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In ancient Greek mathematics, "space" was a geometric abstraction of the three-dimensional reality observed in everyday life. About 300 BC, Euclid gave axioms for the properties of space. Euclid built all of mathematics on these geometric foundations, going so far as to define numbers by comparing the lengths of line segments to the length of a ...
As is usual for a textbook, Curvature of Space and Time has exercises that extend the coverage of its topics and make it suitable as the text for undergraduate courses. . Although there are multiple undergraduate-level textbooks on differential geometry, they have generally taken an abstract mathematical view of the subject, and at the time of publishing of Curvature of Space and Time, courses ...
In his 1988 book A Brief History of Time, he describes The Large Scale Structure of Space–Time as "highly technical" and unreadable for the layperson. The book, now considered a classic, has also appeared in paperback format and has been reprinted many times. a A fiftieth anniversary edition was published by Cambridge University Press in ...
Julia M. Klein of Johns Hopkins Magazine wrote, "There's nothing small about Johns Hopkins physicist Sean Carroll's latest undertaking. The Biggest Ideas in the Universe: Space, Time, and Motion is the first volume in an ambitious trilogy that seeks to explain physics to a popular audience—one willing to grapple with the basics of calculus and other mathematical underpinnings of the field.
Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC [1] in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula.
His book The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds (Marcel Dekker, 1985, ISBN 0-8247-7437-X) explores the geometry and topology of low-dimensional manifolds. [3] [4] The second edition (2002, ISBN 0-8247-0709-5) explains some of his work in applying the material to cosmology. [5]
Most modern approaches to mathematical general relativity begin with the concept of a manifold.More precisely, the basic physical construct representing gravitation — a curved spacetime — is modelled by a four-dimensional, smooth, connected, Lorentzian manifold.
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl 1,3 (R), or equivalently the geometric algebra G(M 4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and ...