01
Construction of the reals and completeness
What is a real number, exactly?
ReadingFree
Understanding Analysis — supplementary materials ↗Stephen Abbott
Check your library; the standard gentle-but-rigorous text.
Advanced · Module 10
Real Analysis
Calculus, rebuilt from the definition of a limit upward. This is the module where mathematics stops being computation.
By the end of this module
You can prove the theorems calculus assumed, and you know exactly where the assumptions bite.
0%0 / 3 complete
02
Sequences, series and convergence
When is an infinite process legitimate?
03
Measure theory and the Lebesgue integral
Why does the Riemann integral fail, and what replaces it?
Quiz
Not written yet for this module. The lectures above are complete and the module still counts toward your progress.