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 Math 4111 Lecture, 09-14-2020




Second Math 4111 Lecture, 09-16-2020




Audio for Second Math 4111 Lecture, 09-16-2020




Third Math 4111 Lecture, 09-18-2020




Audio for Third Math 4111 Lecture, 09-18-2020




Fourth Math 4111 Lecture, 09-21-2020




Audio for Fourth Math 4111 Lecture, 09-21-2020




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


Fifth Math 4111 Lecture, 09-23-2020



Audio for Fifth Math 4111 Lecture, 09-23-2020




Sixth Math 4111 Lecture, 09-25-2020




Audio for Sixth Math 4111 Lecture, 09-25-2020




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.


Seventh Math 4111 Lecture, 09-28-2020




Audio for Seventh Math 4111 Lecture, 09-28-2020




Eighth Math 4111 Lecture, 09-30-2020




Audio for Eighth Math 4111 Lecture, 09-30-2020




Ninth Math 4111 Lecture, 10-02-2020




Audio for Ninth Math 4111 Lecture, 10-02-2020




Tenth Math 4111 Lecture, 10-05-2020




Audio for Tenth Math 4111 Lecture, 10-05-2020




Solutions to Homework 1




Practice Exam for Midterm 1




Solutions to Practice Exam for Midterm 1




Eleventh Math 4111 Lecture, 10-07-2020




Audio for Eleventh Math 4111 Lecture, 10-07-2020




Twelfth Math 4111 Lecture, 10-09-2020




Audio for Twelfth Math 4111 Lecture, 10-09-2020



Thirteenth Math 4111 Lecture, 10-12-2020




Audio for Thirteenth Math 4111 Lecture, 10-12-2020




Fourteenth Math 4111 Lecture, 10-14-2020




Audio for Fourteenth Math 4111 Lecture, 10-14-2020





Fifteenth Math 4111 Lecture, 10-16-2020




Audio for Fifteenth Math 4111 Lecture, 10-16-2020




Sixteenth Math 4111 Lecture, 10-19-2020




Audio for Sixteenth Math 4111 Lecture, 10-19-2020




Seventeenth Math 4111 Lecture, 10-21-2020




Audio for Seventeenth Math 4111 Lecture, 10-21-2020




Eighteenth Math 4111 Lecture, 10-23-2020




Audio for Eighteenth Math 4111 Lecture, 10-23-2020




Nineteenth Math 4111 Lecture, 10-26-2020




Audio for Nineteenth Math 4111 Lecture, 10-26-2020




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



Solutions to Second Homework




Twentieth Math 4111 Lecture, 10-28-2020




Audio for Twentieth Math 4111 Lecture, 10-28-2020




Twenty-First Math 4111 Lecture, 10-30-2020




Audio for Twenty-First Math 4111 Lecture, 10-30-2020




Twenty-Second Math 4111 Lecture, 11-02-2020




Audio for Twenty-Second Math 4111 Lecture, 11-02-2020




Twenty-Third Math 4111 Lecture, 11-04-2020




Audio for Twenty-Third Math 4111 Lecture, 11-04-2020




Twenty-Fourth Math 4111 Lecture, 11-06-2020




Audio for Twenty-Fourth Math 4111 Lecture, 11-06-2020




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


Solutions to Third Homework




Twenty-Fifth Math 4111 Lecture, 11-09-2020




Audio for Twenty-Fifth Math 4111 Lecture, 11-09-2020




Twenty-Sixth Math 4111 Lecture, 11-16-2020




Audio for Twenty-Sixth Math 4111 Lecture, 11-16-2020




Twenty-Seventh Math 4111 Lecture, 11-18-2020




Audio for Twenty-Seventh Math 4111 Lecture, 11-18-2020




First Midterm Exam




Solutions to First Midterm Exam




Twenty-Eighth Math 4111 Lecture, 11-20-2020




Audio for Twenty-Eighth Math 4111 Lecture, 11-20-2020




Twenty-Ninth Math 4111 Lecture, 11-23-2020




Audio for Twenty-Ninth Math 4111 Lecture, 11-23-2020




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


Solutions to Fourth Homework




Thirtieth Math 4111 Lecture, 11-25-2020




Audio for Thirtieth Math 4111 Lecture, 11-25-2020




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


Practice Exam for Midterm 2




Solutions to Practice Exam for Midterm 2




Thirty-First Math 4111 Lecture, 11-30-2020




Audio for Thirty-First Math 4111 Lecture, 11-30-2020




Thirty-Second Math 4111 Lecture, 12-02-2020




Audio for Thirty-Second Math 4111 Lecture, 12-02-2020




Thirty-Third Math 4111 Lecture, 12-04-2020




Audio for Thirty-Third Math 4111 Lecture, 12-04-2020