Athemath

Nifty NT and Algebra

In 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

Schedule

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

Cute Geometry

Instructor: Vivian Loh

This course covers lots of AMC-AIME level topics related to triangles, cyclic quadrilaterals, area, power of a point, and trig, plus a tiny peek into higher topics such as special centers of a triangle.

Difficulty: AMC to Mid AIME

Schedule

LESSON 1: Similarity and Congruence

LESSON 2: Lengths and Areas

LESSON 3: Circle Magic

LESSON 4: Trig

LESSON 5: Triangle Centers I

LESSON 6: Triangle Centers II

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

Schedule

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 Dani

In 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

Schedule

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

Comical Combo

Instructor: Emily Liu

This course will cover the combinatorial techniques and general strategies used in AIME-level problems. Topics include how to deal with restrictions, casework, bijections, recursion, and Principle of Inclusion-Exclusion.

Difficulty: AMC to Late AIME

Schedule

LESSON 1: Basics

LESSON 2: Restrictions

LESSON 3: Casework

LESSON 4: Perspectives

LESSON 5: Frogs and Recursion

LESSON 6: Principle of Inclusion and Exclusion

Affable Algebraic Affairs

Instructor: Julia Xiang

This course covers common algebra topics that appear time and time again on the AMCs and AIMEs, such as polynomials, sequences and series, and trigonometry. We’ll cover the basics, then look at some more complex applications, including some clever manipulations and techniques.

Difficulty: AMC to Late AIME

Schedule

LESSON 1: Factoring and Identities

LESSON 2: Polynomials and Manipulations

LESSON 3: Series and Weird Functions

LESSON 4: Trig Formulas and Substitutions

LESSON 5: Complex Numbers

LESSON 6: Inequalities

Classy Adventures in Combinatorics and Algebra

Instructor: Ekam Kaur

In 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

Schedule

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

Art of Trigonometry (ft. Problem Solving)

Instructor: Ashley Zhu

Art of Trigonometry (ft. Problem Solving) is a mid AIME to beginning olympiad level class focused on how to use trigonometry as a tool to simply solve high difficulty problems. The class will cover applications of trigonometry in both algebra and geometry.

Difficulty: Mid-AIME to Beginner Olympiad

Schedule

LESSON 1: Trig Definitions and Basics

LESSON 2: Trig Formulas (Law of Sine, Law of Cosine, Ratio Lemma, Trig Ceva's, etc.)

LESSON 3: Simplifying Geo Diagrams with Trig

LESSON 4: Trigonometric Equations

LESSON 5: Applications in the Complex Plane

LESSON 6: Is Using Trig Always A Good Idea?

AIME Combo

Instructor: Matilde Iannaccone

In this course we cover some of the fundamental concepts of olympiad combinatorics, such as permutations, probability, catalan numbers, and dismutations as well as different principles like pigeonhole and inclusion-exclusion. By taking this course you will learn how to approach and set up computational olympiad problems.

Difficulty: Mid-AIME to Beginner Olympiad

Schedule

LESSON 1: Everything with Anagrams

LESSON 2: Sets and the Principle of Inclusion-Exclusion

LESSON 3: Probability Fundamentals

LESSON 4: Derangements and Catalan Numbers

LESSON 5: Pigeonhole Principle

LESSON 6: Setting Up Problems

Get to know Number Theory

Instructor: Thanaree (Pimmy) Maneepairoj

In 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

Schedule

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 Cui

This 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

Schedule

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 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

Schedule

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 Xu

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 Olympiad to Mid-Olympiad

Schedule

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

Quirky Geometry

Instructor: Ana Boiangiu

In this class, we will be exploring several heuristics and philosophies that are useful in tackling Olympiad Geometry of any level (with occasional computational exercises). The lectures are designed not to be theory-heavy (so you will not be learning scary lemmas and theorems): instead, the goal is to discover ideas through problem-solving. A solid grasp of chapters 1-3 of EGMO is recommended to attend this course.

Difficulty: Beginner Olympiad to Mid-Olympiad

Schedule

LESSON 1: Midpoints and Parallelograms

LESSON 2: Construct

LESSON 3: Triangle Centers

LESSON 4: Power of a Point

LESSON 5: Eraser

LESSON 6: Quick!