{"product_id":"oriented-matroids-hardback-9781009494113","title":"Oriented Matroids (Hardback) 9781009494113","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eOriented Matroids\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eIntroduction to oriented matroids emphasizing connections to topology and geometry, suitable for graduate courses or independent study.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eLaura Anderson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009494113, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 10 April 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e333 pages\u003cbr\u003e23.5 x 16.1 x 2.4 cm, 0.63 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book is a friendly invitation to the subject of oriented matroids, providing a geometrically inclined introduction and bridging the gap to the more demanding and encyclopaedic Red Book (Björner et al., 1999). It is not always easy to reconcile geometry with combinatorics and this textbook is certainly on the right path. For illustration, 'combinatorial Farkas Property' ('Farkas' is mentioned in the book 72 times!) offers a unified point of view throughout the book and helps the reader understand the rationale behind more technically involved parts of the subject. Both students and teachers will find a selection of relatively new developments in the book (which haven't been covered in a textbook before!), including a glimpse into the general theory of matroids over hyperfield.' Rade Živaljević, Mathematical Institute SASA, Belgrade\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Realizable oriented matroids\u003cbr\u003e 2. Oriented matroids\u003cbr\u003e 3. Elementary operations and properties\u003cbr\u003e 4. The topological representation theorem\u003cbr\u003e 5. Strong maps and weak maps\u003cbr\u003e 6. Single-element extensions\u003cbr\u003e 7. The universality theorem\u003cbr\u003e 8. Oriented matroid polytopes\u003cbr\u003e 9. Subdivisions and triangulations\u003cbr\u003e 10. Spaces of oriented matroids\u003cbr\u003e 11. Hints on selected exercises\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52472087478552,"sku":"9781009494113","price":45.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009494113i.jpg?v=1785716692","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/oriented-matroids-hardback-9781009494113","provider":"Freshly Printed Books","version":"1.0","type":"link"}