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Algebra 2: Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier de Ramji Lal

Algebra 2: Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier: Infosys Science Foundation Series

Autor Ramji Lal
en Limba Engleză Hardback – 12 mai 2017
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 one-semester 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.
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Specificații

ISBN-13: 9789811042553
ISBN-10: 9811042551
Pagini: 432
Ilustrații: XVIII, 432 p.
Dimensiuni: 155 x 235 x 31 mm
Greutate: 0.81 kg
Ediția:1st ed. 2017
Editura: Springer Nature Singapore
Colecția Springer
Seriile Infosys Science Foundation Series, Infosys Science Foundation Series in Mathematical Sciences

Locul publicării:Singapore, Singapore

Cuprins

Chapter 1. Vector Space.- Chapter 2. Matrices and Linear Equations.- Chapter 3. Linear Transformations.- Chapter 4. Inner Product Space.- Chapter 5. Determinants and Forms.- Chapter 6. Canonical Forms, Jordan and Rational Forms.- Chapter 7. General Linear Algebra.- Chapter 8. Field Theory, Galois Theory.- Chapter 9. Representation Theory of Finite Groups.- Chapter 10. Group Extensions and Schur Multiplier.

Recenzii

“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 third-year course in algebra at most universities worldwide, and that for both instructors and students likewise.” (Werner Kleinert, zbMATH 1369.00003, 2017)

Notă biografică

RAMJI LAL is an adjunct professor at the Harish-Chandra 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 K-theory and representation theory.

Textul de pe ultima copertă

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 one-semester 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. 

Caracteristici

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 Includes supplementary material: sn.pub/extras