| Description |
1 online resource (358 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Chicago lectures in physics
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Chicago lectures in physics.
|
| Note |
Includes index. |
| Contents |
1 . Introduction; 2 . Categories; 3. The Category of Groups; 4. Subgroups; 5 . Normal Subgroups; 6. Homomorphisms; 7. Direct Products and Sums of Groups; 8. Relations; 9. The Category of Vector Spaces; 10 . Subspaces; 11 . Linear Mappings; Direct Products and Sums; 12 . From Real to Complex Vector Spaces and Back; 13 . Duals; 14 . Multilinear Mappings; Tensor Products; 15 . Example: Minkowski Vector Space; 16 . Example: The Lorentz Group; 17 . Functors; 18 . The Category of Associative Algebras; 19 . The Category of Lie Algebras; 20 . Example: The Algebra of Observables |
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21. Example: Fock Vector Space22. Representations: General Theory; 23 . Representations on Vector Spaces; 24 . The Algebraic Categories: Summary; 25 . Subsets and Mappings; 26. Topological Spaces; 27. Continuous Mappings; 28 . The Category of Topological Spaces; 29. Nets; 30. Compactness; 31. The Compact-Open Topology; 32. Connectedness; 33. Example: Dynamical Systems; 34. Homotopy; 35. Homology; 36. Homology: Relation to Homotopy; 37. The Homology Functors; 38. Uniform Spaces; 39. The Completion of a Uniform Space; 40. Topological Groups; 41. Topological Vector Spaces |
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42. Categories: Summary43. Measure Spaces; 44. Constructing Measure Spaces; 45. Measurable Functions; 46. Integrals; 47. Distributions; 48. Hilbert Spaces; 49. Bounded Operators; 50. The Spectrum of a Bounded Operator; 51. The Spectral Theorem: Finite-dimensional Case; 52. Continuous Functions of a Hermitian Operator; 53. Other Functions of a Hermitian Operator; 54. The Spectral Theorem; 55. Operators (Not Necessarily Bounded); 56. Self-Adjoint Operators; Index of Defined Terms |
| Summary |
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical physics.
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Mathematical physics. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Other Form: |
Print version: Geroch, Robert. Mathematical physics. Chicago : University of Chicago Press, 1985 vi, 351 pages ; 23 cm Chicago lectures in physics 9780226288611 |
| ISBN |
9780226223063 electronic book |
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022622306X electronic book |
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0226288625 (paperback) |
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0226288617 (hardcover) |
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9780226288611 |
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