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Author: Garrett Birkhoff
Publisher: CRC Press
ISBN: 1439864535
Category : Mathematics
Languages : en
Pages : 513
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Book Description
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
Author: Garrett Birkhoff
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 300
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Book Description
Author: Saunders Mac Lane
Publisher: American Mathematical Society
ISBN: 147047476X
Category : Mathematics
Languages : en
Pages : 650
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Book Description
This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.
Author: Garrett Birkhoff
Publisher: CRC Press
ISBN: 1439864535
Category : Mathematics
Languages : en
Pages : 513
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Book Description
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
Author: S.P. Novikov
Publisher: Springer Science & Business Media
ISBN: 3662105799
Category : Mathematics
Languages : en
Pages : 326
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Book Description
This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.
Author: Paolo Aluffi
Publisher: American Mathematical Soc.
ISBN: 147046571X
Category : Education
Languages : en
Pages : 713
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Book Description
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author: Arthur Baragar
Publisher: Pearson
ISBN:
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition. Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research. Ideal for geometry at an intermediate level.
Author: Saul Stahl
Publisher: John Wiley & Sons
ISBN: 1118552032
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Praise for the First Edition "Stahl offers the solvability of equations from the historicalpoint of view...one of the best books available to support aone-semester introduction to abstract algebra." —CHOICE Introductory Modern Algebra: A Historical Approach, SecondEdition presents the evolution of algebra and provides readerswith the opportunity to view modern algebra as a consistentmovement from concrete problems to abstract principles. With a fewpertinent excerpts from the writings of some of the greatestmathematicians, the Second Edition uniquely facilitates theunderstanding of pivotal algebraic ideas. The author provides a clear, precise, and accessibleintroduction to modern algebra and also helps to develop a moreimmediate and well-grounded understanding of how equations lead topermutation groups and what those groups can inform us about suchdiverse items as multivariate functions and the 15-puzzle.Featuring new sections on topics such as group homomorphisms, theRSA algorithm, complex conjugation, the factorization of realpolynomials, and the fundamental theorem of algebra, the SecondEdition also includes: An in-depth explanation of the principles and practices ofmodern algebra in terms of the historical development from theRenaissance solution of the cubic equation to Dedekind'sideals Historical discussions integrated with the development ofmodern and abstract algebra in addition to many new explicitstatements of theorems, definitions, and terminology A new appendix on logic and proofs, sets, functions, andequivalence relations Over 1,000 new examples and multi-level exercises at the end ofeach section and chapter as well as updated chapter summaries Introductory Modern Algebra: A Historical Approach, SecondEdition is an excellent textbook for upper-undergraduatecourses in modern and abstract algebra.
Author: DIPAK CHATTERJEE
Publisher: PHI Learning Pvt. Ltd.
ISBN: 9788120328709
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Appropriate for undergraduate courses, this second edition has a new chapter on lattice theory, many revisions, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley's theorem, the Lagrange's theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student's ability to further explore and inter-connect various essential notions.
Author: Saunders Mac Lane
Publisher: CRC Press
ISBN: 1439863644
Category : Mathematics
Languages : en
Pages : 375
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Book Description
Saunders Mac Lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. In his autobiography, he gives us a glimpse of his "life and times," mixing the highly personal with professional observations. His recollections bring to life a century of extraordinary accomplis
Author: CHATTERJEE, DIPAK
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120351495
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Appropriate for undergraduate courses, this third edition has new chapters on Galois Theory and Module Theory, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley’s theorem, the Lagrange’s theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student’s ability to further explore and interconnect various essential notions. Besides undergraduate students of mathematics, this text is equally useful for the postgraduate students of mathematics.
