MATH 301: Real Analysis I
Mathematics Department, Bryn Mawr College, Fall
2011
Professor: Victor Donnay 
Lecture: MW 11:30 – 1 pm
TTh 8:15 – 9:45 am Rm.
336 
Office: Park Science Building #330 

Phone: 5265352, Email: vdonnay@brynmawr.edu 
Office Hours: tba 
Course
TA: Frank Romascavage, Rm. 436 Park,
Email: fromascava@brynmawr.edu, Phone: ext 5267482
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.
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.
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 5^{th} or 6^{th}
week (Sept 2630^{th} or Oct. 37^{th}).
Midterm
2 in the 10^{th}
or 11^{th} week (Nov. 711^{th} or 1418^{th}).
Homework:
Homework will
be assigned each week. Part of the homework will be due the following Monday
(Tuesday) (the basics) and part will be due the following Wednesday (Thursday)
(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 two 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.
Homework Grading Policy:
The homework makes up 15% of
your grade. 10% of this total will be awarded for effort. Each homework problem
is scored either 3 (= demonstrates mastery of the material), 2 ( = developing; shows some mastery but not yet complete), 1
( = made an effort but not yet able to do the problem), 0 ( = not attempted).
You will receive full credit
for effort on each problem for which your score is 3, 2 or 1. You will not
receive credit for effort on problems that are scored a 0. The percentage of
homework problems that receive effort credit will be translated into a score
out of 10 at the end of the semester.
5% of your homework grade
will be awarded for demonstrating mastery of the material and will be
determined by your scores on the homework.
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 homeworks will be
assessed a penalty: 25% deduction if one class late, 50% deduction if two
classes late, 75% deduction if 3 classes (one week) late; not accepted after
one week.
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 (Tuesdays) at 5pm and will cover the basic material that we
have covered in the previous week. The quizzes will be assessed Mastery (M),
Developing (D), Not Yet (NY). If you do not
demonstrate mastery on the first try, you can redo. The goal is for you to learn the material. Persistent
is a key trait for success in all endeavors; if you are willing to keep working
at it, I am pleased to support and encourage your efforts.
Math Culture
Requirement:
Students will attend
two math talks over the course of the semester and write a onepage reaction
paper for each talk. There are many aspects to mathematics; attending these
talks will give you opportunity to learn about these opportunities. The first
talk must be done by Friday Nov 4^{th}. The paper must be handed in
within one week of the talk.
Options Include:
a. Weekly
Math Colloquium, Monday at 4pm, that alternates between Bryn Mawr and
Haverford.
b. The
Distressing Math Collective, Thur 7pm, Park 328.
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.
Final grades
will be determined using the following percentages:
Homework,
Quizzes, Class participation 
20% 
Midterm 1 
22.5% 
Midterm 2 
22.5% 
Final Exam 
35% 
Total 
100% 