An Invitation To General Algebra And Universal Constructions
Download An Invitation To General Algebra And Universal Constructions full books in PDF, epub, and Kindle. Read online free An Invitation To General Algebra And Universal Constructions ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: George M. Bergman |
Publisher |
: Springer |
Total Pages |
: 574 |
Release |
: 2015-02-05 |
ISBN-10 |
: 9783319114781 |
ISBN-13 |
: 3319114786 |
Rating |
: 4/5 (81 Downloads) |
Synopsis An Invitation to General Algebra and Universal Constructions by : George M. Bergman
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
Author |
: Brendan Fong |
Publisher |
: Cambridge University Press |
Total Pages |
: 351 |
Release |
: 2019-07-18 |
ISBN-10 |
: 9781108482295 |
ISBN-13 |
: 1108482295 |
Rating |
: 4/5 (95 Downloads) |
Synopsis An Invitation to Applied Category Theory by : Brendan Fong
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Author |
: Béla Bajnok |
Publisher |
: Springer Nature |
Total Pages |
: 443 |
Release |
: 2020-10-27 |
ISBN-10 |
: 9783030561741 |
ISBN-13 |
: 3030561747 |
Rating |
: 4/5 (41 Downloads) |
Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
Author |
: Ana Cannas da Silva |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 202 |
Release |
: 1999 |
ISBN-10 |
: 0821809520 |
ISBN-13 |
: 9780821809525 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Geometric Models for Noncommutative Algebras by : Ana Cannas da Silva
The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Author |
: J. P. May |
Publisher |
: University of Chicago Press |
Total Pages |
: 262 |
Release |
: 1999-09 |
ISBN-10 |
: 0226511839 |
ISBN-13 |
: 9780226511832 |
Rating |
: 4/5 (39 Downloads) |
Synopsis A Concise Course in Algebraic Topology by : J. P. May
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author |
: Joachim Kock |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 162 |
Release |
: 2007-12-27 |
ISBN-10 |
: 9780817644956 |
ISBN-13 |
: 0817644954 |
Rating |
: 4/5 (56 Downloads) |
Synopsis An Invitation to Quantum Cohomology by : Joachim Kock
Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory
Author |
: Ralph S. Freese |
Publisher |
: American Mathematical Society |
Total Pages |
: 496 |
Release |
: 2022-10-28 |
ISBN-10 |
: 9781470467975 |
ISBN-13 |
: 1470467976 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Algebras, Lattices, Varieties by : Ralph S. Freese
This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.
Author |
: Alain Connes |
Publisher |
: Springer |
Total Pages |
: 364 |
Release |
: 2003-12-15 |
ISBN-10 |
: 9783540397021 |
ISBN-13 |
: 3540397027 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Noncommutative Geometry by : Alain Connes
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author |
: Matej Brešar |
Publisher |
: Springer |
Total Pages |
: 227 |
Release |
: 2014-10-14 |
ISBN-10 |
: 9783319086934 |
ISBN-13 |
: 3319086936 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Introduction to Noncommutative Algebra by : Matej Brešar
Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.
Author |
: Philippe Flajolet |
Publisher |
: Cambridge University Press |
Total Pages |
: 825 |
Release |
: 2009-01-15 |
ISBN-10 |
: 9781139477161 |
ISBN-13 |
: 1139477161 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Analytic Combinatorics by : Philippe Flajolet
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.