nerd.ac
Concept maps for studying mathematics. Each map shows how the ideas of a course depend on one another. Click any box for a summary, a question to check yourself, and pointers into freely available texts.
Differentiable manifolds
Charts and smooth maps, tangent spaces, immersions and submersions, vector fields and flows, Lie groups, differential forms and Stokes, and Riemannian geometry.
Draws on Gallier & Quaintance and Nicolaescu Open the map →Real analysis
Why the Riemann integral falls short, how measure theory fixes it, and the convergence theorems that make the Lebesgue integral work.
Follows Axler, Measure, Integration & Real Analysis, Ch. 1–3 Open the map →