Math 5151, Introduction to Real Analysis 1
Fall 1999
MW 6:00 - 7:15 p.m.
102 Arnold Hall

Instructor:   Dr. Tim Howard
Office:         215 Faculty Office Building
Phone:         568-2172
Email:          thoward@colstate.edu
Web site:     http://math.colstate.edu/thoward/
Office Hours: M-Th 10 - 11 a.m., MW 1-2 p.m. and 4:30-5:30 p.m.   (see also the schedule grid on my web page).  Other hours are available by appointment.

The policies in this syllabus may be subject to change. Check the above www address weekly for the latest version.
Most recent update:  October 13, 1999.




Text.  An Introduction to Analysis, Second Edition, by James R. Kirkwood.

Course Description.  Topology of Euclidean spaces, sequences, limits of sequences, convergent sequences, monotone sequences, Cauchy sequences, limits of functions, continuous functions, the derivative, the mean value theorem, L’Hospitals’s rule, and Taylor’s theorem.

Prerequisites.  Math 2155, Foundations for Advanced Mathematics.

Grading.

Your course grades will be based on homework, three or four tests, a written paper to be orally submitted in class, and a final exam.  Each of these will be weighted as follows:

Component
Weight
Homework exercises
30%
Tests
50%
Final exam
20%

Your letter grade for the course will be computed according to how many of the total points you receive as follows:

        A: 90 - 100% of the total points     B: 80 - 89%     C: 70 - 79%     D: 60 - 69%

Tests. We will have two or three tests during the semester.  No makeup tests will be given; please refer to the absentee policy below for more information.  Each student is responsible for frequently checking the announcements listed on the course web page for updates.

Final Exam. The final exam is scheduled for Wednesday, December 15, 6:15-8:15 p.m.

Other Noteworthy Dates.

  • Wed., August 25 -- last day for course schedule changes
  • Mon., Sept. 6 -- Labor Day, no classes
  • Oct. 11,12 -- Fall Break, no classes
  • Oct. 18 -- Mid term (last day to withdraw with a grade of "W")
  • Nov. 24-26 -- Thanksgiving holiday, no classes
  • Course web page.  Any modifications to the course policies and/or course syllabus will be announced on the course web page.  You are expected to check the web page at least once per week.  If you miss a class day, you should take special care to check the course page as soon as possible after that class period.

    Absentee Policy.  You are expected to attend every course meeting. According to the attendance policy published on page 6 of the Student Handbook, if you accumulate 10 or more course hours of absence during the semester, I am authorized to assign the grade of "WF".

    No makeup tests will be given. If a student misses a test with instructor approval, the weight of the final will be increased to replace the missing test score (likewise for additional missed tests).  If the absence has not been approved by the instructor, then a zero will be recorded for that test score.

    Academic Withdrawal. The student handbook states the following:

    To leave the university with a clear record at times other than at the end of a semester students must complete a "withdrawal form."  This form, which includes instructions, is available in the Office of the Registrar, Richards Hall.
    Any course dropped after August 25 becomes a part of your academic record.  From that date until mid-term (Oct. 18) a grade of "W" will be assigned for withdrawal forms submitted to the Registrar.  A grade of "WF" will be assigned for withdrawal forms received after mid-term.  The student is responsible for completing the paperwork and submitting it to the Registrar’s Office.

    Students with Disabilities: If you have a documented disability, as described by the Americans with Disabilities Act (ADA), it is recommended that you contact the Office of Disability Services at (706)568-2330.  The office will assist you in arranging appropriate accommodations with the instructor.
     

    Tentative List of Topics

    Chapter 1:  The Real Number System

    1.1  Sets and functions
    1.2  Properties of the real numbers as an ordered field
    1.3  The Completeness Axiom

    Chapter 2:  Sequences of Real Numbers

    2.1  Sequences of real numbers
    2.2  Subsequences
    2.3  The Bolzano-Weierstrass Theorem

    Chapter 3:  Topology of the Real Numbers

    Chapter 4:  Continuous Functions

    4.1  Limits and continuity
    4.2  Monotone and inverse functions

    Chapter 5:  Differentiation

    5.1  The derivative of a function
    5.2  Some mean value theorems
    Real Analysis Course Page
    Tim Howard's Home Page
    CSU Math Dept.
    CSU Home Page