Basic Algebra II

Second Edition

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Author: Nathan Jacobson

Publisher: Courier Corporation

ISBN: 0486135217

Category: Mathematics

Page: 704

View: 7378

This classic text and standard reference comprises all subjects of a first-year graduate-level course, including in-depth coverage of groups and polynomials and extensive use of categories and functors. 1989 edition.

Basic Algebra II

Second Edition

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Author: Nathan Jacobson

Publisher: Courier Corporation

ISBN: 048647187X

Category: Mathematics

Page: 686

View: 3985

This classic text and standard reference comprises all subjects of a first-year graduate-level course, including in-depth coverage of groups and polynomials and extensive use of categories and functors. 1989 edition.

Basic Algebra I

Second Edition

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Author: Nathan Jacobson

Publisher: Courier Corporation

ISBN: 0486135225

Category: Mathematics

Page: 528

View: 8733

A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

Basic Modern Algebra with Applications

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Author: Mahima Ranjan Adhikari,Avishek Adhikari

Publisher: Springer Science & Business Media

ISBN: 8132215990

Category: Mathematics

Page: 637

View: 880

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Basic Algebraic Geometry 2

Schemes and Complex Manifolds

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Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 3642380107

Category: Mathematics

Page: 262

View: 5012

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

Progress in Commutative Algebra 2

Closures, Finiteness and Factorization

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Author: Christopher Francisco,Lee C. Klingler,Sean M. Sather-Wagstaff,Janet C. Vassilev

Publisher: Walter de Gruyter

ISBN: 311027860X

Category: Mathematics

Page: 325

View: 3025

This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.

Gender Consciousness and Privilege

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Author: Celeste Brody,Kasi Allen Fuller,Penny Poplin Gosetti,Susan Randles Moscato,Nancy Gail Nagel,Glennellen Pace,Patricia Schmuck

Publisher: Routledge

ISBN: 1135699038

Category: Education

Page: 192

View: 9842

Develops a new framework for working in schools that helps educators make informed decisions about change at individual, classroom, curricular and school levels on behalf of gender equity. Addresses the issue of understanding the impact of education on the two sexes, and looks at responsibility for creating gender-fair environments, organising work and creating environments for learning. The book draws on a two-year study into the role that gender played as three Catholic high schools prepared to move from single sex to coeducation. It does not weigh the advantages of single sex against coeducative approaches, but studies gender in a setting where the particpants' consciousness of gender issues was heightened: faculty and administration were formally and informally discussing gender concepts and students were talking about male and female issues. The book shows that the combination of leadership, staff and curricular awareness, and an understanding of gender fair and gender affirmative practices can serve to improve institutional effectiveness and lead to higher levels of student achievement.

Basic Algebra

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Author: Nathan Jacobson

Publisher: W H Freeman & Company

ISBN: N.A

Category: Mathematics

Page: 499

View: 5947

The second edition of a book designed to introduce mathematics students to abstract algebra.

An Introduction to Homological Algebra

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Author: Charles A. Weibel

Publisher: Cambridge University Press

ISBN: 113964307X

Category: Mathematics

Page: N.A

View: 7134

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.