Exam 1 will cover Sections 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3. The following items should be included in your preparation for Exam 1:
KNOW THE TEXTBOOK DEFINITIONS OF THE FOLLOWING: prime integer; composite integer; GCD of integers a, b (a, b not both zero); a is congruent to b mod n (a, b, n integers, n>1); ring; commutative ring; commutative ring with identity; integral domain; field; unit; zero divisor; subring; A ring R is isomorphic to a ring S if
State the Division Algorithm for Z (Theorem 1.1)
KNOW THE PROOFS OF THE FOLLOWING: Fact 2, Fact 3, Fact 4, Fact 5, Theorem 1.5, Theorem 2.3, Corollary 2.10, Theorem 3.3, Theorem 3.10
KNOW THE SOLUTIONS TO THE FOLLOWING KEYED HOMEWORK EXERCISES: 1.1.1, 1.1.8, 1.2.1, 1.2.14, 1.2.28, 1.3.1, 1.3.17, 1.4.1, 2.1.17, 2.1.19, 2.1.21, 2.2.7, 2.2.10, 3.1.5(d), 3.1.10, 3.1.13, 3.1.17, 3.1.19, 3.2.7(c ), 3.2.12(a), 3.2.26, 3.3.7 3.3.15
Exam 2 will cover Sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, and 5.2. The following items should be included in your preparation for Exam 2:
KNOW THE TEXTBOOK DEFINITIONS OF THE FOLLOWING: GCD of f(x) and g(x) (page 91); irreducible (page 95); reducible (page 95); root (page 101); congruence mod p(x) (page 119); congruence class (page 120); F[x]/(p(x)) (page 122)
KNOW THE PROOFS OF THE FOLLOWING: Fact 8, Fact 12, Fact 14, Fact 15, Fact 16, Theorem 4.2, Corollary 4.6, Theorem 4.7, Theorem 4.8, Theorem 4.14, Theorem 4.15, Corollary 4.18, Theorem 4.20, Lemma 4.28, Theorem 5.3, Theorem 5.9,
KNOW THE SOLUTIONS TO ALL KEYED HOMEWORK EXERCISES in Sections 4.1, 4.2, 4.3, 4.4, 4.5, 5.1, and 5.2
The final exam will cover Sections 3.1, 3.2,3.3, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, 5.2, 5.3, 7.1. The following items should be included in your preparation for the final:
KNOW THE TEXTBOOK DEFINITIONS OF THE FOLLOWING: ring (Page 42); commutative ring (Page 42); ring with identity (Page 43); integral domain (Page 46); field (Page 47); unit (Page 60); zero divisor (Page 62); A ring R is isomorphic to a ring S if....; GCD of f(x) and g(x) (page 91); irreducible (page 95); reducible (page 95); root (page 101); f(x) is congruent to g(x) mod p(x) (page 119); group (Page 163); Abelian group (Page 163.
State the Division Algorithm for F[x] (Theorem 4.4) and for Z (Theorem 1.1)
KNOW THE PROOFS OF THE FOLLOWING: Fact 8, Fact 19 (The number of this fact might be 18?), Theorem 3.3, Theorem 3.10, Theorem 4.2, Corollary 4.6, Theorem 4.7, Theorem 4.8, Theorem 4.14, Theorem 4.15, Corollary 4.18, Theorem 4.20, Lemma 4.28, Theorem 5.3, Theorem 5.9, Theorem 5.11.
KNOW THE SOLUTIONS TO THE FOLLOWING KEYED HOMEWORK EXERCISES: 3.1.5(d), 3.1.10, 3.1.13, 3.1.17, 3.2.7(c), 3.2.12(a), 3.2.26, 3.3.23, 3.3.28, 4.1.1, 4.1.3(a), 4.1.5(a)(c), 4.2.13, 4.2.14, 4.3.9, 4.4.24, 4.5.1, 4.5.4, 4.5.5, 4.5.7, 4.5.18, 4.6.3, 5.1.3, 5.1.10, 5.1.12, 5.2.5, 5.2.8, 5.2.11, 5.3.1, 5.3.4, 5.3.6, 5.3.9, 7.1.6, 7.1.16, 7.1.21.