Math 828    Real Analysis     Fall 2000
 
Instructor: Prof. J. H. Shapiro
Office: D304 Wells Hall
Phone: 3-3831
Email: shapiro@math.msu.edu
Office Hours: MWF 11:30-12:20, & by appointment.
 
Text:  Wheeden & Zygmund: Measure and Integral ... (required).
 
Additional References (on reserve in the Math Library):
H.S. Bear, A Primer of Lebesgue Integration
H.L. Royden, Real Analysis
 
Prerequisites:
You need a good working knowledge of undergraduate-level real analysis, in particular, limits and continuity. You must know how to do ``delta-epsilon'' proofs, and be comfortable with notions like ``supremum'', ``limsup, ``infimum'', ``liminf''. You need to be on good terms with the topology of Euclidean space R^n, especially the concepts of ``open set'', ``closed set'', ``boundary'', and ``compact set''. You must know the fundamental properties of continuous functions (e.g., a real-valued function that is continuous on a compact set is bounded, and attains its maximum and minimum ), and know how they are proved. See, for example, Chapter 1 of the text.
 
Course Material:
The course will cover most of Chapters 2-11 of the text, with some additional topics if time permits. The subject is Lebesgue measure and integral, first in Euclidean space, and then in abstract situations. The material is fundamental to all analysis-based pure and applied mathematics courses.
 
Course Organization:
Your preliminary grade will depend solely on examinations and homework: 600 points total, apportioned as follows.

 

No exams or homework sets will be dropped. In most cases your preliminary grade will be your final grade. However, other factors, such as: exceptional effort, positive contributions to the classroom experience, improvement over time ...  , can play a role in raising your preliminary grade, whereas it can be lowered by negative factors such as lack of effort, declining performance, disruptive behavior ....

 

Homework:
Problems will be assigned each day, and a selection of the week's problems will be collected for grading every Monday. In order to get credit for a problem set, you must be present (both physically and mentally) for the entire class at which it is due. You must write up problems neatly and logically, providing appropriate explanations of what you are doing. You can lose points if the grader cannot easily follow your work!
 
Collaboration.
Work on the homework problems must be your own! You may discuss with me, or with your classmates any of difficulties you are having with the homework problems, however you must acknowledge any help you get from classmates. If I suspect widespread unacknowledged collaboration I reserve the right to count exams more and homework less. Cases of flagrant cheating on either homework or exams will be handled according to the University's policy on Integrity of Scholarship and Grades (see Academic Programs 2000-02, page 64). See also the Spartan Life website at
www.vps.msu.edu/SpLife/reg3.htm
and
www.vps.msu.edu/Splife/rule32.htm.
 
Policy on Makeup Work:
The only valid reasons for missing an exam or a homework assignment are: (1) illness, or (2) a conflicting University activity that cannot be rescheduled. Claims involving such contingencies must be supported by verifiable documentation signed by: (1) your physician in case of illness, or (2) your faculty supervisor in case of a non-rescheduleable University activity. Each case will be handled on an individual basis.
 
Grading Policies:
Graduate students will be eligible for grades of DF on the same basis that undergraduates are eligible for grades of I (see Academic programs 2000-02, page pp. 63-64). Specifically: To qualify for a DF or an I, a student must: (a) have completed 12 weeks of the term, but be unable to complete the class because of illness or other compelling reason, and (b) have done satisfactory work in the course, and in the instructor's judgment, be able to complete the course without repeating it.
 
Important Dates:
Thursday, Sept. 24: Last day to drop a course with 100% refund.

Tuesday, Oct. 17: Middle of term-last day to drop a course with no grade.

 

File translated from TEX by TTH, version 2.25.
On 17 Aug 2000, 17:24.