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| Author | : Audrey Terras |
| Publisher | : Cambridge University Press |
| Total Pages | : 331 |
| Release | : 2019 |
| Genre | : Mathematics |
| ISBN | : 1107164079 |
This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.
| Author | : Pierre Cartier |
| Publisher | : Springer Nature |
| Total Pages | : 277 |
| Release | : 2021-09-20 |
| Genre | : Mathematics |
| ISBN | : 3030778452 |
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
| Author | : Scott Balchin |
| Publisher | : Springer Nature |
| Total Pages | : 326 |
| Release | : 2021-10-29 |
| Genre | : Mathematics |
| ISBN | : 3030750353 |
This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2010-01-14 |
| Genre | : Mathematics |
| ISBN | : 0486474178 |
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
| Author | : Nadiya Gubareni |
| Publisher | : CRC Press |
| Total Pages | : 363 |
| Release | : 2021-06-23 |
| Genre | : Mathematics |
| ISBN | : 1000209539 |
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
| Author | : Thomas Judson |
| Publisher | : Orthogonal Publishing L3c |
| Total Pages | : 0 |
| Release | : 2023-08-11 |
| Genre | : |
| ISBN | : 9781944325190 |
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
| Author | : S. R. Nagpaul |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821874295 |
This book presents interesting applications of abstract algebra to practical real-world problems. Especially for those whose interest in algebra is not confined to abstract theory, the text makes the study of abstract algebra more exciting and meaningful. The book is appropriate as either a text for an applied abstract algebra course or as a supplemental text for a standard course in abstract algebra. While fully developed, the algebraic theory presented is just what is required for the applications discussed in the book. This book is included in the Brooks/Cole Series in Advanced Mathematics (Series Editor: Paul Sally, Jr.).
| Author | : Dan Saracino |
| Publisher | : Waveland Press |
| Total Pages | : 320 |
| Release | : 2008-09-02 |
| Genre | : Mathematics |
| ISBN | : 1478610131 |
The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.
| Author | : L. Pachter |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 2005-08-22 |
| Genre | : Mathematics |
| ISBN | : 9780521857000 |
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
| Author | : Phyllis J Cassidy |
| Publisher | : World Scientific |
| Total Pages | : 320 |
| Release | : 2002-05-30 |
| Genre | : Mathematics |
| ISBN | : 9814490504 |
Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop.
