MATH 301: Real Analysis II
Mathematics Department, Bryn Mawr College, Fall
2009
Professor: Victor Donnay 
Lecture: Mon, Wed, Fri 910 or 11 12 Rm. 336 
Office: Park Science Building #330 

Phone: 5265352, Email: vdonnay 
Office Hours: tba 
Prerequisites: The prerequisite for the course is Math
201 (Multivariable calculus). Math 203 (Linear Algebra) and Math 206
(Transitions) are strongly recommended. We will be studying material that you (might)
have seen in Calculus (Math 101, 102 and 201). In those courses, the focus was
on how to do various types of problems. In Real Analysis, the focus is on
understanding the underlying ideas of calculus using formal mathematical
reasoning.
Texts: Real Analysis, by Frank Morgan. We will cover
chapters 1 16.
To
help you connect this new material to what you have already learned in
calculus, I will regularly assign “connections” problems from the Stewart
Calculus text book.
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: There will be regular TA
sessions for the course. My expectation is that you will attend the TA sessions
regularly. The problems I assign are challenging and I do not expect students
to be able to complete all the homework unless they attend the TA sessions.
TA Session Times:
Tuesday 4 – 5pm,
Wednesday 7 – 9 pm, Thursday
3 – 4:30pm all in Rm. 336 with Chris Micklewright, cmicklewri@brynmawr.edu. We have reserved Rm. 336 starting a halfhour before
the TA session and continuing for a halfhour after the TA session so you can
keep working on your hw there with your classmates.
Learning Goals of the
Course: In this course, you will:
Learn to 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 calculus including:

limit
of a sequence,

open
and closed sets,

continuity
of a function,

conditions
which insure the existence of a maximum (or minimum) of a function,

derivative
and integral of a function.
You will
demonstrate your mastery of this material by:

knowing
the definitions of these key concepts and the statements of the main theorems
associated with them,

giving
examples which illustrate these definitions and theorems,

giving
rigorous mathematical proofs employing these concepts.
Exams:
There will be
two midterm exams and a final exam. These exams are all selfscheduled. The tentative schedule for the Midterm exams
is:
Midterm
1 in the 6^{th} week (Oct. 59^{th}).
Midterm
2 in the 10^{th} week
(Nov. 9 – 13^{th}).
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). You are allowed two late homework assignments without penalty. Late homework
must be turned in no later than the next class. After your 2 late homework
assignments, any late homework will be assessed a penalty. You are not allowed
to look at any posted solutions until you have handed in your homework.
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 will be asked to revise one HW problem from
the previous assignment (if there is a problem you have not mastered) 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.
We will occasionally use Mathematica during class time, but no previous Mathematica experience is assumed.
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.
Math Enrichment: You will be required to attend 2 math
enrichment activities during the semester (talks, movies, poster sessions,
panel discussions) and write a 1 page (typed) “reaction paper” about the
activity. I will read and comment
on your papers but they will not be graded. As you get exposed to more advanced
mathematics through the Real Analysis course, I also want you to become aware
of the wide range of opportunities available to mathematics students.
Final grades
will be determined using the following percentages:
Homework 
15% 
Quizzes 
12% 
Class
participation 
3% 
Midterm 1 
20% 
Midterm 2 
20% 
Final Exam 
30% 
Total 
100% 