A Concrete Approach To Abstract Algebra,Student Solutions Manual (e-only)
A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.
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abelian apply Mathematical Induction bijection coefficient commutative conjugates contradiction divides divisible by 11 E-primes Eisenstein's Criterion element of G elements of order equivalence classes exists field over Q four elements function G g(x greatest common divisor groups of order hence homomorphism infinite number injective Intermediate Value Theorem irreducible in Q[x isomorphism Lagrange's Theorem linear factors linearly independent minimum polynomial monic divisors monic linear polynomials monic polynomials multiple roots multiplicative inverse multiply this equation need to show nonzero element nth root number of elements Observe plug positive integer prime factorization Q(VPT quadratic formula rational root test real numbers Reflexive relatively prime result holds root of f(x Section solutions solvable by radicals spanning set splitting field square subgroup subspace sum of terms suppose surjective symmetric tells Theorem 156 three elements three real roots vector space yields Zp[x