Format: Paperback / softback, 262 pages, height x width: 240x170 mm, 24 Illustrations, color; 30 Illustrations, black and white
Series: De Gruyter Textbook
Pub. Date: 19-Aug-2024
ISBN-13: 9783111014814
This book is ideal as an introduction to algebraic topology and applied algebraic topology featuring a streamlined approach including coverage of basic categorical notions, simplicial, cellular, and singular homology, persistent homology, cohomology groups, cup products, Poincare Duality, homotopy theory, and spectral sequences. The focus is on examples and computations, and there are many end of chapter exercises and extensive student projects.
Format: Paperback / softback, 422 pages, height x width: 240x170 mm, weight: 698 g, 5 Illustrations, black and white
Pub. Date: 22-Jul-2024
ISBN-13: 9783111139517
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
zbMATH Open, the world's most comprehensive and longest-running abstracting and reviewing service in pure and applied mathematics was founded by Otto Neugebauer in 1931. It celebrated its 90th anniversary by becoming an open access database. In December 2019, the Joint Science Conference (Gemeinsame Wissenschaftskonferenz) agreed that the Federal and State Governments of Germany would support FIZ Karlsruhe in transforming zbMATH into an open platform. In future, zbMATH Open will link mathematical services and platforms so as to provide considerably more content for further research and collaborative work in mathematics and related fields.
This book presents how zbMATH Open has reacted to a rapidly changing digital era. Topics covered include: the linkage of zbMATH Open with different community platforms and digital maths libraries, the use of zbMATH Open as a bibliographical tool, API solutions, current advancements in author profiles, the indexing of mathematical software packages (swMATH), and issues concerning mathematical formula search in zbMATH Open. We also reflect on the gender publication gap in mathematics, and focus on one of the central pillars of zbMATH Open: the community of reviewers.
Oxford Graduate Texts in Mathematics
Oxford Graduate Texts in Mathematics
Follows the recent trends by presenting a categorical and homological approach
Introduces and uses representations of quivers
Contains a large number of examples, exercises, and figures
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work.
Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.