Name: Elements of Modern Algebra By Linda Gilbert (University of South Carolina, Upstate)
SKU: 9781285463230
Price: 40.98 USD
Availability: InStock

Elements of Modern Algebra Summary

Elements of Modern Algebra by Linda Gilbert (University of South Carolina, Upstate)

ELEMENTS OF MODERN ALGEBRA, Eighth Edition, with its user-friendly format, provides you with the tools you need to succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem-solving skills.

Elements of Modern Algebra Reviews

1. FUNDAMENTALS. Sets. Mappings. Properties of Composite Mappings (Optional). Binary Operations. Permutations and Inverses. Matrices. Relations. 2. THE INTEGERS. Postulates for the Integers (Optional). Mathematical Induction. Divisibility. Prime Factors and Greatest Common Divisor. Congruence of Integers. Congruence Classes. Introduction to Coding Theory (Optional). Introduction to Cryptography (Optional). 3. GROUPS. Definition of a Group. Properties of Group Elements. Subgroups. Cyclic Groups. Isomorphisms. Homomorphisms. 4. MORE ON GROUPS. Finite Permutation Groups. Cayley's Theorem. Permutation Groups in Science and Art (Optional). Cosets of a Subgroup. Normal Subgroups. Quotient Groups. Direct Sums (Optional). Some Results on Finite Abelian Groups (Optional). 5. RINGS, INTEGRAL DOMAINS, AND FIELDS. Definition of a Ring. Integral Domains and Fields. The Field of Quotients of an Integral Domain. Ordered Integral Domains. 6. MORE ON RINGS. Ideals and Quotient Rings. Ring Homomorphisms. The Characteristic of a Ring. Maximal Ideals (Optional). 7. REAL AND COMPLEX NUMBERS. The Field of Real Numbers. Complex Numbers and Quaternions. De Moivre's Theorem and Roots of Complex Numbers. 8. POLYNOMIALS. Polynomials over a Ring. Divisibility and Greatest Common Divisor. Factorization in _F[x]_ . Zeros of a Polynomial. Solution of Cubic and Quartic Equations by Formulas (Optional). Algebraic Extensions of a Field.

About Linda Gilbert (University of South Carolina, Upstate)

Linda Gilbert received her Ph.D. from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband Jimmie Gilbert, including ELEMENTS OF MODERN ALGEBRA and LINEAR ALGEBRA and MATRIX THEORY (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra.

1. FUNDAMENTALS. Sets. Mappings. Properties of Composite Mappings (Optional). Binary Operations. Permutations and Inverses. Matrices. Relations. 2. THE INTEGERS. Postulates for the Integers (Optional). Mathematical Induction. Divisibility. Prime Factors and Greatest Common Divisor. Congruence of Integers. Congruence Classes. Introduction to Coding Theory (Optional). Introduction to Cryptography (Optional). 3. GROUPS. Definition of a Group. Properties of Group Elements. Subgroups. Cyclic Groups. Isomorphisms. Homomorphisms. 4. MORE ON GROUPS. Finite Permutation Groups. Cayley's Theorem. Permutation Groups in Science and Art (Optional). Cosets of a Subgroup. Normal Subgroups. Quotient Groups. Direct Sums (Optional). Some Results on Finite Abelian Groups (Optional). 5. RINGS, INTEGRAL DOMAINS, AND FIELDS. Definition of a Ring. Integral Domains and Fields. The Field of Quotients of an Integral Domain. Ordered Integral Domains. 6. MORE ON RINGS. Ideals and Quotient Rings. Ring Homomorphisms. The Characteristic of a Ring. Maximal Ideals (Optional). 7. REAL AND COMPLEX NUMBERS. The Field of Real Numbers. Complex Numbers and Quaternions. De Moivre's Theorem and Roots of Complex Numbers. 8. POLYNOMIALS. Polynomials over a Ring. Divisibility and Greatest Common Divisor. Factorization in _F[x]_ . Zeros of a Polynomial. Solution of Cubic and Quartic Equations by Formulas (Optional). Algebraic Extensions of a Field.

Additional information

Sku

CIN1285463234G

ISBN 13

9781285463230

ISBN 10

1285463234

Title

Elements of Modern Algebra by Linda Gilbert (University of South Carolina, Upstate)

Author

Linda Gilbert (University of South Carolina, Upstate)

Condition

Used - Good

Binding type

Hardback

Publisher

Cengage Learning, Inc

Year published

20140101

Number of pages

528

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

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

Elements of Modern Algebra Linda Gilbert (University of South Carolina, Upstate)

Elements of Modern Algebra by Linda Gilbert (University of South Carolina, Upstate)

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Elements of Modern Algebra Summary

Elements of Modern Algebra by Linda Gilbert (University of South Carolina, Upstate)

Elements of Modern Algebra Reviews

About Linda Gilbert (University of South Carolina, Upstate)

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