Concrete Algebra With a View Toward Abstract Algebra

✍ Scribed by Benjamin McKay

• Year: 2021
• Tongue: English
• Leaves: 350
• Series: Lecture notes
• Edition: version August 26, 2021
• Category: Library

✦ Table of Contents

1 The integers
2 Mathematical induction
3 Greatest common divisors
4 Prime numbers
5 Modular arithmetic
6 The Chinese remainder theorem
7 Secret messages
8 Rational, real and complex numbers
9 Polynomials
10 Real polynomials, complex polynomials
11 Factoring polynomials
12 Fields
13 Field extensions
14 Formal power series
15 Resultants and discriminants
16 Permuting roots
17 Rings
18 Galois theory
19 Plane algebraic curves
20 Where plane curves intersect
21 Quotient rings
22 Field extensions and algebraic curves
23 The projective plane
24 Algebraic curves in the projective plane
25 Families of plane curves
26 Elliptic curves
27 The tangent line
28 Inflection points
29 Conics and quadratic forms
30 Projective duality
31 Polynomial equations have solutions
32 Blow up
33 Schubert calculus
34 More projective planes
Hints
Bibliography
List of notation
Index