# Math 210 — Rings and Fields

Assignments are due on Thursday, at the beginning of class. The row that an assignment appears in is the day that it is due.

Date Topic Book Homework Practice Problems Tutorial Topic
Jan. 8 Introduction to the course
10 Induction §1.1   7, 11, 18
11 Division with remainder §1.2   2, 3, 4
15 The Greatest Common Divisor §1.2 6, 15
17 The extended Euclidean algorithm §1.2 H1 1, 8 Induction
18 Unique factorization §1.2 A1 12, 13, 14
22 Modular Arithmetic §1.3 5, 8, 9, 11
24 More modular arithmetic §1.3 H2 12, 16, 18 Gcd
25 Solving equations mod m §1.3 A2 20
29 The Chinese remainder theorem §1.3 21, 22, 23
31 Euler's theorem §1.3 H3 19, 30, 32 Working mod m
Feb. 1 Equivalence relations A3

5 The ring Z/mZ §1.4 1, 2, 3, 5
7 Fields §1.4 H4 13, 14, 16 T4
8 Sums of two squares A4
12 Catch-up day
14 Polynomial rings in one variable §3.1 H5 5, 6, 7, 8 Equivalence classes
15 Division with remainder §3.1 A5 1, 2
19
22
26 Unique factorization in polynomial rings   §3.2
28 Arithmetic mod m(x) H6 6a-c Midterm answers
29 The Chinese remainder theorem §3.1 A6 20b-c

Mar. 4 The ring F[x]/m(x)F[x]
6 Criteria for irreducibility of polynomials §3.3 H7 2, 10 roots of polynomials
7 Polynomial rings with more variables A7
11 Commutative rings §4.1 1, 2
13 Ring homomorphisms; ideals. §4.1 H8 4, 5, 6 T8
14 Examples of ideals §4.1 A8 13, 15, 16
18 Quotient rings §4.2 1, 2,
20 The homomorphism theorems §4.2 H9 3, 4, 5, 11 T9
21 Good Friday A9
25 More homomorphism theorems
27 Fields; maximal ideals §4.2 H10 13, 16, 17 T10
28 The Chinese remainder theorem A10

Apr. 1 The Gaussian integers §4.3 1, 10
3 Factorization in the Gaussian integers §4.3 H11 2, 12 T11
4 Principal ideal domains   A11

15   H12
16   A12