🔴 Level 4: Expert Algebra
The deep end of pre-college algebra: higher-degree polynomials, advanced exponential and logarithmic techniques, complex numbers, function transformations, sequences and series, and a first taste of abstract algebra.
Advanced Equations & Polynomials
Higher-degree polynomial equations, synthetic and long division, the Rational Root Theorem, Descartes' Rule of Signs, and strategies for finding all roots.
2Advanced Exponential & Logarithmic Functions
Solving exponential and logarithmic equations, growth and decay models, change-of-base techniques, and graphing transformations of these functions.
3Advanced Complex Numbers
Polar form, De Moivre's Theorem, complex roots of unity, and connections to trigonometry and rotations in the plane.
4Complex Numbers — Foundations
A complete tour of complex arithmetic from the imaginary unit through addition, multiplication, conjugates, division, and the complex plane. A standalone primer that pairs with Topic 3.
5Advanced Functions & Transformations
Function composition, inverse functions, piecewise definitions, even/odd symmetry, and stacking translations, reflections, and stretches on parent functions.
6Advanced Sequences & Series
Convergence and divergence tests for infinite series, geometric sums, telescoping series, and an introduction to power series — the bridge from algebra to calculus.
7Introductory Abstract Algebra (Optional)
A first look at groups, rings, and fields — the structures that generalise the arithmetic you've been doing all along. Optional capstone for the curious.