Algebra 2

Linear Algebra, Galois Theory, Representation theory, Group extensions and Schur Multiplier

Ramji Lal (Autor)

Buch | Hardcover

432 Seiten

2017 | 1st ed. 2017
Springer Verlag, Singapore
978-981-10-4255-3 (ISBN)

Artikel merken

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.

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.

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.

Erscheinungsdatum	25.05.2017
Reihe/Serie	Infosys Science Foundation Series
	Infosys Science Foundation Series
	Infosys Science Foundation Series in Mathematical Sciences
	Infosys Science Foundation Series in Mathematical Sciences
Zusatzinfo	XVIII, 432 p.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Algebra • finite groups • Galois Theory • Group Extensions • Linear equations • Vector Space
ISBN-10	981-10-4255-1 / 9811042551
ISBN-13	978-981-10-4255-3 / 9789811042553
Zustand	Neuware