Math 4111, Fall, 2020

Dept. of Mathematics, Washington Univ.

**Syllabus
for Math 4111**

Real Analysis

**Instructor:**
Steven G. Krantz

**Classroom:**
The course will be taught OnLine only. No classroom.

**e-mail
address:** sk@math.wustl.edu

**Office:**
103, Cupples I

**Office
Hour: **Monday, Wednesday, Friday from 2:00pm to 4:00pm,
either by email or phone (510-875-8972).

**Phone:**
(510) 875-8972

**Dept.
Office:** 100, Cupples I

**Dept.
Phone:** (314) 935-6760

**Course Home
Page:** http://www.math.wustl.edu/~sk/math4111.html

**Course
Description:** The purpose of this course is

to serve as a rigorous introduction to
analysis on the real number system.

We construct the real numbers from scratch, and we
prove their fundamental properties.

We study a number of important and famous theorems
such as the Weierstrass approximation theorem,

the Weierstrass nowhere differentiable function, the intermediate value
theorem,, and

and so forth. This class is hard work, and it is demanding. But it is worth it.

.

**Textbook:**
S. G. Krantz, * Real Analysis and Foundations,*

4th edition, CRC Press, Boca Raton,
FL, 2016.

**Elements
of the Course:**

Homework: 25% of grade

Midterm Exam: (2 of these) each 25% of grade

Final Exam: 25% of grade

TOTAL: 100%

The homework is an essential part of this course.
Each new idea

builds
on previous ideas, so it is essential to master and internalize each

one
when you encounter it. Be sure to do the homework in a regular and timely

fashion. Homework should
be written out on 8.5" x 11" paper and submitted

on time. It will be graded. We will
use the CrowdMark system for submitting

homework. What you will
do then is scan your homework and submit it OnLine.

When a homework assignment
is formulated, CrowdMark

will let you know and tell you how to submit..

Be familiar with this Web page. This is where homework assignments will be

posted, homework solutions posted, exam solutions posted, due dates will be posted,

and also where exams and other course events
and information

will be announced.

We will decide when our midterm exams will be.

If there are particular days when you do not want an exam (for a religious

holiday or other reason), please let me know.

FIRST HOMEWORK ASSIGNMENT due Tuesday, September 29 at 1.59am.

Section 1.1

1, 2, 3, 4, 5, 7, 11

Section 1.2

2, 3, 5, 7, 8, 9, 10, 13

SECOND HOMEWORK ASSIGNMENT due Tuesday, October 13 at 1:59am.

Section 2.1:

1, 2, 3, 8, 10, 11, 12.

Section 2.2:

1, 2, 4, 8.

THIRD HOMEWORK ASSIGNMENT due Wednesday, October 28 at 1:59am.

Section 2.3:

1, 3, 5, 7

Section 2.4:

2, 3, 9

Section 3.1:

1acf, 3, 6, 9

Section 3.2

2, 4, 6

Section 3.3

1, 4, 7

Section 3.4

1, 3, 5

Section 3.5

1, 5, 6

FOURTH HOMEWORK ASSIGNMENT due Monday, November 16 at 11:59pm.

Section 4.1:

1, 3, 5, 7

Section 4.2:

1, 2, 3, 5

Section 4.3:

1, 2, 4, 8

Section 4.4

1, 3, 4, 6

Section 4.5

1, 3, 6, 7

FIFTH HOMEWORK ASSIGNMENT due Monday, November 30 at 11:59pm.

Section 5.1:

1, 2, 6, 9

Section 5.2:

1, 3, 5, 7

Section 5.3:

1, 3, 5, 9, 14

Section 5.4:

1, 3, 4, 7

Section 6.1:

1, 6, 7, 13

Section 6.2:

2, 4, 5, 8

SIXTH HOMEWORK ASSIGNMENT due Thursday, December 10 at 11:59pm.

Section 6.3:

1, 2, 3, 8

Section 7.1:

1, 2, 6, 7

Section 7.2:

1, 4, 5, 9

Section 7.3:

1, 4, 6, 10

Section 7.4:

1, 2, 5, 9

SEVENTH AND LAST HOMEWORK ASSIGNMENT due Friday, December 18 at 11:59pm.

Section 7.5:

1, 2, 5

Section 8.1:

4, 7, 8

Section 8.2:

1, 2, 4