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: 526-5352, E-mail: vdonnay

Office Hours: tba


Pre-requisites:  We will be studying material that you (might) have seen in Math 102 (Calculus 2),  Math 201 (Multi-variable 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, 3-5pm, Park 349

Thursdays, 6-8pm, 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 27-30.


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 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.


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. 



There will be a mid-term exam and a final exam (both take home exams) in addition to the project. The tentative schedule for the exams is:

            Mid-term exam: in the 7th 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 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 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 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.



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




Final Exam