*Held February 5th, 2022—April 30th, 2022*

### Counting and Probability Principles

Instructor: Sanjana DasIn this course, we cover common methods in counting and their applications, on early to mid AIME-level problems. Topics will include constructive and complementary counting, PIE and constructing sets, bijections (such as Stars and Bars), recursion, and path-counting.

LESSON 1: Counting Basics

LESSON 2: Sets

LESSON 3: Bijections

LESSON 4: Recursion

LESSON 5: Counting Paths

LESSON 6: Counting Test!

### Spicy Counting

Instructor: Pravalika PutalapattuThis course is designed to strengthen students’ counting and probability intuition skills at the early-/mid-AIME level. Students will learn a range of approaches, including constructive and complementary counting, simplification and recursion, invariants, bijections, and strategic bashing. Lectures will be heavily problem-based as AIME counting problems tend to rely on strategies and ideas rather than formulas.

LESSON 1: The Three C's

LESSON 2: Judicious Adding

LESSON 3: Level Up!

LESSON 4: Bijections

LESSON 5: Graph Theory

LESSON 6: Farewell

### Spicy Geometry

Instructor: Serena XuIn this course, we are going to talk about the five unique hearts of triangles and some famous theorems. Topics will include the special property of five centers and some interesting theorems, such as Ceva, Ptolemy, Monge and so on. In particular, we will solve some kinda-wonderful problems in each class!

LESSON 1: Circumcenter and incenter

LESSON 2: Centroid, orthocenter and excenter

LESSON 3: Menelaus and Ceva

LESSON 4: Ptolemy and Simson

LESSON 5: Power of a Point and Radical Axis

LESSON 6: Review and Group Solve

### Algebra in AIME

Instructor: Kaylee JiIn this course, we will cover many algebra topics in mid-to-late AIME: trigonometry, complex numbers, polynomials, and conics. The focus of this course will be solving problems. Expect content to be covered quickly under the assumption that students are vaguely familiar with the concepts discussed.

LESSON 1: Trigonometric Identities

LESSON 2: Complex Numbers

LESSON 3: Polynomials I

LESSON 4: Polynomials II

LESSON 5: Conics

LESSON 6: Review and Test

### Algebra and Combinatorics Trail Mix

Instructor: Nicole ShenIn this course, we will go over some common techniques used on mid AMC- to early AIME-level problems. Students will become familiar with methods and tricks that cover a variety of topics, especially in combinatorics and algebra. Topics include bijections, algebraic manipulation, using inequalities, sequences and series, and recursions.

LESSON 1: Counting Clever Correspondences

LESSON 2: Algebraic Manipulation

LESSON 3: Inequalities

LESSON 4: ∑equences and ∑eries

LESSON 5: Recursion and States

LESSON 6: Look to the Future

### Cute Geometry

Instructor: Vivian LohThis course covers all sorts of AIME-level topics related to triangles, plus a tiny peek into olympiad geo with cyclic quadrilaterals and cool orthocenter properties. Some topics included are area, Power of a Point, and trig bashing.

LESSON 1: Similarity and Congruence

LESSON 2: Lengths and Areas

LESSON 3: Triangle Centers

LESSON 4: Circle Magic

LESSON 5: Trig

LESSON 6: Geometry Test!

### My Favorite Things

Instructor: Isabella Quan
Vieta, trig functions and prime number theories ♪

Mass points, right triangles and coordinate bashing ♩

Manipulation and geometric series ♬

These are a few of my favorite things~

In this class, we’ll be talking about a variety of tricks that are prevalent on the AMCs and early to mid AIME which I find to be particularly elegant or beautiful.

LESSON 1: Odds and Ends of Geometry

LESSON 2: Best Minecraft Mods: Modular Arithmetic

LESSON 3: It's a Sin to not Know Trig: Trigonometry

LESSON 4: I Used Algebra to Destroy the Algebra: Algebraic Manipulations

LESSON 5: Tree Roots and Polynomial Roots: Vieta's

LESSON 6: Stream Sequence by IZ*ONE: Sequences and Series

### Counting Strategies

Instructor: Michelle KangThis course is designed to help you enhance your combinatorics problem solving skills for early to mid AIME level problems. We will cover many different techniques, such as constructive and complementary counting, recursion, expected value, and bijections.

LESSON 1: Counting Principles

LESSON 2: Sets

LESSON 3: Bijections

LESSON 4: Recursion

LESSON 5: Other Topics

LESSON 6: Combo Test