15 interactive notebooks ready to launch.
Explore compactness through open covers and finite subcovers.
Visualize the Cantor set as a classic topological example.
Study connectedness and density in subsets of the real line.
Compare convergence modes for sequences of functions.
Study metrics on function spaces and uniform convergence.
Determine convergence radii for power series.
Construct pathological functions with strange continuity properties.
Visualize a continuous but nowhere differentiable function.
Explore space-filling curves and their surprising properties.
Introduce outer measure as the first step toward Lebesgue integration.
Compare Lebesgue and Riemann integrals with examples that separate them.
Define and compute the Lebesgue integral for measurable functions.
Investigate nonstandard metrics and their topological consequences.
Study complete metric spaces through Cauchy sequences.
Use the Banach fixed-point theorem to prove existence and uniqueness.