence limits.
|2/24/2019| [Show less]
We characterize all polynomials that have integer outputs for integer inputs.