Analysis I, Math 4317
Lectures:
MWF 12-1 pm in Skiles 154
by
Michael Loss (loss@math.gatech.edu)
Office:
Skiles 214 B
Office
hours: M,W 2-3 or by appointment
This page will be
frequently updated,
so, please, consult it often.
Analysis,
it is sometimes said, is the art of taking limits! Many interesting
mathematical objects arise as limits and one is faced with the
challenge of calculating with them. The square root of two, the
elementary
transcendental functions are elementary
examples, however, solutions of partial
differential equations, most of the time, appear as limits as well. It
is therefore important
to understand how to compute with limits. Analysis provides a number of
notions and tools
for dealing with limits and this course is a gentle introduction to
them. Since the notions in analysis are subtle, it is
sometimes difficult to get an intuitive feeling of
what these things mean.
The only way to stay on firm ground in this field is by understanding
and doing proofs.
You have to be able to prove certain statements, i.e., to either derive
a statement through logical steps from another one, or to find a
counterexample. Thus, this course
is not so much about solving particular problems but teach you the
language of analysis.
Among the topics to discuss are elementary set theory, the real
numbers,
metric spaces, continuous functions as well as differentiation and
integration.
The course is based on the text `Introduction to Analysis' (IA) by
Maxwell Rosenlicht,
Dover 1986, ISBN 0-486-65038-3. Please read the assigned text before
coming to class.
Moreover, for some other topics I supply some notes on the web. You
will find them
on this
link.
Practice is important. You will have to do homework that is
regularly graded. In addition there will be two tests and a final exam.
Your grade will be based on how well you solve the homework and
the tests. The lowest test score will be dropped. Homework counts 30%,
the test counts 30% and the final counts 40% towards your grade.
Here are some
Practice
Tests
Now
a
few
words
about
the
homework.
Every
week
I
assign
problems
and
half
of
them
will
be
graded,
but
I
am
not
telling
you
which
ones.
It
goes without saying that you to do
the homework yourself, i.e., you do not copy from others. I do not mind
that, should you get stuck, you ask your fellow students for help, but
you have to try first yourself. Let me also remind you to uphold the
honor code at all times. You find
more information at http://www.deanofstudents.gatech.edu/Honor/
Please turn in the home work always on Wednesdays,
the week after in class.
Here is a tentative syllabus. I do not want ot stick to it in a rigid
fashion.
There may be a topic that for some reason will require that we spend
more time
on it. I would like to have this option. It is better to
understand fewer topics
very well than lots of topics badly.
Please note that weeks 3-14
have an exercise group assigned to the homework.
At the end I indicated the day and times students can get
together and work on the
solutions.
The names that have question marks are students that are not on
the roster of t-square.
There were four students on the roster that did not sign up for
an exercise group.
Please do this right away if you have not already done so.
Because of this, the groups,
except for the first one, are tentative.
Each group solves
the
homework in detail and submits it to me on Friday
of the
following week in class.
This group - solutions with my corrections will be posted
on the web.
The
Final Exam is on Monday December 13 from 11:30-2:20 in Skiles Room 154
Practice
Final
Solutions
for the practice final
There
will be a review session on Thursday December 9 from 6-8 pm in Skiles
Room 202
Week 1: August 23 - 27 Assigned Text:
Chapter 1 in IA
Homework: Do all the problems at the end of Chapter 1 in IA.
Week 2: August 30 - September 3.
Assigned
Text:
Chapter
2
in
IA
Homework: Do problems 2, 4, 6, 7, 9, 10, 11, 12, 13, 16 on
pages 29-31
Christopher Stevens, Eric Tollefson, Sarwat
Nasir M 8-10 am
Homework 2 Solutions
Week 3: September 6-10.
Assigned
Text:
Chapter
3,
Section
1-
3,
in
IA
Homework: Do problems 1, 2, 5, 6, 7, 10, 11, 12, 13, 14 on pages
61-62 of IA.
Beck Brian , Zhongyuan Yu, McCullough
Andrew M 1- 3 pm
Homework 3 Solutions
Week 4: September 13 - 17.
Assigned
Text:
Chapter
3,
Section
4
-
6,
in
IA
Homework: Do problems 15, 16, 18, 20, 24, 26, 28, 30, 32, 33, on
pages 62-64 of IA.
Quinn Chrzan, Elizabeth
Knybel, Ahmet Ozlu, Tugce Isik M 2 - 4 pm
Homework 4 Solutions
Week 5: September 20 - 24.
Assigned
Text:
Chapter
3, Section
4-6,
in IA
Homework: Do problems 17, 19, 21, 27,
29, 31, 34, 35, 37, 38 on pages 62-65 in IA.
Hain Stephen, Weyer
Daniel, Reames Benjamin, Youmans Michael Th 5 - 7 pm
Homework 5 Solutions
Week 6: September 27 - October 1.
Assigned
Text:
Chapter
4, Section
1-
3,
in IA
Homework: 1a), 1d), 2, 4, 9, 10, 11, 13, 14, 15 on page 91, 92
od IA.T
Loibl Matthew, Loranger
Trevor, Ozuretmen Can M 2 - 4 pm
There will be a 50 minute
test in class on Wednesday September 29 on the topics covered
in the week 1-5
Homework 6 Solutions
Solutions
of
Test
1
Week
7:
October
4
-
8.
Assigned
Text:
Chapter
4,
Section
1-3
in
IA
Homework:
3,
6,
7,
12,
16,
17,
18,
19,
20,
21
on
pages
91-93
of
IA.
Kaddouri Samar, Matt Perez ???
T 4 - 6 pm
Homework
7
Solutions
Week 8: October 11-15.
Assigned
Text:
Chapter
4,
Section
4-6
in
IA
Homework:
25,
27,
30,
32,
33b,
34,
35,
36,
37,
38
p.
93/94
of
IA.
Bolding Mark , Coogle
Richard T 2 - 4 pm
(October 15 is the last day to drop the course)
Homework
8 Solutions
Some
remarks
about
the
solutions
Week 9: October 18 - 22.
Assigned
Text:
Chapter
4,
Section
4-6
in
IA
Homework:
23,
26,
28,
29,
41,
43,
44,
45,
46
p.
93-95
in
IA.
Warrayat Amena, Blanca-Pimentel Antonio,
Olcay Sarmaz ???, F 10 -12
Homework
9
Solutions
Week 10: October 25 - 29.
Assigned
Text:
Chapter
5
in
IA
Homework:
Problems
1-6
and
8
on
p
108/109
in
IA.
Please
do
8
instead
of
7
which
is
too
hard.
Jia Leroy, Martie Lee , Sarju Vasavada???,
Kumar, Lori F
6 - 8 pm
Homework 10
part 1 Solutions
Homework 10
part 2 Solutions
Week 11: November 1 - 5.
Assigned
Text:
Chapter
5
in
IA
Homework:
Problems
9-14
on
page
109/110
De la Croix Jean-Pierre,
Fayyaz Ubaid Ullah, Dursun Joseph M 2-4
There will be a 50 minute test in
class on Wednesday November 3 on the topics covered
in the week 1-10.
Solutions
of
Test
2
Notes
on
integration
Homework
11
Solutions
Week 12: November 8 - 12.
Assigned
Text:
Chapter
6
Sections
1,
2
in
IA
Homework:
problems
1-3,
7-11
on
page
132/133
of
IA
Roop Jonathan,
Seeds Gregory T 1-3 pm
Notes on
equicontinuity
Week 13: November 15 - 19.
Assigned
Text:
Chapter
6
Sections
3-4
in
IA
Homework:
problems
12-17,19,
21and
22
on
pages
133/134
in
IA.
Jeffries Alex , Michelle
Delcourt, By Robert T 11-1 pm
Homework
13
Solutions
Week
14:
November
22
-26.
Assigned
Text:
Chapter
6
Section
5
in
IA
Homework:
problems
20,
23,
24
a),
b),
25,
26,
28
on
pages
134/135
in
IA.
Moore Tucker, Al-Khalil
Bilal, Macon George T 6 - 8 pm
Homework
14
Solutions
Week 15: November 29 - December 3.
Assigned
Text:
Chapter
8,
Sections
1,
2,
3
in IA
Week 16: December 6 - 10.
Assigned
Text:
Continue
Chapter
8
Section
3
in
IA