Descripciones mejoradas de Syndetics:

In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and other areas of mathematics -- analysis (the infinitesimal calculus) and geometry. Readers will see that the various areas of mathematics are not hermetically sealed off from each other and that most of the truly important achievements in mathematics have been the product of a fruitful interaction of different areas. Using this book, readers will gain a true understanding of the subject while being creative mathematically as opposed to simply imitating template problems.

Tabla de contenidos provista por Syndetics

• 0 Background(p. 7)
• Section 1 Geometry(p. 13)
• 1 What Is Congruence?(p. 14)
• 2 Some Two-Dimensional Geometry(p. 22)
• 3 Symmetry(p. 32)
• Section 2 Polynomials(p. 45)
• 4 The Root of It All(p. 46)
• 5 The Renaissance of Algebra(p. 49)
• 6 Complex Numbers(p. 59)
• 7 Symmetric Polynomials and The Fundamental Theorem of Algebra(p. 68)
• 8 Permutations and Lagrange's Theorem(p. 78)
• 9 Orbits and Cauchy's Formula(p. 86)
• 9A Hamilton's Quaternions (Optional)(p. 95)
• Section 3 Numbers(p. 101)
• 10 Back to Euclid(p. 102)
• 11 Euclid's Lemma for Polynomials(p. 113)
• 12 Fermat and the Rebirth of Number Theory(p. 122)
• 13 Lagrange's Theorem Revisited(p. 136)
• 14 Rings and Squares(p. 142)
• 14A More Rings and More Squares(p. 149)
• 15 Fermat's Last Theorem (for Polynomials)(p. 157)
• 15A Still more Fermat's Last Theorem (Optional)(p. 165)
• Section 4 The Grand Synthesis(p. 169)
• 16 Constructible Polygons and the Method of Mr. Gauss(p. 170)
• 17 Cyclotomic Fields and Linear Algebra(p. 177)
• 18 A Lagrange Theorem for Fields and Nonconstructibility(p. 191)
• 19 Galois Fields and the Fundamental Theorem of Algebra Revisited(p. 196)
• 20 Galois' Theory of Equations(p. 207)
• 21 The Galois Correspondence(p. 212)
• 22 Constructible Numbers and Solvable Equations(p. 217)
• Index(p. 223)