# Mathematical Physics

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

21. Example: Fock Vector Space

22. 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

42. Categories: Summary

43. 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

**Physical Sciences: **
Astronomy and Astrophysics |
Physics and Astronomy |
Theoretical Physics

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