Who cares about topology? (Old version)
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3Blue1Brown's original 2016 animated video on the inscribed rectangle problem. It shows how pairs of points on a loop map to a Möbius strip, explaining why every closed curve contains an inscribed rectangle and what topology is for.
More resources on Topology & Geometry
Differential Geometry
Explore differential geometry with Frederic Schuller's course! Master manifolds, tensors, and more in this topology & geometry playlist.
Topology Without Tears
Free textbook by Sidney A. Morris introducing point-set topology from open sets and the euclidean topology through continuity, metric spaces, compactness, connectedness, and Tychonoff's theorem. Readers learn to write rigorous topology proofs, with later chapters extending to topological groups.
Hatcher's Algebraic Topology (free PDF)
Allen Hatcher's standard graduate textbook, freely downloadable from Cornell, covering fundamental groups, homology, cohomology and homotopy theory, with CW complexes introduced in Chapter 0 and used throughout. Readers learn to build spaces from cells and compute their algebraic invariants.
topology.jdabbs.com
Topology.jdabbs.com is an educational site offering concise notes and explanations on topology and geometry, designed to help learners grasp fundamental concepts and theorems. Expect definitions, examples, proofs, and problem sets covering topics from basic topological spaces to more advanced geometric ideas.
Differential Geometry
Dover reprint of Kreyszig's 1959 text on curves and surfaces in three-dimensional space using tensor notation. Covers curvature, torsion, the first and second fundamental forms, geodesics, and Gauss's theorema egregium, preparing readers for Riemannian geometry.