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Undergraduate Algebra Serge Lang

Undergraduate Algebra By Serge Lang

Undergraduate Algebra by Serge Lang

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Undergraduate Algebra Summary

Undergraduate Algebra by Serge Lang

The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Undergraduate Algebra Reviews

From the reviews of the third edition: As is very typical for Professor Lang's self demand and style of publishing, he has tried to both improve and up-date his already well-established text. ... Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author's great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. ... The present textbook ... will remain one of the great standard introductions to the subject for beginners. (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)

Table of Contents

I The Integers.- 1. Terminology of Sets.- 2. Basic Properties.- 3. Greatest Common Divisor.- 4. Unique Factorization.- 5. Equivalence Relations and Congruences.- II Groups.- 1. Groups and Examples.- 2. Mappings.- 3. Homomorphisms.- 4. Cosets and Normal Subgroups.- 5. Permutation Groups.- 6. Cyclic Groups.- 7. Finite Abelian Groups,.- III Rings.- 1. Rings.- 2. Ideals.- 3. Homomorphisms.- 4. Quotient Fields.- IV Polynomials.- 1. Euclidean Algorithm.- 2. Greatest Common Divisor.- 3. Unique Factorization.- 4. Partial Fractions.- 5. Polynomials over the Integers.- 6. Transcendental Elements.- 7. Principal Rings and Factorial Rings.- V Vector Spaces and Modules.- 1. Vector Spaces and Bases.- 2. Dimension of a Vector Space.- 3. Matrices and Linear Maps.- 4. Modules.- 5. Factor Modules.- 6. Free Abelian Group.- VI Some Linear Groups.- 1. The General Linear Group.- 2. Structure of GL2(F).- 3. SL2(F).- VII Field Theory.- 1. Algebraic Extensions.- 2. Embeddings'.- 3. Splitting Fields'.- 4. Galois Theory.- 5. Quadratic and Cubic Extensions.- 6. Solvability by Radicals.- 7. Infinite Extensions.- VIII Finite Fields.- 1. General Structure.- 2. The Frobenius Automorphism.- 3. The Primitive Elements.- 4. Splitting Field and Algebraic Closure.- 5. Irreducibility of the Cyclotomic Equation over Q.- 6. Where Does It All Go? Or Rather, Where Does Some of It Go?.- IX The Real and Complex Numbers.- 1. Ordering of Rings.- 2. Preliminaries.- 3. Construction of the Real Numbers.- 4. Decimal Expansions.- 5. The Complex Numbers.- X Sets.- 1. More Terminology.- 2. Zona's Lemma.- 3. Cardinal Numbers.- 4. Well-ordering.- 1. The Natural Numbers.- 2. The Integers.- 3. Infinite Sets.

Additional information

CIN0387964045G
9780387964041
0387964045
Undergraduate Algebra by Serge Lang
Serge Lang
Undergraduate Texts in Mathematics
Used - Good
Hardback
Springer-Verlag New York Inc.
19861222
388
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Undergraduate Algebra