Author : Ashish K. Srivastava
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 21,27 MB
Release : 2020-06-23
Category : Education
ISBN : 1470443686
This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.
Author : Ezra Miller
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 35,24 MB
Release : 2005-06-21
Category : Mathematics
ISBN : 9780387237077
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author : Charles A. Weibel
Publisher : Cambridge University Press
Page : 470 pages
File Size : 12,94 MB
Release : 1995-10-27
Category : Mathematics
ISBN : 113964307X
The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 30,24 MB
Release : 2008-01-08
Category : Mathematics
ISBN : 9783540730514
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Author : John R. Harper
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 14,56 MB
Release : 1985
Category : Mathematics
ISBN : 9780821850398
A survey of the areas where combinatorial methods have proven especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces.
Author : Kostrikin, Aleksei Ivanovich Kostrikin
Publisher :
Page : 287 pages
File Size : 46,48 MB
Release : 1990
Category :
ISBN : 9780387546995
Author : Ayman Badawi
Publisher : Springer
Page : 154 pages
File Size : 11,26 MB
Release : 2018-03-01
Category : Mathematics
ISBN : 3319741950
Based on the 4th Seminar on Algebra and its Applications organized by the University of Mohaghegh Ardabili, this volume highlights recent developments and trends in algebra and its applications. Selected and peer reviewed, the contributions in this volume cover areas that have flourished in the last few decades, including homological algebra, combinatorial algebra, module theory and linear algebra over rings, multiplicative ideal theory, and integer-valued polynomials. Held biennially since 2010, SAA introduces Iranian faculty and graduate students to important ideas in the mainstream of algebra and opens channels of communication between Iranian mathematicians and algebraists from around the globe to facilitate collaborative research. Ideal for graduate students and researchers in the field, these proceedings present the best of the seminar’s research achievements and new contributions to the field.
Author : Bruno Benedetti
Publisher : Springer
Page : 222 pages
File Size : 16,60 MB
Release : 2015-10-31
Category : Mathematics
ISBN : 3319201557
Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.
Author : Dumitru I. Stamate
Publisher : Springer Nature
Page : 182 pages
File Size : 46,95 MB
Release : 2020-09-01
Category : Mathematics
ISBN : 3030521117
This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).
Author : Tomasz Kaczynski
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 24,7 MB
Release : 2006-04-18
Category : Mathematics
ISBN : 0387215972
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
