Ascending Algebra
Instructor: Maiya Qiu
This course will cover common techniques used for AIME level algebra problems and feature topics including algebraic manipulation, root finding, roots of unity, and symmetric polynomials.
Difficulty: AMC to Mid AIME
LESSON 1: Algebraic Techniques I
LESSON 2: Algebraic Techniques II
LESSON 3: Intro to Polynomials
LESSON 4: Even More Polynomials
LESSON 5: Everything Algebraic
LESSON 6: Fun±
Combo Essentials
Instructor: Erin Bian
Combo Essentials will cover the most important combinatorics topics on the mid- to late- AIME and early USA(J)MO. We will discuss useful techniques such as PIE, induction, pigeonhole, and invariants. This course aims to give students a better understanding and intuition for combinatorics as a whole.
Difficulty: Mid AIME to Beginner Olympiad
LESSON 1: Counting & Casework
LESSON 2: Inclusion-Exclusion
LESSON 3: Induction & Recursion
LESSON 4: Pigeonhole Principle
LESSON 5: Graph Theory
LESSON 6: Invariants & Monovariants
Combo Heuristics
Instructor: Greta Qu
This course will cover various thinking processes and strategies used to solve olympiad problems (with some computational applications as well!). Rather than focusing on techniques, the topics emphasize intuitive reasoning and gaining a deep understanding of the subject. This class is suitable for anyone with a solid combinatorial background looking to try some cool problems!
Difficulty: Late AIME to Mid-Olympiad
LESSON 1: Underlying Structure
LESSON 2: Processes
LESSON 3: Constructions
LESSON 4: Intro to Graph Theory
LESSON 5: Forcing Moves
LESSON 6: Some Fun Challenges!
ComboneNT
Instructor: Wendy Leong
ComboneNT is a course focusing on Combo-flavoured Number Theory – that is, how characteristics of the integers, such as divisibility, can translate into useful combinatorial properties. It presents insights and techniques from both the Combo and NT perspectives, exploring how such ideas have surfaced in recent years, and offering strategies for AMC, AIME, and introductory Olympiad problems.
Difficulty: AMC to Mid AIME
LESSON 1: Prime Number Properties, GCD and LCM, Divisibility
LESSON 2: Modular Arithmetic
LESSON 3: Counting Techniques
LESSON 4: Introduction to Olympiad I
LESSON 5: Introduction to Olympiad II
LESSON 6: Fun!
Cozy Combo
Instructor: Lanie Deng
This course will cover many combinatorics topics seen on the AMC and AIME, such as permutations, probability. Principle of Inclusion-Exclusion, and different bijections.
Difficulty: Mid-AMC to Mid-AIME
LESSON 1: Counting/Permutations
LESSON 2: Casework
LESSON 3: Probability Basics
LESSON 4: PIE + Pigeonhole Principle
LESSON 5: Bijections
LESSON 6: TBD, something fun!
Fun + Heights
Instructor: Selena Ge
Fun + Heights is a beginning to middle olympiad level class focusing on fun(ctional equations) and diophantine equation-based number theory. This class will cover fundamentals in functional equations and the uses of prime divisors in number theory.
Difficulty: Beginner to Mid-Olympiad
LESSON 1: Cauchy's Functional Equation
LESSON 2: FEs Continued
LESSON 3: Polynomial Manipulation
LESSON 4: Intro to Diophantine Equations
LESSON 5: Orders in Diophantines
LESSON 6: Lifting the Exponent in Diophantines
Geometry Will Keep You Awake
Instructor: Haruka Kimura
This is a beginner- to mid-Olympiad course on synthetic geometry. We will cover fundamental techniques through lots of walkthroughs and hands-on practice. Knowledge of basic geometric properties is strongly recommended. With experience comes intuition, and with intuition, your geometry journey will become smoother and more enjoyable :P
Difficulty: Beginner Olympiad to Mid Olympiad
LESSON 1: Understanding Geometry
LESSON 2: Chasing Angles and Lengths
LESSON 3: Configurations
LESSON 4: Courage
LESSON 5: Practice!
LESSON 6: The Geometry Mindset
Joyful Geometry
Instructor: Aashita Mandiwal
This course will cover important synthetic geometry properties and techniques that are fundamental to tackling harder computational geometry problems. It will also serve as a bridge to beginning olympiad geometry and introduce proof techniques.
Difficulty: Mid AIME to Beginner Olympiad
LESSON 1: Triangles I
LESSON 2: Circles I
LESSON 3: Triangles II
LESSON 4: Circles II
LESSON 5: Harder Applications and Techniques
LESSON 6: Intro to Olympiad Geometry
Math Puns Make Me Number
Instructor: Sylvia Chen
This course will cover number theory fundamentals for solving late AMC and AIME problems. A lot of harder problems can be solved using just these fundamentals, so we'll work with a lot of examples and provide proofs for well-known theorems to deepen number theoretical understanding.
Difficulty: Late AMC to Late AIME
LESSON 1: Primes + divisors
LESSON 2: Divisibility + bases
LESSON 3: Mod basics
LESSON 4: Exponents + orders
LESSON 5: p-adic valuation
LESSON 6: Fun!
Olympiad Number Theory
Instructor: Elena Beckman
This course will cover several common strategies and topics used in olympiad number theory problems, such as modular arithmetic, orders, and useful theorems like Fermat's Little Theorem and the lifting-the-exponent lemma.
Difficulty: Late AIME to Mid-Olympiad
LESSON 1: Modular Arithmetic
LESSON 2: Fermat's Little Theorem
LESSON 3: Orders/Primitive Roots
LESSON 4: Fermat's Christmas Theorem
LESSON 5: Lifting the Exponent
LESSON 6: TBD, problems/groupsolving!