MTH 311 Real Analysis (Fall 2022):


Schedule (updated as the semester progresses):

Week of
| Topics to Read | Remarks, Materials, Assignments

8/29 Introduction. Chapter 1:
§1.1 The Irrationality of √2.
§1.2 Preliminaries.
§1.3 The Axiom of Completeness.
Notes for §1.1
Notes for §1.2
Notes for §1.3

Homework Guidelines

9/5 No class on Monday (Labor Day)

§1.4 More on Completeness.
§1.5 Cardinality.
Notes for §1.4
Notes for §1.5

Homework 1 due 9/7:
Read Sections 1.2, 1.3 and do
exer. 1.2.1, 1.2.5, 1.2.7 (a,b), 1.2.8, 1.2.11 (a,b), 1.2.12, 1.3.1
Latex template for homework: here

Homework 1 Solutions

9/12 §1.6 Cantor's Theorem.
Chapter 2:
§2.1 Rearrangements of Infinite Series.
§2.2 The Limit of a Sequence.
Notes for §1.6
Notes for §2.1
Notes for §2.2

Homework 2 due 9/14:
Read Sections 1.3, 1.4 and do
exer. 1.3.2, 1.3.4 (a), 1.3.5 (a), 1.3.8, 1.4.1, 1.4.4, Bonus: 1.4.5

Homework 2 Solutions

9/19 §2.3 Limit Theorems.
§2.4 The Monotone Convergence Theorem
and Infinite Series.
§2.5 Subsequences.
Notes for §2.3

Homework 3 due 9/21:
Read Sections 1.5, 1.6, 2.1, 2.2 and do
exer. 1.5.5 (c), 1.6.6, 2.2.2, 2.2.6, 2.2.7 (a,b), Bonus: 1.5.4 (a)

9/26 Homework 4 due 9/30:
Read Sections 2.3, 2.4 and do
exer. 2.3.1, 2.3.3, 2.3.4 (b,c), 2.3.7 (a,b,c), Bonus: 2.3.7 (d,e)