Math 4100 - Real Analysis - Fall 2006


Instructor: 
Office:
E-mail:
 Neil Lyall
Boyd GSRC 527A
lyall (followed by @math.uga.edu)
 Location:
Time:
Office hours:
 Boyd GSRC (Building 1023) Room 302
MWF 9:05-9:55
MWF 10:00-11:00 and by appointment


Textbook:  Understanding Analysis, by Stephen Abbott

Syllabus:   We will cover most of the book and a little more besides

Handouts:  Handout 1

Homework: 
 Homework will be assigned weekly, see below
      
Exams: There will one take-home midterm exam and one standard (in-class) final exam


Midterm Exam 1 - Friday the 6th of October (in class)      

Midterm Exam 2 - Monday the 20th of November (in class)

Final Exam - Wednesday the 13th of December,  8:00-11:00

Grading: Homework: 35%  Two Midterms: 15% each
 Final: 35%


Homework

You should be attempting all of the problems in the book

* indicates Math 6100 questions (bonus for Math 4100)
Homework 1
Some Preliminaries and Properties of Completeness
Due Wed 08/30

 1.2
 3,5,7,8  (in addition try questions 1,2,4,6,  but don't hand in)
1.3
 2a,3,4,5,7,9
1.4
 2,3,5, Additional Problems 1


Homework 2
Countability and Review of Limits of Sequenences
Due Fri 09/08

 More 1.4
 8,9,12 (Question 12 is a challenging one. In part (b) first try to show that the collection of all polyinomials with integer coefficient of degree n is countable)
1.5
 5,6,7, Additional Problems 2  
2.2
 1,2,8


Homework 3
Limit Theorems and Completeness Revisited
Due Wed 09/13

 2.3
 2,3,7 (in addition try questions 4,6,8)
2.4 4,5 (in addition try questions 2,3)
2.5 1 (in addition try question 3)
2.6 1,2,6*


Homework 4
Infinite Series
Due Fri 09/22

 2.7
 1,2,5,6,11 (in addition try questions 3,4,8)

Additional Problems 3
Handout 1


Homework 5
Topology of the Reals
Due Wed 10/04

 3.2
 2,3,4,10,12, 
3.3
 1,2,5,7,9, Additional Problems 4


Midterm Exam 1


Homework 6
Functional Limits and Continuity
Due Fri 10/20

 4.2
 1,3,4, 4(c)*
4.3
 2,6, 6(c)*,7,9*,12*
4.4
 1,3,5,6 (also try questions 2,4,8)
4.5
 2,4*,7,8*


Homework 7
Differentiation and Riemann Integration
Due Fri 11/10

 5.2
 3,5,7 (also try questions 1,2,8)
5.3
 Additional Problems 5
7.2
 1,4 (also try questions 2,3)
7.3
 3,4
7.4
 4,5
7.5
 2,9,10
7.6
 1


Homework 8
Sequences and Series of Functions
Due Fri 11/17

 6.2
 3,8
6.3
 4
6.4
 3,7
7.5
 5


Midterm Exam 2


Homework 9
Metric Spaces
Due Fri 12/01
 8.2
 1,2,3,4,5,6
Please also try (but do not hand in)
 10,11


Additional Problems 6


Final Exam



Academic Honesty: All students are responsible for maintaining the highest standards of honesty and integrity in every phase of their academic careers. The penalties for academic dishonesty are severe and ignorance is not an acceptable defense.

See http://www.uga.edu/ovpi/academic_honesty/culture_honesty.htm; especially sections 5 and 7.