EASTERN COLLEGE


  1. MATH 404: Real Analysis

  2. Fall 2006


Walter Huddell

Email: whuddell@eastern.edu

Office: McInnis 217, x5530

Office Hours: TTh 2:00-3:30

In addition to these posted hours I am often available at other times. Please do not hesitate to make an appointment with me. I can be contacted best via email or voice mail.


Course Description: This course provides an axiomatic construction of the real number system. Topics include sequences, Cauchy sequences, metric spaces, topology of the real line, continuity, completeness, connectedness compactness, convergence and uniform convergence of functions and Reimann integration.



Course Objectives: Upon the completion of this course the student should be able to:

  1. Rigorously define the real numbers.

  2. Prove that various sequences are convergent and/or Cauchy in a metric space.

  3. Prove theorems regarding compactness and connectedness in a metric space.

  4. Construct counter-examples to show to show that certain hypotheses for classical theorems of real analysis are necessary.

  5. Prove that certain sequences of functions converge uniformly.

  6. Prove that certain functions are continuous in a metric space.

  7. Rigorously define and calculate a Reimann integral.


Text: Reed, Michael, Fundamental Ideas of Analysis.


Attendance Policy: Your attendance is absolutely essential to your success in this class. If you know you are going to be absent, please notify the professor. More than two absences will affect your grade and more than four absences constitutes grounds for failure of the course, per the college policy.


Policy for Students with Disabilities: If you have a documented special educational need, please notify me at the beginning of the semester, or at the time you are first able to document the need, and I will work with you and the academic support center to create appropriate accommodations.


College Policies: All college policies for undergraduate students apply to this class. Please consult the undergraduate catalog or see the professor if you have questions. Academic dishonesty is a serious offense that will seriously jeopardize your grade, since plagiarism or cheating results in a double zero on the assignment in question.


Teaching Methods: This course will involve lecture as well as a good amount of homework to be completed outside of class. The only way to learn mathematics is by doing mathematics and work will be assigned accordingly. Lectures will be informal enough so as too allow students the freedom to interact with the instructor. Questions are welcome and encouraged.


Testing and Grading Procedures: Letter grades will be given using the following breakdown:

97-100 A+

93-96 A

90-92 A-

87-89 B+

83-86 B

80-82 B-

77-79 C+

73-76 C

70-72 C-

67-69 D+

63-66 D

60-62 D-

<60 F


Grading will be based on the following percentage scheme:


Exam I: 30%

Exam II: 30%

Final: 30%

HW/Class Participating/Attendance: 10%


Exams I & II will fall on October 5th and November 16th respectively. They will be in class and will be closed book and closed-notes. The class participation portion will be based on homework, which will be checked throughout the semester. All assigned homework is expected to be completed. The final is scheduled for Thursday, December 14th from 9:00-11:00 a.m.