Math 458 Theory of Integration

Math 458-24 Theory of Integration Fall 2006
Instructor	Office	Phone	Hours
Jimmie Lee Johnson	A. A. Robin Campus Schaumburg, Illinois Room 153	(312) 341-3552 Voice Mail	Th 5:00-6:30pm and by appointment.
6:30-9:00pm Sch 353		(847) 619-7939 Shared Line	I am often around earlier.
6:30-9:00pm Sch 353	E-mail: jjohnson@roosevelt.edu Web Page: http://faculty.roosevelt.edu/jjohnson/

Text: Measure, Integral and Probability, by Marek Capinski and Ekkehard Kopp, Springer-Verlag., 2nd ed. 2004..

Prerequisite: Graduate standing and grades of C or better in Math 300 Linear Algebra and Math 352 Analysis, which are undergraduate mathematics courses.

Class will consist of oral reports, quizzes, examples, theorem proving and the answering of questions. Prior to each class, you must do the assigned reading or you will be lost; make notes of topics you feel need elaboration in class. For each class, be prepared to give a short explanation of a definition or proof of a theorem orally, at the chalkboard. You are responsible for all assigned reading even if it is not discussed in class. Class will usually include
     1. a short quiz each week;
     2. now and then, a short oral presentation of current material by selected students;
     3. discussion of new material via examples and the proof of new theorems.

Quizzes will be given each week beginning September 14th, except for the weeks of the exams. The quizzes will be closed book, and will count for 10% of your grade. The two lowest quiz grades will be dropped. No make-ups; a missed quiz will count as one of the dropped grades.

Homework will be collected, discussed, graded and returned; Homework, along with oral presentation scores, will count for 20% of your grade. Late homework may be downgraded, if it is later than a week, but it is still worth more than no credit at all.

Exams will be given on October 19th and November 16th. These will be closed book exams. The average of the exam swill count for 35% of your grade. No make-ups except for excused absences with advance notice. The grade on the subsequent exam will be used for both.

Final Examination will be given on Thursday, December 21st, closed book and comprehensive. It will count for 35% of your grade.

Grades: Regulations covering grades (especially I and W) are on pages 254-255 of the 2006-2008 Undergraduate Catalog or on pages 203-205 of the 2005-2007 Graduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination (including most of the homework) but misses the final exam because of an excused absence with advanced notice. The last day to drop a class (with a grade of "W") is Friday, November 17th, and the drop form must be submitted to the Registrar's Office. Anyone registered after that must be graded solely on academic performance.

Objectives: To this end, the completion of a variety of homework problems and the occasional oral presentation are expected of each student. For assessment purposes, copies of some graded homework assignments and exams of each student will be placed in a file in the school office. Further review of these materials for assessment purposes will not affect the student's standing.

Syllabus

Date	Sections	Topics - changeable
September 7	1.1,1.2,1.3	Basic Set Theory; Riemann Integral; Numbers at Random
September 14	2.1, 2.2,	Null Sets; Outer Measure;
September 21	2.3	Lebesgue Measure
September 28	2.4, 2.5, 2.6, 2.7	Basic properties; Borel Sets; Probability; Proofs.
October 5	3.1, 3.2, 3.3	Extended Real Line; Measurable Functions; Examples
October 12	3.4,3.5, 3.6	Properties; Probability; Proofs.
October 19	Exam #1	Chapters 1, 2, 3. - Lecture afterward.
October 26	4.1, 4.2, 4.3	Integral; Monotone Convergence; Integrable Functions
November 2	4.4, 4.5	Dominated Convergence; Riemann Integral.
November 9	4.6,4.7, 4.8	Approximation, Probability; Proofs.
November 16	Exam #2	Chapters 3, 4. - Lecture afterward.
November 23	No Class!	Thanksgiving Break
November 30	5.1, 5.2, 5.3	L¹, completeness, Hilbert space L²,
December 7	6.1, 6.2	Multi-dimensional measure; Product s-fields.
December 14	6.3	Fubini's Theorem.
December 21	Final	Comprehensive.

This page is at http://faculty.roosevelt.edu/jjohnson/Fall2006/M458F06.htm and was last revised December 8, 2006.