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Algebra


1. 

Handbook of Linear Algebra, Second Edition

Handbook of Linear Algebra, Second Edition

By: Leslie Hogben

Publisher: Chapman and Hall/CRC

Publication Date: 26-NOV-2013

Insert Date: 18-APR-2014

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With a substantial amount of new material, this best-selling handbook provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides readers from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition includes 20 new chapters that cover combinatorial matrix theory topics, numerical linear algebra topics, more applications of linear algebra, the use of Sage for linear algebra, and much more. ...

2. 

Linear Algebra: Concepts and Methods

Linear Algebra: Concepts and Methods

By: Martin Anthony; Michele Harvey

Publisher: Cambridge University Press

Publication Date: 10-MAY-2012

Insert Date: 23-JAN-2014

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Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments....

3. 

The Humongous Book of Algebra Problems

The Humongous Book of Algebra Problems

By: W. Michael Kelley

Publisher: Alpha

Publication Date: 07-NOV-2013

Insert Date: 19-OCT-2013

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When the numbers just don't add up... Following in the footsteps of the successful The Humongous Books of Calculus Problems , bestselling author Michael Kelley has taken a typical algebra workbook, and made notes in the margins, adding missing steps and simplifying concepts and solutions. Students will learn how to interpret and solve problems as they are typically presented in algebra courses-and become prepared to solve those problems that were never discussed in class but always seem to find their way onto exams. Annotations throughout the text clarify each problem and fill in...

4. 

Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras

Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras

By: F.F. Bonsall; J. Duncan

Publisher: Cambridge University Press

Publication Date: 02-MAR-1971

Insert Date: 05-OCT-2013

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The theory of the numerical range of a linear operator on an arbitrary normed space had its beginnings around 1960, and during the 1970s the subject has developed and expanded rapidly. This book presents a self-contained exposition of the subject as a whole. The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures. ...

5. 

Handbook of Categorical Algebra

Handbook of Categorical Algebra

By: Francis Borceux

Publisher: Cambridge University Press

Publication Date: 03-NOV-1994

Insert Date: 05-OCT-2013

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The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred...

6. 

Universal Algebra: Fundamentals and Selected Topics

Universal Algebra: Fundamentals and Selected Topics

By: Clifford Bergman

Publisher: Chapman and Hall/CRC

Publication Date: 20-SEP-2011

Insert Date: 28-AUG-2013

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Starting with the most basic notions, this text introduces all the key elements needed to read and understand current research in the field. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, clones, and free algebras. The second part covers topics that demonstrate the power and breadth of the subject, such as Jónsson’s lemma, finitely and nonfinitely based algebras, primal and quasiprimal algebras, Murskiĭ’s theorem, and directly representable varieties. Examples and exercises are...

7. 

Algebraic Number Theory, Second Edition

Algebraic Number Theory, Second Edition

By: Richard Mollin

Publisher: Chapman and Hall/CRC

Publication Date: 05-JAN-2011

Insert Date: 28-AUG-2013

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Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard’s cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and...

8. 

Jordan Canonical Form

Jordan Canonical Form

By: Steven H. Weintraub

Publisher: Morgan & Claypool Publishers

Publication Date: 08-DEC-2009

Insert Date: 23-AUG-2013

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Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of...

9. 

1001 Algebra II Practice Problems For Dummies

1001 Algebra II Practice Problems For Dummies

By: 

Publisher: For Dummies

Publication Date: 04-JUN-2013

Insert Date: 21-AUG-2013

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Practice makes perfect—and helps deepen your understanding of algebra II by solving problems 1001 Algebra II Practice Problems For Dummies takes you beyond the instruction and guidance offered in Algebra II For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in algebra II. Plus, an online component provides you with a collection of algebra problems presented in multiple choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in Algebra II class Helps you refine your...

10. 

Modern Computer Algebra, Third Edition

Modern Computer Algebra, Third Edition

By: Joachim von zur Gathen; Jürgen Gerhard

Publisher: Cambridge University Press

Publication Date: 25-APR-2013

Insert Date: 31-JUL-2013

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Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the "bible of computer algebra", gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time...

11. 

Solving Polynomial Equation Systems II

Solving Polynomial Equation Systems II

By: Teo Mora

Publisher: Cambridge University Press

Publication Date: 05-MAY-2005

Insert Date: 30-JUL-2013

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The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in issues of implementation. The same language describes the applications of Groebner technology to the central problems of commutative algebra. The book can be also used as a reference on elementary ideal theory and a source for the state-of-the-art in...

12. 

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

By: Yves Crama; Peter L. Hammer

Publisher: Cambridge University Press

Publication Date: 28-JUN-2010

Insert Date: 30-JUL-2013

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This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language,...

13. 

An Introduction to Homological Algebra

An Introduction to Homological Algebra

By: Charles A. Weibel

Publisher: Cambridge University Press

Publication Date: 29-APR-1994

Insert Date: 11-JUL-2013

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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...

14. 

Basic Abstract Algebra

Basic Abstract Algebra

By: P. B. Bhattacharya; S. K. Jain; S. R. Nagpaul

Publisher: Cambridge University Press

Publication Date: 25-NOV-1994

Insert Date: 11-JUL-2013

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This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains...

15. 

Matrix Analysis, Second Edition

Matrix Analysis, Second Edition

By: Roger A. Horn; Charles R. Johnson

Publisher: Cambridge University Press

Publication Date: 31-OCT-2012

Insert Date: 04-JUN-2013

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Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of this acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of...

16. 

A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory

A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory

By: Bangming Deng; Jie Du; Qiang Fu

Publisher: Cambridge University Press

Publication Date: 31-DEC-2012

Insert Date: 04-JUN-2013

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The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the...

17. 

Local Cohomology, Second Edition

Local Cohomology, Second Edition

By: M. P. Brodmann; R. Y. Sharp

Publisher: Cambridge University Press

Publication Date: 30-NOV-2012

Insert Date: 04-JUN-2013

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This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum–Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton–Hansen Connectedness Theorem for projective varieties,...

18. 

Algebra I: A Basic Course in Abstract Algebra

Algebra I: A Basic Course in Abstract Algebra

By: Rajendra Kumar Sharma; Sudesh Kumari Shah; Asha Gauri Shankar

Publisher: Pearson Education India

Publication Date: 30-JUN-2011

Insert Date: 14-MAY-2013

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Algebra is a compulsory paper offered to the undergraduate students of Mathematics. The majority of universities offer the subject as a two /three year paper or in two/three semesters. Algebra I: A Basic Course in Abstract Algebra covers the topic required for a basic course. ...

19. 

Algebra: Abstract and Modern

Algebra: Abstract and Modern

By: U. M. Swamy; A. V. S. N. Murthy

Publisher: Pearson Education India

Publication Date: 02-FEB-2012

Insert Date: 14-MAY-2013

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Algebra: Abstract and Modern, spread across 16 chapters, introduces the reader to the preliminaries of algebra and then explains topics like group theory and field theory in depth. It also features a blend of numerous challenging exercises and examples that further enhance each chapter. Covering all the necessary topics on the subject, this text is an ideal text book for an undergraduate course on mathematics. ...

20. 

Vectors, Pure and Applied

Vectors, Pure and Applied

By: T. W. Körner

Publisher: Cambridge University Press

Publication Date: 31-DEC-2012

Insert Date: 25-APR-2013

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Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online. ...