UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2020-2021 Academic Year

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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

We kick off the academic year with some competition-style problems gathered from AMC, AIME, and Olympiads.

Handouts: Handout | Solutions

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

Handouts: Handout | Solutions

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

Handouts: Handout | Solutions

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


We will study recursive formulas for generating primes.

Handouts: Handout

We will take our first peak into algorithms, with the goal of discussing the P vs NP problem the following week.

Handouts: Handout

We continue our unit on algorithms by discussing the most famous open problem in the field, P vs NP.

Handouts: Handout

The Fundamental Theorem of Algebra... Everyone's heard of it. If it's so fundamental then why haven't we seen a proof?! Look no further, we consider complex polynomials and graphing techniques to prove that every complex polynomial has a root.

Handouts: Handout

To start off the new year we are going to split the class into two competing groups. There will be a variety of problems to work on and it will be up to the teams to organize how they feel is best.


We start our unit on graphs with a dive into planar graphs and the Euler characteristic.

Handouts: Handout | Solutions

We continue our unit on graph theory with a handout on graph colorings. We will define what it means to color a graph, connect this to coloring maps (geographically speaking), and prove some bounds on how many colors are needed.

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We continue with a proof of the 5-color theorem and some Ramsey theory.

Handouts: Solutions | Handout

We look at continued fractions and their relation to rational and irrational numbers.

Handouts: Handout

We introduce the concept of metrics using a motivating example: the taxicab metric. This worksheet is especially useful for all those of you who are part time students and part time taxi drivers in New York City.

Handouts: Handout | Solutions