MATH 301: Real Analysis II

Mathematics Department, Bryn Mawr College, Fall 2009


Professor: Victor Donnay

Lecture: Mon, Wed, Fri  9-10 or 11- 12  Rm. 336

Office: Park Science Building #330


Phone: 526-5352, E-mail: vdonnay

Office Hours: tba



Pre-requisites:  The pre-requisite for the course is Math 201 (Multi-variable 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, We have reserved Rm. 336 starting a half-hour before the TA session and continuing for a half-hour 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 self-sufficient 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.



There will be two mid-term exams and a final exam. These exams are all self-scheduled.  The tentative schedule for the Mid-term exams is:

                  Mid-term 1  in the 6th week  (Oct. 5-9th).  

Mid-term 2 in the 10th week  (Nov. 9 – 13th).




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 mini-problems, 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.



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:





Class participation


Midterm 1


Midterm 2


Final Exam