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
Notes for §2.4
Notes for §2.5

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)

Homework 3 Solutions

9/26 §2.6 The Cauchy Criterion.
§2.7 Properties of Infinite Series.
Notes for §2.6
Notes for §2.7

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)

Homework 4 Solutions

10/3 More on Infinite Series.
Chapter 3:
§3.1 The Cantor Set.
§3.2 Open and Closed Sets.
Notes for §3.1
Notes for §3.2

Exam I is on Friday, 10/7: study guide
(Exam I solutions )

10/10 No class on Friday (Fall Recess)

§3.2 Open and Closed Sets Continued.
Homework 5 due 10/11:
Read Sections 2.5, 2.6, 2.7 and do
exer. 2.5.1, 2.6.2, 2.7.2, 2.7.4, Bonus: 2.7.5.

Homework 5 Solutions

10/17 §3.3 Compact Sets.
§3.4 Perfect Sets and Connected Sets.

Chapter 4:
§4.1 Discussion.
§4.2 Functional Limits.
Notes for §3.3, 3.4
Notes for §4.1, 4.2

Homework 6 due 10/21:
Read Sections 3.2, 3.3, 3.4 and do
exer. 3.2.2, 3.2.3, 3.3.1, 3.3.2, 3.3.5 (a, b)
Bonus: 3.2.7 (b) and 3.3.5 (c)

Homework 6 Solutions

10/24 §4.3 Continuous Functions.
§4.4 Continuous Functions
on Compact Sets.
Notes for §4.3
Notes for §4.4

Homework 7 due 10/31:
Read Sections 4.1, 4.2 and
do exer. 4.2.1 (a,b), 4.2.5 (c,d), 4.2.7, 4.2.10
Bonus: 3.4.2 (from Section 3.4)

Homework 7 Solutions

10/31 §4.5 The Intermediate Value Theorem.

Chapter 5:
§5.1 Discussion
§5.2 Derivatives
Notes for §4.5
Notes for §5.2

Homework 8 due 11/9:
Read Sections 4.3, 4.4 and
do exer. 4.3.1, 4.3.6 (a,b,c), 4.4.1, 4.4.3, 4.4.7
Bonus: 4.3.6 (d,e)

Homework 8 Solutions

11/7 §5.3 The Mean Value Theorem

Chapter 6:
§6.1 Discussion
Notes for §5.3
Notes for §6.1

11/14 §6.2 Uniform Convergence

Review for Exam II
Exam II is on Wednesday, 11/16: study guide
(Exam II solutions )

Homework 9 due 11/18:
Read Sections 5.1, 5.2, 5.3 and
do exer. 5.2.1, 5.2.2, 5.2.5, 5.3.3
Bonus: 5.3.7

Homework 9 Solutions

11/21 §6.2 Uniform Convergence Continued

No class on Tuesday (Thursday schedule)

Thanksgiving Recess 11/23 - 11/27
Notes for §6.2

11/28 §6.3 Uniform Convergence and
Differentiation
§6.4 Series of Functions
§6.5 Power Series
Notes for §6.3
Notes for §6.4
Notes for §6.5

Homework 10 due 12/2:
Read Sections 6.1, 6.2, 6.3 and
do exer. 6.2.1, 6.2.3 (a,b), 6.2.9 (a), 6.3.1, 6.3.5 (a,b)
Bonus: 6.3.4

Homework 10 Solutions

12/5 §6.6 Taylor Series

Chapter 7:
The Riemann Integral
Notes for §6.6

Homework 11 due 12/9:
Read Sections 6.4 - 6.6 and
do exer. 6.4.6, 6.4.8, 6.5.1, 6.5.4, 6.6.2, 6.6.5
Bonus: 6.5.3

Homework 11 Solutions

12/12 Chapter 8:
Constructing R from Q

Final Exam:
12/14 (Wednesday) 10:30 - 12:30 (SLC 405)
Final exam study guide