{"title":"Books by American Mathematical Society","description":null,"products":[{"product_id":"9780821832226","title":"Representation Theory of Finite Groups: Algebra and Arithmetic","description":"'We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his\/her own' - from the Preface. Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, it has been one of the great tools in the study and classification of finite groups. The theory contains some particularly beautiful results: Frobenius' theorem, Burnside's theorem, Artin's theorem, Brauer's theorem - all of which are covered in this textbook. Some seem uninspiring at first but prove to be quite useful. Others are clearly deep from the outset.And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers.The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":56295051886965,"sku":"9780821832226","price":87.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821832226_c79ac6fd-efde-450b-a4ca-ba28a3cefecd.jpg?v=1786015723"},{"product_id":"9780821802366","title":"Problems and Theorems in Linear Algebra","description":"There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, Prasolov provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It would be a fine supplementary text for an undergraduate or graduate algebra course.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":56295118274933,"sku":"9780821802366","price":144.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821802366_35f28bcf-dbc9-4bad-baa6-8dc75cbd229e.jpg?v=1786015722"},{"product_id":"9780821829226","title":"Cohomological Analysis of Partial Differential Equations and Secondary Calculus","description":"This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress.Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with \"\"Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182\"\" in this same series, \"\"Translations of Mathematical Monographs\"\", and shows the theory 'in action'.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":56295119520117,"sku":"9780821829226","price":152.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821829226_bf12a895-d895-485d-86cc-4a28f19fdded.jpg?v=1786015723"},{"product_id":"mathematical-publishing","title":"Mathematical Publishing","description":"Mathematicians are expected to publish their work: in journals, conference proceedings, and books. It is vital to advancing their careers. Later, some are asked to become editors. However, most mathematicians are trained to do mathematics, not to publish it. But here, finally, for graduate students and researchers interested in publishing their work, Steven G. Krantz, the respected author of several 'how-to' guides in mathematics, shares his experience as an author, editor, editorial board member, and independent publisher.This new volume is an informative, comprehensive guidebook to publishing mathematics. Krantz describes both the general setting of mathematical publishing and the specifics about all the various publishing situations mathematicians may encounter. As with his other books, Krantz's style is engaging and frank. He gives advice on how to get your book published, how to get organized as an editor, what to do when things go wrong, and much more.He describes the people, the language (including a glossary), and the process of publishing both books and journals. Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 130 research articles and 45 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS. He is also the founder of the \"\"Journal of Geometric Analysis\"\". Other titles available from the AMS by Steven G. Krantz are \"\"How to Teach Mathematics\"\", \"\"A Primer of Mathematical Writing\"\", \"\"A Mathematician's Survival Guide\"\", and \"\"Techniques of Problem Solving\"\".","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57481389244789,"sku":"9780821836996","price":34.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821836996.jpg?v=1786089646"},{"product_id":"polyhedral-computation","title":"Polyhedral Computation","description":"Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general-purpose algorithms. They are, however, highly structured, and attention has turned to exploiting this structure, particularly symmetry. Initial applications of this approach have permitted computations previously far out of reach, but much remains to be understood and validated experimentally. The papers in this volume give a good snapshot of the ideas discussed at a Workshop on Polyhedral Computation held at the CRM in Montreal in October 2006 and, with one exception, the current state of affairs in this area. The exception is the inclusion of an often cited 1980 technical report of Norman Zadeh, which was never published in a journal and has passed into the folklore of the discipline. This paper illustrates beautifully the work still to be done in the field: it gives a simple pivot rule for the simplex method for which it is still unknown if it yields a polynomial time algorithm.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57520098410869,"sku":"9780821846339","price":76.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821846339.jpg?v=1787581683"},{"product_id":"theorie-des-fonctions-algebriques-de-deux-variables-independantes-volume-i-ii","title":"Theorie Des Fonctions Algebriques De Deux Variables Independantes, Volume I \u0026 II","description":"This single volume contains the two original volumes, which were written ten years apart from each other. The first volume is a preliminary discussion of multiple integrals and the associated geometry. The authors treat the connections with algebraic surfaces and integrals of total differentials. The last two chapters of Volume I are devoted to the study of numerical invariants introduced by Clebsch and Noether, and to the double integrals attached to them.The second volume is a more developed discussion of both the geometry and the analysis of algebraic functions, including results obtained by Picard, Castelnuovo, and Enriques in the time after the publication of Volume I. Most of the geometry revolves around linear systems of curves, either in the plane or on a surface. There is also a special chapter on the geometry of hyperelliptic surfaces. The major part of the analysis in Volume II is centered on integrals of the second kind, including their periods and the number of distinct such integrals in specific instances. The book concludes with a long section of notes on various interesting topics.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57520099393909,"sku":"9780828402484","price":59.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780828402484.jpg?v=1787581691"},{"product_id":"statistical-problems-with-nuisance-parameters","title":"Statistical Problems with Nuisance Parameters","description":null,"brand":"Gardners","offers":[{"title":"Default Title","offer_id":57680086106485,"sku":"9780821846872","price":141.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821846872.jpg?v=1792423098"},{"product_id":"selected-papers-on-analysis-and-differential-equations","title":"Selected Papers on Analysis and Differential Equations","description":"This volume contains translations of papers that originally appeared in the Japanese journal ‘Sugaku’. These papers range over a variety of topics in ordinary and partial differential equations, and in analysis. Many of them are survey papers presenting new results obtained in the last few years. This volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.|This volume contains translations of papers that originally appeared in the Japanese journal ‘Sugaku’. These papers range over a variety of topics in ordinary and partial differential equations, and in analysis. Many of them are survey papers presenting new results obtained in the last few years. This volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57680086860149,"sku":"9780821848814","price":150.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9780821848814.jpg?v=1792423100"}],"url":"https:\/\/backstory.london\/collections\/author-american-mathematical-society.oembed","provider":"Backstory","version":"1.0","type":"link"}