Algebra 2
Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier
Authors: Lal, Ramji
Free Preview Provides a concise and rigorous introduction to linear algebra
 Includes a large number of motivating illustrations and challenging exercises
 Is written by an expert with over 43 years of teaching experience of the subject
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 About this Textbook

This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for onesemester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics.
 About the authors

RAMJI LAL is an adjunct professor at the HarishChandra Research Institute (HRI), Allahabad, Uttar Pradesh. He started his research career at the Tata Institute of Fundamental Research (TIFR), Mumbai, and served the University of Allahabad in different capacities for over 43 years: as a professor, head of the department and the coordinator of the DSA program. He was associated with HRI, where he initiated a postgraduate (PG) program in mathematics and coordinated the Nurture Program of National Board for Higher Mathematics (NBHM) from 1996 to 2000. After his retirement from the University of Allahabad, he was an advisor cum adjunct professor at the Indian Institute of Information Technology (IIIT), Allahabad for over three years. His areas of interest include group theory, algebraic Ktheory and representation theory.
 Reviews

“The text is enhanced by a large number of examples and exercises, and the presentation of the material is equally lucid, detailed, rigorous and versatile. Together with Volume 1, this book forms a very solid and useful source for a first, second, and thirdyear course in algebra at most universities worldwide, and that for both instructors and students likewise.” (Werner Kleinert, zbMATH 1369.00003, 2017)
 Table of contents (10 chapters)


Vector Spaces
Pages 130

Matrices and Linear Equations
Pages 3171

Linear Transformations
Pages 7395

Inner Product Spaces
Pages 97129

Determinants and Forms
Pages 131193

Table of contents (10 chapters)
 Download Preface 1 PDF (47.3 KB)
 Download Sample pages 2 PDF (296.3 KB)
 Download Table of contents PDF (116 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Algebra 2
 Book Subtitle
 Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier
 Authors

 Ramji Lal
 Series Title
 Infosys Science Foundation Series in Mathematical Sciences
 Copyright
 2017
 Publisher
 Springer Singapore
 Copyright Holder
 Springer Nature Singapore Pte Ltd.
 eBook ISBN
 9789811042560
 DOI
 10.1007/9789811042560
 Hardcover ISBN
 9789811042553
 Softcover ISBN
 9789811350894
 Series ISSN
 23644036
 Edition Number
 1
 Number of Pages
 XVIII, 432
 Topics