Math 451 Winter 2021

Homework 1: Due Thursday 01/28 and Tuesday 02/02

Read Chapter 1 Sections 1-4.

Sign up by posting your name under one of the problem discussions on Canvas. All problems are referring to Chapter 1. If there are already 2 people signed up for that problem, choose a different problem.

By Thursday on 01/28, please post a neatly written and scanned solution of that problem to that Canvas discussion.

By Tuesday 02/02, please comment on and check for correctness a solution posted to a problem that is not yours. If there are already 2 people checking that problem, please check a different problem.

Homework 2: Due Thursday 02/04

Chapter 1: 2.5, 3.5(b), 3.6, 3.7(c), 4.3(j,m,q), 4.4(j,m,q), 4.7, 4.8, 4.14(a)

Chapter 2: 7.1(a,b,c)

Note: No proofs/explanations needed for problems 4.3(j,m,q), 4.4(j,m,q) or 7.1(a,b,c).

Homework 3: Due Thursday 02/11

Chapter 1: 3.8, 4.10

Notes: Prove the "Fact" at the bottom of page 29 of the notes

Read Chapter 1, Section 5 and Chapter 2, Sections 7 and 8

Chapter 2: 7.3(e,j,o), 7.5, 8.2(a,c)

For 8.2(a,c), you may use the convergence definition in class for sequences in Q or the definition from the book Sections 7,8.

Homework 4: Due Thursday 02/18

Chapter 2: 8.6(a), 8.8(c), 8.9(b,c), 8.10, 9.6, 10.10. For 8.9(c), you may assume 8.9(a).

Read and use example 6 of Section 8 to prove Lemma 9.5 in Section 9.

Prove if a_{n} converges to a, then a_{n+k} converges to a.

Homework 5: Due Thursday 02/25

Prove the Fact on page 46 of the notes.

Chapter 2: 9.15, 10.12, 11.4 (no proof needed), 11.11, 12.3 (no proof needed), 14.5

In a problem, when the book says "show..." it means to prove the statement.

Homework 6: Due Thursday 03/04

Do Case 2 or Case 3 of the proof of pages 61-62.

Chapter 2: 14.1(a,b,c), 14.6(a), 14.7, 14.9, 14.12, 14.14

(Optional) Prove the "homework" part of the proof stated on page 65. The proof starts on page 64 and ends on page 65.

Prepare for the take-home midterm that starts on March 5!

Homework 7: Due Monday 03/22

Do the worksheet on limits attached below. Read Section 20 of the book.

Chapter 3: 17.8 (a,c), 17.9(b,d), 17.13(b), 17.14, 18.6, 18.10, 20.16

Homework 8: Due Thursday 04/01

Chapter 5: 28.3(b), 28.4(a,b), 29.3, 29.5, 29.11, 29.13, 31.1

Homework 9: Due Monday 04/19

Chapter 6: 32.2, 32.8, 33.5, 33.7, 33.8(a), 34.2, 34.5