MATH 302: Real Analysis II
Mathematics
Department, Bryn Mawr College, Spring 2010
Professor:
Victor Donnay 
Lecture:
Mon, Wed, Fri 9 10 
Office:
Park Science Building #330 

Phone:
5265352, Email: vdonnay 
Office
Hours: tba 
Prerequisites: We will
be studying material that you (might) have seen in Math 102 (Calculus 2), Math 201 (Multivariable calculus),
Math 203 (Linear Algebra). We will build on the material taught in Math 301
(Real Analysis I).
Texts: Real
Analysis, by Frank Morgan.
Course Web Site: accessible from Prof. Donnay's homepage,
Materials for the course will be found
primarily on the web site; some materials will be posted on the course
Blackboard site.
TA: Chris Micklewright, cmicklewri@brynmawr.edu, will be the TA for the course and will hold TA sessions for
course:
Tuesday
3 – 5 pm, Rm. 336
Wednesday
7 – 9 pm, R. 338
Course Outline: In the first part of the semester, we will cover the rest of the
material in the Real Analysis text: Ch 14 – 21 and Ch 2730. We will
start with Ch. 2728 on metric spaces and then go back to Ch. 14.
Analysis is the basis upon which much of
applied mathematics is built. We will continue to apply the analysis we learn
to Dynamical Systems and Chaos Theory.
Goals of the Course: In this
course, you will:
Communicate
your mathematical reasoning in writing and verbally, both via informal
arguments and via more formal proofs.
Develop
your ability to work as an independent and selfsufficient learner:
What to do when you do not know what to
do
How to take what you have learned in
one situation and apply it to a new and different situation (transfer of
knowledge)
Get comfortable with not knowing the
answer immediately
Learn material we have not covered in
class by reading the book and applying this newly learned information to solve
problems.
Decide for yourself whether you
understand material and learn how to ask yourself questions to check your
understanding.
Become part of a community of learners who
support, encourage and learn from one another.
Learn the key
concepts of analysis including:

metric
space,

derivative
and integral of a function

sequences
and limits (pointwise and uniform) of functions

infinite
sum of numbers (series), convergence and absolute convergence

infinite
sum of functions (power series)

integration
and differentiation of series of functions.
You
will demonstrate your progress in these areas by undertaking a group project.
Group
Project: The project will involve a presentation to the class
(roughly 15 minutes long) and a written report. We will start these projects
early in the semester so you will have plenty of time to work on them.
Depending on which topic you choose, you group will either give their
presentation part way during the semester or at the end of the semester. The
written report is due on the last day of the term.
Computer Assignments: We will
have occasional computer assignments and will sometimes use computers during
class time. We will use Mathematica and Excel; but no previous experience is
assumed.
Exams:
There will be a midterm exam and a final
exam (both take home exams) in addition to the project. The tentative schedule
for the exams is:
Midterm
exam: in the 7^{th} week
(March 1 – 5th).
Homework:
Homework will be assigned each week on
Friday. Part of the homework will be due the following Wednesday (the basics)
and part will be due the following Friday (more advanced).
Late Homework: Twice during the semester you may hand in homework late without any
penalty. You have up to one week
after the homework is due to hand it in. After you have used up your quota of
late homeworks, additional late work will not be accepted unless there is a special
situation (ex. serious medical problem) and you get my permission ahead of time.
The best way to learn mathematics is by
doing. At this level of more theoretical mathematics, problems can take a lot
of thought and experimentation to complete. Part of the goal of the course is
to help you develop strategies to attack these hard problems (draw pictures, make
simpler miniproblems, read the text very carefully, discuss with your
classmates).
Much learning happens by trying, doing as
much and as well as you can, then getting feedback and trying again. So each
week you may resubmit one hw problem from the previous week (HW redo option).
After HW corrections are handed in, I will
post a HW Answer Key in Blackboard under Course Documents. Do you not use the
Answer Key if you are still working on hw corrections.
Quizzes: The
weekly quiz will be available on the shelf outside my office (Rm. 330),
starting at 5 pm Friday. When you are ready to take the quiz, pick up a copy
and go directly to Collier Science Library and do the quiz. You will have 20
minutes. You may use a calculator. You may not use any books or notes. When you
are done with the quiz, immediately return the quiz to my office: you can slide
the quiz under my door. The quizzes will typically have a mixture of true/false
questions and short answers related to the topics listed on the weekly review
sheet.
The quiz must be completed and returned to my
office by 4pm on Monday.
Quiz Redo Policy: If you have made any mistakes on the quiz, you will have the
opportunity to correct the mistakes, hand in your corrections and improve your
score on the quiz. You should
submit both the corrected quiz and the original quiz stapled together.
Schedule Summary:
Mondays – Quiz
dues by 4pm. Quiz corrections from previous week also due.
Wednesdays –
hw due.
Fridays – hw due
and one hw correction from previous week’s hw is due. Can pick up next quiz.
Math Culture Component: So as to broaden
their knowledge of the wide variety of areas of math, students will attend two
math presentations and write short “reaction” papers describing their
impressions of the presentation.
Classroom:
During class, there will be a mixture of
lecturing by the professor and time spent by the students working out problems,
discussing their results in groups and having whole class discussions. Research
has shown that this type of active participation leads to improved learning.
The group work does not go well when members
of the group are absent. Therefore it is important that you attend to class.
Please be respectful of your fellow students. If you decide to take this
course, you must commit to attending class regularly.
Final grades will be determined using the
following percentages:
Homework, quizzes, math culture, class
participation 
25% 
Midterm 
25% 
Final Exam 
25% 
Project 
25% 
Total 
100% 