Elements of Algebra: Geometry, Numbers, Equations

Contents......Page all_18572_to_00191.cpc0007.djvu
Preface......Page all_18572_to_00191.cpc0005.djvu
1.2 Straightedge and Compass Constructions......Page all_18572_to_00191.cpc0011.djvu
1.3 The Constructible Numbers......Page all_18572_to_00191.cpc0015.djvu
1.4 Some Famous Constructible Figures......Page all_18572_to_00191.cpc0017.djvu
1.5 The Classical Construction Problems......Page all_18572_to_00191.cpc0020.djvu
1.6 Quadratic and Cubic Equations......Page all_18572_to_00191.cpc0021.djvu
1.7 Quartic Equations......Page all_18572_to_00191.cpc0023.djvu
1.8 Solution by Radicals......Page all_18572_to_00191.cpc0024.djvu
1.9 Discussion......Page all_18572_to_00191.cpc0025.djvu
2.1 Natural Numbers......Page all_18572_to_00191.cpc0028.djvu
2.2 Integers and Rational Numbers......Page all_18572_to_00191.cpc0030.djvu
2.3 Divisibility......Page all_18572_to_00191.cpc0032.djvu
2.4 The Euclidean Algorithm......Page all_18572_to_00191.cpc0033.djvu
2.5 Unique Prime Factorisation......Page all_18572_to_00191.cpc0035.djvu
2.6 Congruences......Page all_18572_to_00191.cpc0036.djvu
2.7 Rings and Fields of Congruence Classes......Page all_18572_to_00191.cpc0038.djvu
2.8 The Theorems of Fermat and Euler......Page all_18572_to_00191.cpc0039.djvu
2.9 Fractions and the Euler Phi Function......Page all_18572_to_00191.cpc0042.djvu
2.10 Discussion......Page all_18572_to_00191.cpc0044.djvu
3.1 Irrational Numbers......Page all_18572_to_00191.cpc0048.djvu
3.2 Existence and Meaning of Irrational Numbers......Page all_18572_to_00191.cpc0050.djvu
3.3 The Real Numbers......Page all_18572_to_00191.cpc0051.djvu
3.4 Arithmetic and Rational Functions on R......Page all_18572_to_00191.cpc0052.djvu
3.5 Continuity and Completeness......Page all_18572_to_00191.cpc0054.djvu
3.6 Complex Numbers......Page all_18572_to_00191.cpc0056.djvu
3.7 Regular Polygons......Page all_18572_to_00191.cpc0058.djvu
3.8 The Fundamental Theorem of Algebra......Page all_18572_to_00191.cpc0061.djvu
3.9 Discussion......Page all_18572_to_00191.cpc0063.djvu
4.1 Polynomials over a Field......Page all_18572_to_00191.cpc0067.djvu
4.2 Divisibility......Page all_18572_to_00191.cpc0068.djvu
4.3 Unique Factorisation......Page all_18572_to_00191.cpc0071.djvu
4.4 Congruences......Page all_18572_to_00191.cpc0072.djvu
4.5 The Fields F(\alpha)......Page all_18572_to_00191.cpc0073.djvu
4.6 Gauss's Lemma......Page all_18572_to_00191.cpc0075.djvu
4.7 Eisenstein's Irreducibility Criterion......Page all_18572_to_00191.cpc0077.djvu
4.8 Cyclotomic Polynomials......Page all_18572_to_00191.cpc0079.djvu
4.9 Irreducibility of Cyclotomic Polynomials......Page all_18572_to_00191.cpc0081.djvu
4.10 Discussion......Page all_18572_to_00191.cpc0083.djvu
5.2 Algebraic Numbers and Fields......Page all_18572_to_00191.cpc0086.djvu
5.3 Algebraic Elements over an Arbitrary Field......Page all_18572_to_00191.cpc0087.djvu
5.4 Degree of a Field over a Subfield......Page all_18572_to_00191.cpc0088.djvu
5.5 Degree of an Iterated Extension......Page all_18572_to_00191.cpc0091.djvu
5.6 Degree of Constructible Numbers......Page all_18572_to_00191.cpc0093.djvu
5.7 Regular n-gons......Page all_18572_to_00191.cpc0095.djvu
5.8 Discussion......Page all_18572_to_00191.cpc0096.djvu
6.1 Ring and Field Isomorphisms......Page all_18572_to_00191.cpc0099.djvu
6.2 Isomorphisms of Q(\alpha) and F(\alpha)......Page all_18572_to_00191.cpc0101.djvu
6.3 Extending Fields and Isomorphisms......Page all_18572_to_00191.cpc0104.djvu
6.4 Automorphisms and Groups......Page all_18572_to_00191.cpc0107.djvu
6.5 Function Fields and Symmetric Functions......Page all_18572_to_00191.cpc0108.djvu
6.6 Cyclotomic Fields......Page all_18572_to_00191.cpc0110.djvu
6.7 The Chinese Remainder Theorem......Page all_18572_to_00191.cpc0111.djvu
6.8 Homomorphisms and Quotient Rings......Page all_18572_to_00191.cpc0113.djvu
6.9 Discussion......Page all_18572_to_00191.cpc0115.djvu
7.1 Why Groups?......Page all_18572_to_00191.cpc0118.djvu
7.2 Cayley's Theorem......Page all_18572_to_00191.cpc0119.djvu
7.3 Abelian Groups......Page all_18572_to_00191.cpc0121.djvu
7.4 Dihedral Groups......Page all_18572_to_00191.cpc0122.djvu
7.5 Permutation Groups......Page all_18572_to_00191.cpc0125.djvu
7.6 Permutation Groups in Geometry......Page all_18572_to_00191.cpc0126.djvu
7.7 Subgroups and Cosets......Page all_18572_to_00191.cpc0129.djvu
7.8 Normal Subgroups......Page all_18572_to_00191.cpc0131.djvu
7.9 Homomorphisms......Page all_18572_to_00191.cpc0132.djvu
7.10 Discussion......Page all_18572_to_00191.cpc0135.djvu
8.1 Galois Groups......Page all_18572_to_00191.cpc0138.djvu
8.2 Solution by Radicals......Page all_18572_to_00191.cpc0140.djvu
8.3 Structure of Radical Extensions......Page all_18572_to_00191.cpc0142.djvu
8.4 Nonexistence of Solutions by Radicals when n \geq 5......Page all_18572_to_00191.cpc0144.djvu
8.5 Quintics with Integer Coefficients......Page all_18572_to_00191.cpc0146.djvu
8.6 Unsolvable Quintic Equations with Integer Coefficients......Page all_18572_to_00191.cpc0148.djvu
8.7 Primitive Roots......Page all_18572_to_00191.cpc0149.djvu
8.8 Finite Abelian Groups......Page all_18572_to_00191.cpc0151.djvu
8.9 Discussion......Page all_18572_to_00191.cpc0153.djvu
9.1 The Theorem of the Primitive Element......Page all_18572_to_00191.cpc0156.djvu
9.2 Conjugate Fields and Splitting Fields......Page all_18572_to_00191.cpc0158.djvu
9.3 Fixed Fields......Page all_18572_to_00191.cpc0160.djvu
9.4 Conjugate Intermediate Fields......Page all_18572_to_00191.cpc0162.djvu
9.5 Normal Extensions with Solvable Galois Group......Page all_18572_to_00191.cpc0164.djvu
9.6 Cyclic Extensions......Page all_18572_to_00191.cpc0165.djvu
9.7 Construction of the Radical Extension......Page all_18572_to_00191.cpc0166.djvu
9.8 Construction of Regular p-gons......Page all_18572_to_00191.cpc0167.djvu
9.9 Division of Arbitrary Angles......Page all_18572_to_00191.cpc0169.djvu
9.10 Discussion......Page all_18572_to_00191.cpc0170.djvu
References......Page all_18572_to_00191.cpc0172.djvu
Index......Page all_18572_to_00191.cpc0180.djvu