UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2020-2021 Academic Year

 Search handouts:

For meetings prior to Fall 2020, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2A
Beginners 2BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
10/11/2020

We will start the year with a wide variety of competition style problems.

10/18/2020

We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.

10/25/2020

We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.

11/1/2020

We will study the limitations of polynomials as prime generating functions.

11/8/2020

We will study recursive formulas for generating primes.

11/15/2020

We introduce some classic algorithms and the notion of runtime.

11/22/2020

Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem.

Handouts: P vs NP
12/6/2020

We prove the Fundamental Theorem of Algebra with a focus on graphing.

12/13/2020

The students battle it out in a full class Kahoot competition.

1/10/2021
1/17/2021

We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem.

Handouts: Planar Graphs
1/24/2021

We will explore many interesting results about graph coloring.

Handouts: Graph Coloring
1/31/2021

We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory.

Handouts: Graph Coloring
2/7/2021

Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.

2/21/2021

We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric.

2/28/2021

We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces.

Handouts: Handout
3/7/2021

In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index.

Handouts: Gini Index
3/14/2021
4/4/2021

Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.

Handouts: handout
4/11/2021

Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.

4/18/2021

We will show that certain regions of Euclidean space must contain integer lattice points.

Handouts: Lattices
4/25/2021

We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.

5/2/2021

We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.

5/9/2021
5/16/2021
5/23/2021
6/6/2021