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Department of Mathematics
Course Outline
Math 101. Introduction to Analysis =
&=
nbsp; &=
nbsp; Fall
2012
Time and Place: =
MWF
10:00 am - 10:50 am, Millikan 218
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 8:45 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 continu=
ity of
real valued functions of a single real variable. This will require an in-depth stud=
y of
the real numbers system and its properties since many important facts about
continuous functions (eg., the intermediate-value theorem) would not be valid
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, which will be presented = by the students to the class. In add= ition, students will be required to give a formal presentation at the end of the semester on a special topic related to the course material (see attached li= st of special topics).
Assigned
Grading Policy. Grades wi=
ll be
based on presentations and solutions to assigned problems, two 50-minute
examinations, weekly assignments, and a formal presentation. 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; =
Fall
2012
Tentative Schedule of Topics,
Presentations and Examinations
Date &=
nbsp; &nbs=
p; Topic
W Sep 5 Introduction
to mathematical reasoning
F &=
nbsp; Sep 7&n=
bsp; Ways
of proving mathematical statements
M &n=
bsp; Sep 10 &=
nbsp; Propositional
logic
W Sep 12 &=
nbsp; The
natural numbers and the principle of induction
F &=
nbsp; Sep 14 &=
nbsp; Divisibility
M &n=
bsp; Sep 17 &=
nbsp; The
real numbers system. Numbers: rational and irrational
W Sep 19 &=
nbsp; Properties
of real numbers
F &=
nbsp; Sep 21 &=
nbsp; Properties
of real numbers (continued)
M &n=
bsp; Sep 24 &=
nbsp; Properties
of real numbers (continued)
W Sep 26 &=
nbsp; Order
in the set of real numbers
F &=
nbsp; Sep 28 &=
nbsp; Order
in the set of real numbers (continued)
M &n=
bsp; Oct 1 Completeness
W Oct 3 Consequences
of completeness
F &=
nbsp; Oct 5 Consequences
of completeness (continued)
M &n=
bsp; Oct 8 Topology
of the real line
W Oct 10 &=
nbsp; Review
F &=
nbsp; Oct 12 &=
nbsp; Exam<=
/b> 1
M =
Oct 15<=
span
style=3D'mso-tab-count:1'> &=
nbsp; Sequences of real numbers
W &nb=
sp; Oct 17<=
span
style=3D'mso-tab-count:1'> &=
nbsp; Convergence
F &nb=
sp; Oct 19<=
span
style=3D'mso-tab-count:1'> &=
nbsp; Monotone sequences
M =
Oct 22&nbs=
p; Fall Recess
W Oct 24 &=
nbsp; Bounded
sequences
F &=
nbsp; Oct 26 &=
nbsp; Cauchy
sequences and convergence
M &n=
bsp; Oct 29 &=
nbsp; Continuous
functions
W Oct 31 &=
nbsp; Properties
of continuous functions
F &=
nbsp; Nov
2 Properties
of continuous functions (continued)
M &n=
bsp; Nov
5&n=
bsp;
W Nov 7&n=
bsp;
F &=
nbsp; Nov 9 The extremal value theorem
(continued) M &n=
bsp; Nov 12 &=
nbsp; Problems
W Nov 14 &=
nbsp; Review
F &=
nbsp; Nov 16 &=
nbsp; Exam
2
M &n=
bsp; Nov 19 &=
nbsp; Special
Topic
W Nov 21 &=
nbsp; Special
Topic
F &=
nbsp; Nov 23 &=
nbsp; Thanksgiving Recess
M &n=
bsp; Nov 26 Special
Topic
W Nov 28&=
nbsp; Special
Topic
F &=
nbsp; Nov 30 Special
Topic
M &n=
bsp; Dec 3 Spe=
cial
Topic
W Dec 5 Spe=
cial
Topic
F =
Dec 7 Special Topic
M &n=
bsp; Dec 10 S=
pecial
Topic
W Dec 12 S=
pecial
Topic