🗺️ Course Map
Your journey to math mastery
Advanced Algebra
Quadratics, systems, functions, sequences, and sigma notation
Quadratic Equations & Factoring
Solve quadratic equations by factoring, completing the square, and the quadratic formula
Systems of Equations & Functions
Solve systems of linear and nonlinear equations; analyze function properties
Sequences, Series & Sigma Notation
Work with arithmetic/geometric series, telescoping sums, and sigma notation
Coordinate Geometry
Lines, slopes, distance, midpoint, circles, transformations, vectors
Lines, Slopes & Equations
Find slopes, write equations of lines, and determine parallel/perpendicular relationships
Distance, Midpoint & Circle Equations
Apply distance/midpoint formulas and work with circle equations in standard and general form
Geometric Transformations & Vectors
Apply translations, rotations, reflections, and basic vector operations
Combinatorics & Probability
Permutations, combinations, probability, and the pigeonhole principle
Permutations & Arrangements
Count arrangements using permutations, factorials, and the multiplication principle
Combinations & Binomial Theorem
Use combinations for selection problems and apply the binomial theorem
Probability & Pigeonhole Principle
Calculate probabilities of events and apply the pigeonhole principle to existence proofs
Number Theory & Proofs
Divisibility, modular arithmetic, primes, GCD/LCM, and proof techniques
Divisibility & Modular Arithmetic
Apply divisibility rules, work with modular arithmetic, and solve congruences
GCD, LCM & Prime Factorization
Find GCD/LCM using prime factorization and the Euclidean algorithm
Proof Techniques & Problem Solving
Apply direct proof, proof by contradiction, mathematical induction, and invariants