{"title":"Group Theory","description":"\u003cp\u003eGroup theory is a fundamental branch of mathematics focused on the study of algebraic structures known as groups, which describe symmetry, operations, and transformations. This subject includes both introductory and advanced works that explore the abstract principles and applications of group theory—from permutation groups to matrix groups and symmetry in geometry and physics.\u003c\/p\u003e\u003cp\u003eSelect group theory for a targeted exploration of mathematical systems governed by group structures, distinct from general algebra, number theory, or broader mathematics categories. To refine your research or reading further, consider thematic areas like finite or infinite groups, applications in science, or connections to related mathematical disciplines, depending on your specific goals.\u003c\/p\u003e","products":[{"product_id":"groups-vector-spaces-physicv31-9789971509552-new","title":"Groups \u0026 Vector Spaces for Physic..(V31)","description":"\u003cp\u003eThese notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of \"Algebra and Groups\" is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine \"mathematical\" thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543575134498,"sku":"9789971509552-new","price":47.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789971509552.jpg?v=1776385224"},{"product_id":"theory-group-representation-appli-9789971502171-new","title":"Theory of Group Representation \u0026 Appli","description":"\u003cp\u003eThe material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543584997666,"sku":"9789971502171-new","price":87.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789971502171.jpg?v=1776385341"},{"product_id":"modular-representation-theory-finite-p-adic-groups-9789814651806-new","title":"Modular Representation Theory of Finite and P-Adic Groups","description":"\u003cp\u003eThis volume is an outgrowth of the program \u003cem\u003eModular Representation Theory of Finite and \u003cem\u003ep\u003c\/em\u003e-Adic Groups\u003c\/em\u003e held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of \u003cem\u003ep\u003c\/em\u003e-adic groups and finite groups and their related algebras. 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Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are very closely interrelated. As a result, from a new perspective, we may study the classical artinian rings through their interaction and overlap with Harada rings. The objective of this seminal work is to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings. In the process, we cover many topics on artinian rings, using a wide variety of concepts from the theory of rings and modules. In particular, we consider the following topics, all of which are currently of much interest and ongoing research: Nakayama permutations, Nakayama automorphisms, Fuller's theorem on i-pairs, artinian rings with self-duality, skew-matrix rings, the classification of Nakayama rings, Nakayama group algebras, the Faith conjecture, constructions of local quasi-Frobenius rings, lifting modules, and extending modules. 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The exception is the binary icosahedral group in which only the generators and relations are exhibited.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544102633762,"sku":"9789811292750-new","price":165.41,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811292750.jpg?v=1776398392"},{"product_id":"starting-category-theory-9789811286001-new","title":"Starting Category Theory","description":"\u003cp\u003eOne of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cem\u003eStarting Category Theory\u003c\/em\u003e serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. 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A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eA special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. 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