MTH 311/411 Real Analysis (Fall 2020):


Schedule (updated as the semester progresses):

Week of
| Topics | Remarks, Materials, Assignments

8/23 Introduction. Chapter 1:
§1.1 The Irrationality of √2.
§1.2 Preliminaries.
§1.3 The Axiom of Completeness.
Notes §1.1
Notes §1.2
Notes §1.3

8/30 §1.4 More on Completeness.
§1.5 Cardinality.
§1.6 Cantor's Theorem.
Notes §1.4
Notes §1.5
Notes §1.6

Homework 1 due 9/2:
All students: 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
Graduate (MTH 411) student:
in addition, do exer. 1.2.7 (c,d) and 1.2.11 (c)
(MTH 311 students are welcome to do these problems for extra credit.)
Latex template for homework: here.
Make sure to read homework guidelines.

Homework 1 Solutions

Quiz 1

9/6 Chapter 2:
§2.1 Rearrangements of Infinite Series.
§2.2 The Limit of a Sequence.
§2.3 Limit Theorems.
Notes §2.1
Notes §2.2
Notes §2.3

Homework 2 due 9/9:
All students: 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, 1.4.3, 1.4.4, 1.4.5
Graduate (MTH 411) student:
in addition, do exer. 1.3.4 (b), 1.3.5 (b), 1.3.10 (a)
(MTH 311 students are welcome to do these problems for extra credit.)

Homework 2 Solutions


9/13 §2.4 The Monotone Convergence Theorem
and Infinite Series.
§2.5 Subsequences.
Notes §2.4
Notes §2.5

Homework 3 due 9/16:
All students: read Sections 1.5, 1.6, 2.1, 2.2 and
do exer. 1.5.4 (a), 1.5.5, 1.5.6 (a), 1.6.6, 2.2.2, 2.2.6, 2.2.7
Graduate (MTH 411) student:
in addition, do exer. 1.5.6 (b), 1.5.8, 2.2.4
(MTH 311 students are welcome to do these problems for extra credit.)

Quiz 2

9/20 Homework 4 due 9/23:
All students: 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)
Graduate (MTH 411) student:
in addition, do exer. 2.3.6, 2.3.7 (d,c)
(MTH 311 students are welcome to do these problems for extra credit.)