UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2023-2024 Academic Year

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For meetings prior to Fall 2023, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2Advanced 3AMC 10/12 TrainingAMC 8 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2A
Beginners 2BBNP ABNP BChess clubIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads
10/1/2023

We'll do a variety of Olympiad problems to warm up for the year of problem-solving.

The problems will range in level, from practice problems through BAMO up to Putnam, so there should be something for everyone.

Handouts: Handout
10/8/2023

We'll focus on writing clear proofs as we do problems from books and from a variety of actual Olympiads.

Handouts: Problems
10/15/2023

This week, we will solve competition problems with invariants.

When there is some repeated process, rather than studying what does change, we may want to look at what stays the same.

This allows us to make connections between the starting and ending positions, and we can rule out many possibilities this way.

Handouts: Handout
10/22/2023

We'll look at a few problems involving polynomials and the tricks to solve them.

Handouts: Handout
10/29/2023

We consider some more techniques for working with polynomials, such as Vieta's Formulas and tools for working with irreducible polynomials.

Handouts: Handout
11/5/2023

We will do competition problems using inequalities such as AM-GM and Cauchy-Schwarz.

Handouts: Handout
12/3/2023

We will go over the basics of generating functions, and see how they can be used in olympiad problems about counting.

Handouts: Handout
12/10/2023

We'll continue thinking about generating functions, showing some more advanced techniques for particular competition problems.

Handouts: Handout
1/7/2024

We'll take a look at a variety of different combinatorics problems, from olympiad training books and actual competitions.

Handouts: Handout
1/14/2024

I've selected the easier half of this year's Putnam problems, and broken them into approachable pieces with some hints.

Handouts: Handout
1/21/2024

Inspired by a problem from last week's worksheet on the 2023 Putnam, this week we will be diving into uses of expected values in probability problems.

Handouts: Handout
1/28/2024

We'll take a look at some interesting number theory problems from problem books and competitions.

Handouts: Handout
2/4/2024

This week, we will talk about combinatorial geometry.

We'll start with the classic Lazy Caterer's Problem and build up to harder problems about counting geometrical objects.

Handouts: Handout
2/18/2024

We use the complex plane interpretation to solve geometry problems using complex algebra.

Handouts: Handout
2/25/2024

We'll take a look at a particular kind of coordinate system based on triangles.

We'll then use these barycentric coordinates to prove theorems and solve competition problems based on triangles.

Handouts: Handout
3/3/2024

Many combinatorial problems have the same solution - the Catalan numbers.

We will use some of these problems to practice bijective combinatorial proofs, and then apply those techniques to competition problems.

Handouts: Handout
3/10/2024

We'll prove some formulas for summing binomial coefficients, and use them to solve competition problems.

Handouts: Handout
3/31/2024

We return to number theory, and solve some problems with factorization and gcds.

Handouts: Handout
4/7/2024

We'll pick up last week's theme of factorization, but instead of focusing on gcds, we focus on direct applications of unique factorization into primes.

Handouts: Handout
4/14/2024

We will study multiplicative functions such as the sum-of-divisors function and Euler's totient function, and use them to solve Olympiad number theory problems.

Handouts: Handout