{"product_id":"topological-geometry-paperback-9780521298391","title":"Topological Geometry (Paperback) 9780521298391","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTopological Geometry\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eProvides a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eIan R. Porteous (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521298391, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 5 February 1981\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e500 pages\u003cbr\u003e22.8 x 15.2 x 2.7 cm, 0.73 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eReview of the hardback: '… a remarkable book, which is likely to remain very useful, both for teaching and research, during many years to come.' J.Dieudonné in Zentralblatt Für Mathematik\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe earlier chapter of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological spaces and of continuous and differentiable maps that leads up to the definitions of smooth manifolds and their tangent spaces and of Lie groups and Lie algebras. The calculus is presented as far as possible in basis free form to emphasize its geometrical flavour and its linear algebra content. In this second edition Dr Porteous has taken the opportunity to add a chapter on triality which extends earlier work on the Spin groups in the chapter on Clifford algebras. The details include a number of important transitive group actions and a description of one of the exceptional Lie groups, the group G2. A number of corrections and improvements have also been made. There are many exercises throughout the book and senior undergraduates in mathematics as well as first-year graduate students will continue to find it stimulating and rewarding.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eForeword\u003cbr\u003e Guide\u003cbr\u003e 1. Maps\u003cbr\u003e 2. Real and complex numbers\u003cbr\u003e 3. Linear spaces\u003cbr\u003e 4. Affine spaces\u003cbr\u003e 5. Quotient structures\u003cbr\u003e 6. Finite-dimensional spaces\u003cbr\u003e 7. Determinants\u003cbr\u003e 8. Direct sum\u003cbr\u003e 9. Orthogonal spaces\u003cbr\u003e 10. Quaternions\u003cbr\u003e 11. Correlations\u003cbr\u003e 12. Quadric Grassmannians\u003cbr\u003e 13. Clifford Algebras\u003cbr\u003e 14. The Cayley algebra\u003cbr\u003e 15. Normed linear spaces\u003cbr\u003e 16. Topological spaces\u003cbr\u003e 17. Topological groups and manifolds\u003cbr\u003e 18. Affine approximation\u003cbr\u003e 19. The inverse function theorem\u003cbr\u003e 20. Smooth manifolds\u003cbr\u003e 21. Triality\u003cbr\u003e Bibliography\u003cbr\u003e List of symbols\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005080850712,"sku":"9780521298391","price":80.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521298391i_98357e16-616c-4718-8779-adeab89c5844.jpg?v=1691374918","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/topological-geometry-paperback-9780521298391","provider":"Freshly Printed Books","version":"1.0","type":"link"}