ocw.mit.edu
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MIT OpenCourseWare offers free, openly accessible course materials from MIT across a wide range of subjects, including mathematics. It provides lecture notes, assignments, exams, and sometimes video lectures for math courses that cover topics such as tangent spaces.
More resources on Tangent Spaces
Math Stack Exchange: Tangent Space Discussions
Community Q&A on tangent spaces
Lectures on the Geometric Anatomy of Theoretical Physics
Learn tangent-spaces & geometric anatomy for theoretical physics with Frederic Schuller's lectures. Explore advanced concepts.
nLab: Tangent Space
Comprehensive reference with category theory perspective, linked in advanced Reddit discussions
Differential Geometry
Explore tangent spaces with this differential geometry course by George Lusztig. Learn key concepts at MIT OpenCourseWare.
Lectures on the Geometric Anatomy of Theoretical Physics
Learn geometric anatomy for theoretical physics with Frederic Schuller! This course explores tangent-spaces and more.
mathworld.wolfram.com
MathWorld is an extensive online mathematics encyclopedia from Wolfram Research that provides detailed articles on mathematical topics—definitions, theorems, formulas, and worked examples—with rich cross-references and diagrams. It covers a wide range of subjects, including differential geometry topics like tangent spaces.