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# Basic Algebra I (2E) by Nathan Jacobson

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Basic Algebra I (2E) written by Nathan Jacobson
"Nathan Jacobson Basic Algebra is two volumes must be regarded as a landmark in algebraical literature. The enormous wealth of material, the depth of treatment, and the masterly exposition render these volumes exceptionally valuable. All courses on algebra, from the second undergraduate year to the specialist studies for doctoral students, can benefit from this authoritative treatise by Professor Jacobson." Walter Ledermann, University of Sussex Volume1
A number of teachers and students of the text have communicated to the author corrections and suggestions for improvements as well as additional exercise. Especially noteworthy were suggestions send by Mr. Huah Chu of National Taiwan University, Professor J. D. Reid of Wesleyan University, Tsuneo Tamagawa of Yale University.
Firstly this text was start as introduction of some basic new ideas. Notable examples are the developement of category theory, which provides a useful frame work for a large part of mathematics, homological algebra and applications of model theory of algebra. It is now taken for grantd that the methodology of algebra is an essential tool in mathematics.
Basic Algebra 1 by Nathan jacobson explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as Lie and Jordan algebras, lattices, and Boolean algebras. Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication.

Book Detail :-
Title: Basic Algebra I
Edition: Second Edition
Author(s): Nathan Jacobson
Publisher: W H Freeman & Co (Sd)
Series:
Year: 1985
Pages: 259
Type: PDF
Language: English
ISBN: 0716714809,9780716714804
Country: US
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Author Nathan Jacobson (1910–1999) was an American mathematician. Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. Recognized as one of the leading algebraists of his generation, he wrote more than a dozen standard textbooks. He graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University in 1934. While working on his thesis, Non-commutative polynomials and cyclic algebras, he was advised by Joseph Wedderburn. Jacobson taught and researched at Bryn Mawr College (1935–1936), the University of Chicago (1936–1937), the University of North Carolina at Chapel Hill (1937–1943), and Johns Hopkins University (1943–1947) before joining Yale University in 1947. He remained at Yale University until his retirement.
He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He served as president of the American Mathematical Society from 1971 to 1973, and was awarded their highest honour, the Leroy P. Steele prize for lifetime achievement, in 1998. He was also vice-president of the International Mathematical Union from 1972 to 1974. Nathan Jacobson is Director of , Educational Technology, MAN FACTORS, INC, San Diego, California

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Book Contents :-
Basic Algebra I (2E) written by Nathan Jacobson cover the following topics.
0. Introduction: Concepts from Set Theory The Integers
1. Monoids and Groups
2. Rings
3. Modules Over a Principal Ideal Domain
4. Galois Theory of Equations
5. Real Polynomial Equations and Inequalities
6. Metric Vector Spaces and the Classical Groups
7. Algebras Over a Field
8. Lattices and Boolean Algebras
Appendix
Index

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