Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

(Formerly MATHCOUNTS/AMC Counting & Probability) Basic and intermediate counting concepts, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

An introduction to the concepts of geometry, including triangle similarity and congruence, complicated area problems, special quadrilaterals, the art of angle chasing, power of a point, 3-dimensional geometry, and geometric proofs. Please note: This is an 18-week course.

Algebraic subjects covered include polynomials, functions, logarithmic equations, clever substitutions of variables, systems of equations, symmetric sums, advanced factoring methods, and binomial expansion.

Introduction and evaluation of trigonometric functions, trigonometric identities, complex numbers, exponential form of complex numbers, De Moivre's Theorem, geometric representation of complex numbers, roots of unity.

Counting subjects covered include clever one-to-one correspondences, principle of inclusion-exclusion, generating functions, combinatorics, recursion, conditional probability.

An 8 week problem solving seminar (no exams) with number theory using algebraic and counting approaches. Topics also include Diophantine equations (Pell equations), Fermat's Little Theorem, the Phi Function, and Euler's Theorem.