MATH 302: Real Analysis II
Mathematics
Department, Bryn Mawr College, Spring 2009
Professor:
Victor Donnay 
Lecture:
Mon, Wed, Fri
11 12 
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: Dan Wisniewski, will be the TA
for the course and will hold TA sessions for course:
Tuesdays, 35pm, Park 349
Thursdays, 68pm, Park 349
Course
Outline: In
the first part of the semester, we will cover the rest of the material in the
Real Analysis text: Ch 17 – 22 and Ch 2730.
Analysis is the basis upon
which much of applied mathematics is built. In the second part of the semester,
we will apply the analysis we have learned to learn about Dynamical Systems and
Chaos Theory. Material for this part of the course will come from the text A First Course in Chaotic Dynamical Systems,
by Robert Devaney.
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.
You
will demonstrate your progress in these areas by undertaking a group project.
This project will involve presentations to the class and a written report. We
will start these projects early in the semester so you will have plenty of time
to work on them.
Computer
Assignments: We will
have occasional computer assignments and will sometimes use computers during
class time. We will use Mathematica; 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
2 – 6th).
Project: The written project
report (10  15 pages) will be due at the last class meeting of the semester.
The class presentations about the project will occur at various times during
the semester as well as during the final two weeks of the semester.
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
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 there will be some
HW problems where you will be asked to revise and resubmit.
Quizzes: There will be a short quiz each week. It will be due on Mondays at 5pm and will cover the basic
material that we have covered in the previous week.
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, class participation 
25% 
Midterm 
25% 
Final Exam 
25% 
Project 
25% 
Total 
100% 