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Introduction to Groups and Geometries
This text is two textbooks in one: an introduction to group theory, and an introduction to modern geometries using the Kleinian paradigm. The book can be used for a combined one-semester course in both subjects, or, through supplementary projects, it can be used for a one-semester introduction to group theory or a one-semester introduction to modern geometries.
- Author
- David W. Lyons
- Publisher
- Lebanon Valley College
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 19 sections
- 01: Preliminaries
- 1.01: Complex Numbers
- 1.02: Quaternions
- 1.03: Stereographic projection
- 1.04: Equivalence Relations
- 02: Groups
- 2.01: Examples of groups
- 2.02: Definition of a group
- 2.03: Subgroups and cosets
- 2.04: Group homomorphisms
- 2.05: Group actions
- 2.06: Additional exercises
- 03: Geometries
- 3.01: Geometries and models
- 3.02: Möbius geometry
- 3.03: Hyperbolic geometry
- 3.04: Elliptic geometry
- 3.05: Projective geometry
- 3.06: Additional exercises