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
10/11/2020

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

Handouts: Handout | Solutions
10/18/2020

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

Handouts: Handout | Solutions
10/25/2020

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

Handouts: Handout | Solutions
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.

Handouts: Handout
11/15/2020

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

Handouts: Handout
11/22/2020

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

Handouts: Handout
12/6/2020

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
1/10/2021

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.

1/17/2021

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

Handouts: Handout | Solutions
1/24/2021

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.

Handouts: Handout
1/31/2021

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

Handouts: Solutions | Handout
2/7/2021

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

Handouts: Handout | Solutions
2/21/2021

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
2/28/2021

We use the first part as motivation to define metrics in general. We talk about a few different examples and introduce the notion of convergence of a series.

Handouts: Handout | Solutions
3/7/2021

We take a look at a measure of income inequality in a given population.

Handouts: Handout
3/14/2021
Handouts: Handout
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

We use the error formulas derived in the first part, throw in the concept of limits, and see some applications for measurement error.


Handouts: Handout
4/18/2021

We'll define the most common lattice and get some results relating regions to lattice points. We'll also see an application to Polya's Orchard problem.

Handouts: Handout