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Department of Mathematics
Course Outline
Math 101. Introduction to Analysis =
&=
nbsp; &=
nbsp; Spring
2010
Time and Place: =
MWF
10:00 am - 10:50 am,
Millikan 213
Instructor:<=
span
style=3D'mso-spacerun:yes'> =
Dr.
Adolfo J. Rumbos
Office:<=
span
style=3D'mso-spacerun:yes'> =
=
Andrew
259
Phone/e-mail:<=
span
style=3D'mso-tab-count:2'> &=
nbsp; ext. 18713 /
Office Hours:<=
span
style=3D'mso-spacerun:yes'> MWF 9:00 am - 9:45 am, or by
appointment
<=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:"Times New =
Roman";
mso-fareast-font-family:"MS Mincho"'>Text: =
Introduction to Real Analysis by M=
ichael
J. Schramm;
<=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:"Times New =
Roman";
mso-fareast-font-family:"MS Mincho"'>Course Website http://pages.po=
mona.edu/~ajr04747/
Prerequisite:<=
span
style=3D'mso-spacerun:yes'> Linear
Algebra
Course
Description. The main goal of this =
course
is to give a rigorous treatment to the study of continuity of real valued
functions of a single real variable.
This will require an in-depth study of the real numbers system and i=
ts
properties since many important facts about continuous functions (eg., the intermediate-value theorem) would not be val=
id
without some of those properties.
About two thirds of the class time will be spent on st= udent presentations. The instructor= will lecture or lead discussion the other third of the time. The content of the course is dicta= ted by a series of assigned problems, most of which will involve the development of mathematical arguments, whose solutions will be presented by the students to the class. In addition, stude= nts will be required to give a formal presentation at the end of the semester o= n a special topic related to the course material (see attached list of special topics).
Assigned
Grading
Policy. Grades will be based on pres=
entations
and solutions to assigned problems, two 50-minute examinations, weekly
assignments, and a formal presentation.&nb=
sp;
The overall score will be computed as follows:
&=
nbsp; &nbs=
p; Problem
solutions journal &n=
bsp;
&=
nbsp; &=
nbsp; 15%
&=
nbsp; &nbs=
p; Homework
assignments &n=
bsp;  =
; &n=
bsp; 20%
&=
nbsp; &nbs=
p; Problem
solutions presentation &nb=
sp; 10%
&=
nbsp; &nbs=
p; Two
examinations &=
nbsp; &=
nbsp; &nbs=
p; &=
nbsp; 40%
&=
nbsp; &nbs=
p; Formal
presentation &=
nbsp; &nbs=
p; &=
nbsp; 15=
%
Math 101=
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2010
Tentative Schedule of Topics,
Presentations and Examinations
Date &=
nbsp; &nbs=
p; Topic
W Jan 20 =
span>Introduction
to mathematical reasoning
F &=
nbsp; Jan 22 =
span>Ways
of proving mathematical statements
M &n=
bsp; Jan 25 =
span>The
real numbers system. Numbers: rational and irrational
W Jan 27 =
span>Properties
of real numbers
F &=
nbsp; Jan 29 =
span>Properties
of real numbers (continued)
M &n=
bsp; Feb 1 Consequences
of completeness
W Feb 3&n=
bsp; Seq=
uences
of real numbers
F &=
nbsp; Feb 5 Convergence
M &n=
bsp; Feb 8&n=
bsp; Con=
vergence
(continued)
W Feb 10=
R=
eal
valued functions of a real variable
F &=
nbsp; Feb 12=
L=
imits
and continuity
M &n=
bsp; Feb 15=
C=
ontinuity
(continued)
W Feb 17=
<=
/span>Review
F &=
nbsp; Feb 19=
<=
/span>Exam<=
/b> 1
M &n=
bsp; Feb 22=
F=
unctional
limits
W Feb 24=
P=
roperties
of continuous functions
F &=
nbsp; Feb 26=
P=
roperties
of continuous functions (continued)
M =
Mar 1 <=
/span> &=
nbsp; Properties of continuous functions
(continued)
W &nb=
sp; Mar 3 <=
/span> &=
nbsp;
Topology of the real
line
F &nb=
sp; Mar 5 &=
nbsp; Connected sets and compact sets=
M =
Mar <=
span
style=3D'mso-spacerun:yes'> 8  =
; The
intermediate value theorem
W Mar
10 &=
nbsp; The
intermediate value theorem (continued) =
;
F &=
nbsp; Mar
12  =
; Problems
M &n=
bsp; Mar
15 Spring Recess
W Mar 17=
Spring Recess
F &=
nbsp; Mar
19 Spring Recess
M &n=
bsp; Mar 22=
C=
ontinuous
functions over compact sets
W Mar 24=
T=
he
extremal value theorem
F &=
nbsp; Mar 26=
Cesar Chavez Day (observed)
M &n=
bsp; Mar 29=
T=
he
extremal value theorem (continued)
W Mar 31=
R=
eview
F &=
nbsp; Apr 2 Exam
2
M &n=
bsp; Apr 5 Special
Topic
W Apr 7 Special
Topic
F &=
nbsp; Apr 9 Special
Topic
Math 101=
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
Spring
2010
Date &=
nbsp; &nbs=
p; Topic
M &n=
bsp; Apr 12 S=
pecial
Topic
W Apr 14 S=
pecial
Topic
F &=
nbsp; Apr 16 S=
pecial
Topic
M &n=
bsp; Apr 19 S=
pecial
Topic
W Apr 21 S=
pecial
Topic
F =
Apr 23 <=
/span>Special Topic
M &n=
bsp; Apr 26 S=
pecial
Topic
W Apr 28 S=
pecial
Topic
F &=
nbsp; Apr 30 S=
pecial
Topic
M &n=
bsp; May 3&n=
bsp; Special
Topic
W May 5 Spec=
ial
Topic