AoPS Extension Math

Lessons

Holiday Module 1: Exponents/Logarithms, Complex Numbers, Linear Equations, Proportions, Using the Integers, Quadratic Equations, and Special Factorizations and Clever Manipulations

Module 1: What Numbers Really Area, An Introduction to Circles, Angles, Triangles, Quadrilaterals, Polygons, Angle Chasing, Areas, The Power of Coordinates, Power of a Point, and Three Dimensional Geometry

Holiday Module 2: Shifts, Turns, Flips, Stretches, and Squeezes and Learning to Count

Module 2: A Potpourri of Geometry, Functions, Inequalities, Operations and Relations, Sequences and Series, Statistics and Probability, and Sets

Holiday Module 3: Prove It and Parting Shots

Holiday Module 4: Prove It, Logarithms, Not Just for Right Triangles, and More Triangles!

Module 3: Cyclic Quadrilaterals, Conics and Polar Coordinates, Polynomials, Functions, and Taking it to the Limit

Holiday Module 5: Complex Numbers and Vectors and Matrices

Module 4: Cross Products and Determinants, Analytic Geometry, Equations and Expressions, Inequalities, Combinatorics, Sequences and Series, Counting in the Twilight Zone, Again and Again, Probability, Find It and Make It, Collinearity and Concurrency, Geometry Tidbits, and Number Theory

Holiday Module 6: Diophantine Equations, Graph Theory, and Parting Shots

Module 5: Integers: The Basics, Primes and Composites, Multiples and Divisors, Prime Factorization, Divisor Problems, Speical Numbers, and Algebra With Integers

Module 6: Base Numbers, Base Number Arithmetic, Units Digits, Decimals and Fractions, Introduction to Modular Arithmetic, Divisibility Rules, Linear Congruences, and Number Sense

Module 7: Counting is Arithmetic, Basic Counting Techniques, Correcting for Overcounting, Committees and Combinations, More With Combinations, Some Harder Counting Problems, Introduction to Probability, and Basic Probability Techniques

Module 8: Think About It, Geometric Probability, Expected Value, Pascal's Triangle, The Hockey Stick Identity, The Binomial Theorem, and More Challenging Problems

Module 9: Review of Counting and Probability Basics, Sets and Logic, A Piece of PIE, Constructive Counting and 1-1 Correspondences, The Pigenhole Principle, Constructive Expectation, Distributions, and Mathematical Inductions

Module 10: Recursion, Conditional Probability, Combinatorial Identities, Events with States, Generating Functions, Graph Theory, and Challenge Problems