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The beforehand affiliate of this independent argument accommodate a avenue from aboriginal attempt through accepted beeline and boxlike algebra to geometric algebra, with Clifford’s geometric algebras demography pride of place. In alongside with this is an account, additionally from aboriginal principles, of the elementary approach of topological spaces and of connected and differentiable maps that leads up to the definitions of bland manifolds and their departure spaces and of Lie groups and Lie algebras. The calculus is presented as far as accessible in base chargeless anatomy to accent its geometrical flavour and its beeline algebra content. In this additional copy Dr Porteous has taken the befalling to add a affiliate on triality which extends beforehand assignment on the Spin groups in the affiliate on Clifford algebras. The capacity accommodate a cardinal of important transitive accumulation accomplishments and a description of one of the aberrant Lie groups, the accumulation G2. A cardinal of corrections and improvements accept additionally been made. There are abounding contest throughout the book and chief undergraduates in mathematics as able-bodied as first-year alum acceptance will abide to acquisition it aesthetic and rewarding.

Review of the hardback: ‘… a arresting book, which is acceptable to abide actual useful, both for teaching and research, during abounding years to come.’ J.Dieudonné in Zentralblatt Für Mathematik

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ForewordGuide1. Maps2. Real and circuitous numbers3. Beeline spaces4. Affine spaces5. Quotient structures6. Finite-dimensional spaces7. Determinants8. Direct sum9. Orthogonal spaces10. Quaternions11. Correlations12. Quadric Grassmannians13. Clifford Algebras14. The Cayley algebra15. Normed beeline spaces16. Topological spaces17. Topological groups and manifolds18. Affine approximation19. The changed action theorem20. Bland manifolds21. TrialityBibliographyList of symbolsIndex.

Ian R. Porteous

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