***Note that this catalog is currently incomplete. Thanks for your patience!***
Nifty NT and Algebra
Instructor: Sophia JinIn this class, we will be learning important ideas of algebra and number theory that often appear on the AMC or AIME, such as the Division Theorem, Vieta's formulas, modular arithmetic, the Euclidean Algorithm, and the Chinese Remainder Theorem. In addition, we will be exploring some fun topics like weird divisibility rules and finite differences!
Difficulty: AMC to Mid AIME
LESSON 1: Algebraic Identities and Manipulation
LESSON 2: Polynomials
LESSON 3: Modular Arithmetic I
LESSON 4: Modular Arithmetic II
LESSON 5: Bases and Divisibility
LESSON 6: Finite Differences
ComboneNT
Instructor: Wendy LeongComboneNT 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 Topics I
LESSON 5: Introduction to Olympiad Topics II
LESSON 6: Test and Recap
NT Terrain Navigation
Instructor: Jiya DaniIn this course, we will be “navigating terrain” in number theory, exploring different ideas and useful techniques for computational number theory problems. Along with learning some famous fundamental theorems and other important topics, you will also gain more intuition on how to approach tricky problems.
Difficulty: AMC to Late AIME
LESSON 1: Mod Fundamentals
LESSON 2: Bases and Digits
LESSON 3: Famous Theorems
LESSON 4: Factors and Divisibility
LESSON 5: Prime Powers and Factorials
LESSON 6: Intuition and Vibes
Classy Adventures in Combinatorics and Algebra
Instructor: Ekam KaurIn this class, we will cover many of my favorite topics in combinatorics and algebra which commonly appear on the AIME. Some topics we will cover include bijections, combinatorial perspectives, recursion, handling polynomials, and complex numbers. We will see how these topics show up in various ways and you will become more comfortable applying them, and also improve your general problem solving skills.
Difficulty: AIME
LESSON 1: Polynomials
LESSON 2: Bijections and Combinatorial Identities
LESSON 3: Recursion and States
LESSON 4: Trigonometry
LESSON 5: Complex Numbers
LESSON 6: Combinatorial Arguments
Get to Know Number Theory
Instructor: Thanaree (Pimmy) ManeepairojIn this course, you will learn about an introduction in number theory and some of stuffs that very useful for problems. We also cover many of important concepts and some of strategies.
Difficulty: Mid-AIME to Beginner Olympiad
LESSON 1: Basic Things (Divisibility, GCD, LCM, Bezout, Division Algorithm)
LESSON 2: Prime numbers and Congruence
LESSON 3: Famous Theorems (Fermat Little Theorem, Euler, Wilson, Chinese Remainder)
LESSON 4: Lifting the Exponent
LESSON 5: Fusion Problems equations
LESSON 6: Talk About Nontheory Things / Small Quiz
Outstanding Olympiad Geometry
Instructor: Amy CuiThis course will cover many fundamental theorems and concepts in Olympiad geometry. Some topics we will discuss include the Euler Line, the Nine-Point Circle, the Incenter/Excenter Lemma, Power of a Point, Ceva’s Theorem, the Simson Line, and many other cool configurations!
Difficulty: Late AIME to Beginner Olympiad
LESSON 1: Triangles I
LESSON 2: Triangles II
LESSON 3: Circles
LESSON 4: Length and Area Ratios
LESSON 5: Cool Configurations
LESSON 6: Group Solve
Combo Heuristics
Instructor: Greta QuThis 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!
Fun + Heights
Instructor: Catherine XuFun + 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 Olympiad to Mid-Olympiad
LESSON 1: Cauchy's Functional Equation
LESSON 2: FEs, Part 2
LESSON 3: Manipulations and Lagrange Interpolation
LESSON 4: Introduction to Diophantine Equations
LESSON 5: Diophantines, Part 1 - Orders
LESSON 6: Diophantines, Part 2 - Lifting the Exponent