MATH 302: Real Analysis II

Mathematics Department, Bryn Mawr College, Spring 2010

 

Professor: Victor Donnay

Lecture: Mon, Wed, Fri  9 -10

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: Chris Micklewright, cmicklewri@brynmawr.edu, will be the TA for the course and will hold TA sessions for course:

                  Tuesday 3 – 5 pm, Rm. 336

                  Wednesday 7 – 9 pm, R. 338

 

Course Outline: In the first part of the semester, we will cover the rest of the material in the Real Analysis text: Ch 14 – 21 and Ch 27-30. We will start with Ch. 27-28 on metric spaces and then go back to Ch. 14.

 

Analysis is the basis upon which much of applied mathematics is built. We will continue to apply the analysis we learn to Dynamical Systems and Chaos Theory.   

 

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.

 

Learn the key concepts of analysis including:

-           metric space,

-           derivative and integral of a function

-           sequences and limits (pointwise and uniform) of functions 

-           infinite sum of numbers (series), convergence and absolute convergence

-           infinite sum of functions (power series)

-           integration and differentiation of series of functions.

 

You will demonstrate your progress in these areas by undertaking a group project.

 

Group Project: The project will involve a presentation to the class (roughly 15 minutes long) and a written report. We will start these projects early in the semester so you will have plenty of time to work on them. Depending on which topic you choose, you group will either give their presentation part way during the semester or at the end of the semester. The written report is due on the last day of the term.

 

Computer Assignments: We will have occasional computer assignments and will sometimes use computers during class time. We will use Mathematica and Excel; but no previous experience is assumed. 

 

Exams:

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 1 – 5th).  

 

 

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 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 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 each week you may resubmit one hw problem from the previous week (HW redo option).  

 

After HW corrections are handed in, I will post a HW Answer Key in Blackboard under Course Documents. Do you not use the Answer Key if you are still working on hw corrections.

 

Quizzes: The weekly quiz will be available on the shelf outside my office (Rm. 330), starting at 5 pm Friday. When you are ready to take the quiz, pick up a copy and go directly to Collier Science Library and do the quiz. You will have 20 minutes. You may use a calculator. You may not use any books or notes. When you are done with the quiz, immediately return the quiz to my office: you can slide the quiz under my door. The quizzes will typically have a mixture of true/false questions and short answers related to the topics listed on the weekly review sheet.

 

The quiz must be completed and returned to my office by 4pm on Monday.

 

Quiz Redo Policy: If you have made any mistakes on the quiz, you will have the opportunity to correct the mistakes, hand in your corrections and improve your score on the quiz.  You should submit both the corrected quiz and the original quiz stapled together.

 

 

Schedule Summary: 

Mondays – Quiz dues by 4pm. Quiz corrections from previous week also due. 

Wednesdays – hw due.       

Fridays – hw due and one hw correction from previous week’s hw is due. Can pick up next quiz.

 

Math Culture Component: So as to broaden their knowledge of the wide variety of areas of math, students will attend two math presentations and write short “reaction” papers describing their impressions of the presentation.

 

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, math culture, class participation

25%

Midterm

25%

Final Exam

25%

Project

25%

Total

100%