Los Angeles Math Circle

LAMC Calendar // 2018-2019 Academic Year. Jump to:

For meetings prior to Fall 2018, visit the Circle Archive.

AdvancedBeginnersBreaking Numbers into PartsEarly Elementary IEarly Elementary IIHigh School IHigh School IIJunior CircleOlympiad Training
10/7/2018
We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.
10/14/2018
We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.
10/21/2018
We introduce the Gini index, an economic metric to measure wealth inequality.
Handouts: Gini Index
10/28/2018
We introduce Legendre symbols and quadratic reciprocity to study residues modulo primes.
11/4/2018
We explore applications of quadratic reciprocity.
11/11/2018
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
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
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?
Handouts: Golomb Ruler
12/9/2018
1/13/2019
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
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

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
We will introduce the formal defnition of a limit of a sequence and develop basic properties.
2/10/2019
We will continue our practice with formally proving limits of sequences and we will prove some additional properties of sequence limits.
2/24/2019
We characterize all polynomials that have integer outputs for integer inputs.