Concrete Algebra With a View Toward Abstract Algebra

✍ Scribed by Benjamin McKay

• Year: 2019
• Tongue: English
• Leaves: 324
• Series: lecture notes
• Edition: version 7 Sep 2019
• Category: Library

✦ Table of Contents

1 The integers......Page 9
2 Mathematical induction......Page 17
3 Greatest common divisors......Page 27
4 Prime numbers......Page 31
5 Modular arithmetic......Page 35
6 Secret messages......Page 49
7 Rational, real and complex numbers......Page 55
8 Polynomials......Page 61
9 Real polynomials, complex polynomials......Page 69
10 Factoring polynomials......Page 81
11 Fields......Page 89
12 Field extensions......Page 97
13 Resultants and discriminants......Page 105
14 Permuting roots......Page 119
15 Permutations......Page 131
16 Young diagrams......Page 139
17 Groups......Page 153
18 Rings......Page 177
19 Galois theory......Page 185
20 Algebraic curves in the plane......Page 191
21 Where plane curves intersect......Page 201
22 Quotient rings......Page 209
23 Field extensions and algebraic curves......Page 217
24 The projective plane......Page 221
25 Algebraic curves in the projective plane......Page 229
26 Families of plane curves......Page 243
27 Elliptic curves......Page 253
28 The tangent line......Page 257
29 Inflection points......Page 267
30 Conics and quadratic forms......Page 275
31 Projective duality......Page 281
32 Polynomial equations have solutions......Page 283
Hints......Page 287
Bibliography......Page 315
List of notation......Page 317
BookmarkTitle:......Page 319