01
Functions as machines and as objects
What is a function, if not a formula?
Foundations · Module 02
Algebra, Functions & Trigonometry
The school syllabus, rebuilt as a coherent story about transformation rather than a list of procedures to memorise.
By the end of this module
You can manipulate any expression with confidence and see functions as objects rather than formulas.
0%0 / 5 complete
02
Polynomials and the fundamental theorem of algebra
Why do we need complex numbers to solve real equations?
VideoFree
Imaginary Numbers Are Real [Part 1: Introduction] ↗Welch Labs
The historical route: complex numbers were forced on mathematicians by cubics, not quadratics.
03
Exponentials and logarithms
What makes e special?
04
Trigonometry as circular motion
Why does the same function describe a triangle and a wave?
Check yourself
End-of-module quiz
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01e is the unique base for which:
02The fundamental theorem of algebra guarantees a degree-n polynomial has:
03sin²θ + cos²θ = 1 is:
Answer all 3 to finish the module.