# Rings and Fields MATH 210, Winter 2018

 Home Schedule and Homework
 Week Date Topic Section Exercises Homework 09.01 Introduction to the course A, B B: 11, 20, 24, 27 1 11.01 Induction C 10, 13, 14, 15 12.01 Well-ordering principle C Assignment 1 16.01 Division 1.1 5, 8, 9 Solutions 1 2 18.01 Greatest Common Divisor 1.2 5, 9, 11, 13 Notes 1 19.01 Euclid's Algorithm 1.2 15, 21, 28, 30 Assignment 2 23.01 Primes and unique factorization 1.3 15, 18, 21, 26, 30, 34 - 36 Solutions 2 3 25.01 Equivalence relations D 6, 9, 13, 17, 21 26.01 Congruences 2.1 5, 19, 20, 22 Assignment 3 30.01 Modular arithmetic 2.2 7, 8, 14, 15 Solutions 3 4 01.02 Structure of Zm 2.3 1, 2, 15, 18 02.02 Rings: definition 3.1 5, 13, 25, 37 Assignment 4 06.02 Rings: basic properties 3.2 4, 13, 21, 44 Solutions 4 5 08.02 Homomorphisms 3.3 12, 13, 17, 34 09.02 Chinese remainder theorem 14.1 11, 14, 19, 21 Assignment 5 13.02 The Euler function Solutions 5 6 15.02 Polynomial 4.1 5, 11, 14, 19 16.02 Division of polynomials 4.2 4, 5, 6, 7 Assignment 6 Reading week 27.02 GCD of polynomials 4.2 8, 10, 14, 16 Solutions 6 7 01.03 Unique factorization 4.3 3, 6, 10, 23 02.03 Polynomial functions. Roots 4.4 3, 8, 19, 25 Assignment 7 02.03 Midterm 17:00 - 18:30 Solutions 06.03 Z[X] and Q[X]. I 4.5 1, 5, 11, 13 Solutions 7 8 08.03 Z[X] and Q[X]. II 4.5 15, 16, 17, 19 09.03 R[X] and C[X] 4.6 1, 2, 3, 5 Assignment 8 13.03 Congruences in F[X] 5.1 1, 3, 5, 12 Solutions 8 9 15.03 F[X]/m(X) 5.2 5, 10, 14, 15 16.03 Structure of F[X]/m(X) 5.3 2, 5, 9, 12 Assignment 9 20.03 Ideals and congruence 6.1 4, 8, 17, 36 Solutions 9 10 22.03 Quotient rings 6.2 12, 14, 19, 24 23.03 Homomorphisms 6.2 3, 6, 17 Assignment 10 27.03 Isomorphism Theorems 6.2 29, 30, 31 Solutions 10 11 29.03 R/I when I is prime or maximal 6.3 12, 14, 21, 22 30.03 Good Friday Assignment 11 03.04 Chinese remainder theorem 14.3 3, 4, 5, 6 Solutions 11 12 05.04 Euclidean domains and PIDs 10.1 12, 19, 22 06.04 PIDs and UFDs 10.2 13, 17, 19 15.04 Review 5 - 7 Stirling 414 19.04 Review 4 - 6 Stirling 414 21.04 Final Exam 7 - 10