UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2022-2023 Academic Year

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For meetings prior to Fall 2022, visit the Circle Archive.

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Students will start building their understanding of algebraic structures, from magams to groups.


This week we continued studying Algebraic Structures to get into the concept of Groups.


This week we will study Symmetry Groups of regular polygons and platonic solids.


There are many ways to characterize integers: primes versus composite, abundant versus deficient, even naughty versus nice. We will focus on the second of these, trying to make sense of the question, “what’s the probability an integer is abundant?” Exploring this question will compel us to think deeply about primes, and a menagerie of Greek letters, and even the question of naughty versus nice.


During this lecture, we will learn about a group associated to the Rubik's cube. We will study this group to understand how and why the cube can be solved.


In this lecture, we will keep discussing about the 3x3x3 Rubik's cube and we will introduce and discuss the 2x2x2 Rubik's cube.

Handouts: Handout 4

This week, we will introduce the concept of Fields and study some basic examples including the field of constructible real numbers.

Handouts: Handout 5

Competition related to Group Theory and Fields Theory.


This class we will start studying ring theory.

Handouts: Handout 6

This week we will discuss about polynomial rings and how the elements of these rings can be used to draw objects.


This week we will discuss the vanishing set of several polynomials in several variables.


This week we will investigate the relation between affine varieties and ideals in polynomial rings.


The lecture outlines an approach to elementary geometry different from the standard compass-and-ruler constructions. If one uses origami instead, the resulting algebraic structure (Galois group) is more rich. In particular, some problems not solvable by means of compass-and-ruler constructions, like trisecting an angle, become solvable. The room for the lecture is MS 4000A.

Handouts: lecture notes