### Art of Problem Solving, High School

We’re just going to say it like it is: ** Art of Problem Solving** is a math curriculum designed for kids who LOVE math and are really, really good at it. We’re talking about the kiddos who may be starting Algebra 1 at the age of 10.

That’s not to say that other students would not benefit from **AoPS**. But, if your teen enjoys math textbooks with the visual appeal of lots of bright pictures and sideboxes filled full of random fun facts and real world applications of math skills, then **AoPS **will probably not be a good fit.

**AoPS **textbooks are highly regarded for their rigor and depth, but they are dense and intense – which is not a bad thing, if you love math. Written in a conversational style, it’s like reading the transcript from a math lecture. Concepts are introduced and sample problems are explained step-by-step in text and number format.

Students then get the chance to try problems on their own: Exercise problems, review problems, and challenge problems. Don’t worry, though. The Solutions Manual not only gives you the answer, but it also gives you explanations on how to solve the harder problems.

Not sure what level you should start with? Visit the AoPS website’s Recommendation page and look for the Are You Ready? link to find a placement test for each textbook in the series.

Also, be sure to check out the Free Alcumus site on AoPS. You’ll find thousands of problems to supplement some of the textbooks. And, you can even watch video lessons that go with the Introduction to Counting & Probability book.

**1. Introduction to Counting & Probability**

Casework

Multiplication

Permutations

Combinations

Pascal’s triangle

Probability

Combinatorial identities

Binomial Theorem

**2. Introduction to Geometry**

Similar triangles

Congruent triangles

Quadrilaterals

Polygons

Circles

Funky areas

Power of a point

Three-dimensional geometry

Transformations

and much more

**3. Introduction to Number Theory**

Primes and composites

Divisors and multiples

Prime factorization

Divisibility rules

Remainders

Modular arithmetic

Number bases

Linear congruences

How to develop number sense

and more

**4. Intermediate Algebra**

Review of basic algebra topics

Complex numbers

Quadratics and conic sections

Polynomials

Multivariable expressions

Sequences and series

Identities

Inequalities

Exponents and logarithms

Piecewise-defined functions

Functional equations

and more

**5. Intermediate Counting & Probability**

Inclusion-exclusion

1-1 correspondences

Pigeonhole Principle

Constructive expectation

Fibonacci and Catalan numbers

Recursion

Conditional probability

Generating functions

Graph theory

and more

**6. Pre-Calculus**

Trigonometry

Complex numbers

Vectors

Matrices

**7. Calculus**

Limits

Continuity

Derivatives

Integrals

Power series

Plane curves

Differential equations

**About the Authors:** Richard Rusczyk is the founder of the Art of Problem Solving website. He was a national MATHCOUNTS participant in 1985, a three-time participant in the Math Olympiad Summer Program, a perfect AIME scorer in 1989, and a USA Mathematical Olympiad winner. He is author or co-author of 6 Art of Problem Solving textbooks. Sandor Lehoczky participated in the Math Olympiad Summer Program in 1989, and in 1990 earned the sole perfect AIME score and led the national first place team on the AHSME (now AMC 12). Lehoczky and Rusczyk were co-founders of the Mandelbrot Competition.