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ELEMENTS OF MODERN ALGEBRA 7e, with its user-friendly format, provides you with the tools you need to get 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.
Table of Contents
|Properties of Composite Mappings (Optional)||p. 25|
|Binary Operations||p. 30|
|Permutations and Inverses||p. 37|
|Key Words and Phrases||p. 62|
|A Pioneer in Mathematics: Arthur Cayley||p. 62|
|The Integers||p. 65|
|Postulates for the Integers (Optional)||p. 65|
|Mathematical Induction||p. 71|
|Prime Factors and Greatest Common Divisor||p. 86|
|Congruence of Integers||p. 95|
|Congruence Classes||p. 107|
|Introduction to Coding Theory (Optional)||p. 114|
|Introduction to Cryptography (Optional)||p. 123|
|Key Words and Phrases||p. 134|
|A Pioneer in Mathematics: Blaise Pascal||p. 135|
|Definition of a Group||p. 137|
|Properties of Group Elements||p. 145|
|Cyclic Groups||p. 163|
|Key Words and Phrases||p. 188|
|A Pioneer in Mathematics: Niels Henrik Abel||p. 189|
|More on Groups||p. 191|
|Finite Permutation Groups||p. 191|
|Cayley's Theorem||p. 205|
|Permutation Groups in Science and Art (Optional)||p. 208|
|Cosets of a Subgroup||p. 215|
|Normal Subgroups||p. 223|
|Quotient Groups||p. 230|
|Direct Sums (Optional)||p. 239|
|Some Results on Finite Abelian Groups (Optional)||p. 246|
|Key Words and Phrases||p. 255|
|A Pioneer in Mathematics: Augustin Louis Cauchy||p. 256|
|Rings, Integral Domains, and Fields||p. 257|
|Definition of a Ring||p. 257|
|Integral Domains and Fields||p. 270|
|The Field of Quotients of an Integral Domain||p. 276|
|Ordered Integral Domains||p. 284|
|Key Words and Phrases||p. 291|
|A Pioneer in Mathematics: Richard Dedekind||p. 292|
|More on Rings||p. 293|
|Ideals and Quotient Rings||p. 293|
|Ring Homomorphisms||p. 303|
|The Characteristic of a Ring||p. 313|
|Maximal Ideals (Optional)||p. 319|
|Key Words and Phrases||p. 324|
|A Pioneer in Mathematics: Amalie Emmy Noether||p. 324|
|Real and Complex Numbers||p. 325|
|The Field of Real Numbers||p. 325|
|Complex Numbers and Quaternions||p. 333|
|De Moivre's Theorem and Roots of Complex Numbers||p. 343|
|Key Words and Phrases||p. 352|
|A Pioneer in Mathematics: William Rowan Hamilton||p. 353|
|Polynomials over a Ring||p. 355|
|Divisibility and Greatest Common Divisor||p. 367|
|Factorization in F[x]||p. 375|
|Zeros of a Polynomial||p. 384|
|Solution of Cubic and Quartic Equations by Formulas (Optional)||p. 397|
|Algebraic Extensions of a Field||p. 409|
|Key Words and Phrases||p. 421|
|A Pioneer in Mathematics: Carl Friedrich Gauss||p. 422|
|The Basics of Logic||p. 423|
|Answers to True/False and Selected Computational Exercises||p. 435|
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