{"product_id":"mathematical-crystallography-reviews-in-mineralogy-geochemistry-15-9780939950195","title":"Mathematical Crystallography (Reviews in Mineralogy \u0026 Geochemistry  15)","description":"\u003cp\u003eVolume 15 of Reviews in Mineralogy is written with two goals in mind. The first is to derive the 32 crystallographic point groups  the 14 Bravais lattice types and the 230 crystallographic space group types. The second is to develop the mathematical tools necessary for these derivations in such a manner as to lay the mathematical foundation needed to solve numerous basic problems in crystallography and to avoid extraneous discourses. To demonstrate how these tools can be employed  a large number of examples are solved and problems are given. The book is  by and large  self-contained. In particular  topics usually omitted from the traditional courses in mathematics that are essential to the study of crystallography are discussed. For example  the techniques needed to work in vector spaces with noncartesian bases are developed. Unlike the traditional group-theoretical approach  isomorphism is not the essential ingredient in crystallographic classification schemes. Because alternative classification schemes must be used  the notions of equivalence relations and classes which are fundamental to such schemes are defined  discussed and illustrated. For example  we will find that the classification of the crystallographic space groups into the traditional 230 types is defined in terms of their matrix representations. Therefore  the derivation of these groups from the point groups will be conducted using the 37 distinct matrix groups rather than the 32 point groups they represent.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45665817559093,"sku":"ByrdShop_0939950197","price":66.26,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780939950195.jpg?v=1782408400","url":"https:\/\/atxbooks.com\/products\/mathematical-crystallography-reviews-in-mineralogy-geochemistry-15-9780939950195","provider":"ATX Books","version":"1.0","type":"link"}