🟣 Level 3: Advanced Algebra
Dive deeper into advanced algebraic concepts including functions, non-linear systems, matrices, vectors, and abstract algebra introductions.
Functions and Their Properties
Understand function definitions, domain, range, and types of functions.
2Quadratic Equations
Master solving quadratic equations using various methods.
3Graphing Quadratic Functions
Learn to graph parabolas and identify key features like vertex and intercepts.
4Exponential Functions
Explore exponential growth and decay models and their graphs.
5Logarithmic Functions
Understand logarithms as inverses of exponentials and their properties.
6Systems of Nonlinear Equations
Solve systems involving quadratics, circles, and other nonlinear functions.
7Harmonic Sequences & Series
Explore harmonic sequences and the divergence of the harmonic series.
8Special Sequences
Discover Fibonacci, square, and triangular numbers.
9Conditional Probability & Independence
Master conditional probability and independent events.
10Expected Value & Variance
Learn to calculate expected value and variance for random variables.
11Matrix Determinants & Inverses (2x2)
Calculate determinants and inverses for 2x2 matrices.
12Matrix Determinants & Inverses (3x3)
Extend your matrix skills to 3x3 determinants and inverses.
13Introduction to Vector Spaces
Step into linear algebra with the definition and properties of vector spaces.
14Span, Linear Independence & Basis
Understand the core building blocks of vector spaces.
15Boolean Algebra: Simplification
Advanced simplification techniques and logic circuits.
16Canonical Forms & Karnaugh Maps
Learn systematic simplification using K-Maps.
17Group Theory: Foundations
Introduction to groups, subgroups, and cyclic groups.
18Group Theory: Structure & Theorems
Explore homomorphisms, Lagrange's Theorem, and more.