Book Description
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Author : Michael Hitrik
Publisher : American Mathematical Society
Page : 102 pages
File Size : 17,49 MB
Release : 2022-11-10
Category : Mathematics
ISBN : 1470454211
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Author : Michael Hitrik
Publisher :
Page : 0 pages
File Size : 37,48 MB
Release : 2022
Category : Mathematical physics
ISBN : 9781470472801
Author : Valentin Blomer
Publisher : American Mathematical Society
Page : 160 pages
File Size : 42,45 MB
Release : 2023-02-13
Category : Mathematics
ISBN : 1470456788
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Author : Zhaobing Fan
Publisher : American Mathematical Society
Page : 108 pages
File Size : 49,62 MB
Release : 2023-01-18
Category : Mathematics
ISBN : 1470456265
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Author : Hideto Asashiba
Publisher : American Mathematical Society
Page : 282 pages
File Size : 16,33 MB
Release : 2022-09-29
Category : Mathematics
ISBN : 1470464845
This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory. The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.
Author : Tomasz Downarowicz
Publisher : American Mathematical Society
Page : 108 pages
File Size : 36,61 MB
Release : 2023-01-18
Category : Mathematics
ISBN : 1470455870
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Author : André Gil Henriques
Publisher : American Mathematical Society
Page : 100 pages
File Size : 49,74 MB
Release : 2023-02-13
Category : Mathematics
ISBN : 1470455404
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Author : Kannan Soundararajan
Publisher : American Mathematical Society
Page : 100 pages
File Size : 40,10 MB
Release : 2022-11-09
Category : Mathematics
ISBN : 1470469308
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Author : Tiago J. Fonseca
Publisher : American Mathematical Society
Page : 158 pages
File Size : 19,72 MB
Release : 2023-01-18
Category : Mathematics
ISBN : 147046019X
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Author : Anand P. Patel
Publisher : American Mathematical Society
Page : 114 pages
File Size : 14,28 MB
Release : 2023-02-13
Category : Mathematics
ISBN : 1470461579
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