Math 442 Foundations of Analysis II (3 credits)
     Class Number: 20551

Meets 4:30p - 5:45p TuTh in LD 002

Final Exam: Tuesday, May 1, 3:30p - 5:30p

Carl Cowen
    Office:  LD 224P
    E-mail:  ccowen "at" iupui "dot" edu
    Phone:   278-8846
    FAX:     274-3460

Office Hours:
   MWF 10:40a - noon, or by appointment

Professor Misiurewicz's webpage for Math 442

Cowen's Syllabus for Math 442

Draft version: Summary of Key ideas, definitions, results

Homework 1, Due March 22

Homework 2, Due March 22

Homework 3, Due April 3

Homework 4, Due April 10

Homework 5, revised, with partial solutions, Due April 17

Problems for Thought (revised), Will not be graded

     Class Schedule

(page numbers refer to Pugh's "Real Mathematical Analysis")

March 6       Stone-Weierstrass Theorem, alternating harmonic series
              pages 217-228
March 8       More on Stone-Weierstrass Theorem, alternating harmonic series,
              review of series, power series
              pages 179-185, 207-213

Spring Break: March 12-16, No Class, No Office Hours 

March 27     Midterm Test I 
              
       Reference for the remainder of the course: "Real Analysis"
                2nd edition, H. Royden, on reserve at IUPUI Library

March 29      Introduction to Lebesgue measure, definition of outer measure
              Pugh pages 363-367  Royden pages 52-56
April 3       Corrections for Midterm Test I Due, Homework 3 Due
              Continuation of discussion of outer measure, definition
                 of measurability
April 5       Theorems on measurability 

April 10      Homework 4 Due
              Continuation of discussion of measurability and definition
                of Lebesgue measure
              Properties of Lebesgue measure
April 12      Continuation of properties of Lebesgue measure:
                Lebesgue measure is a countably additive, translation
                 invariant measure on the sigma-algebra of measurable
                 sets on R (which contains the Borel sigma-albebra
                 and all sets of measure zero).

April 17      Completion on ideas on Lebesgue measure, definition
                 of measurable function
              Homework 5 Due

April 19    Midterm Test II 

April 24      Properties of measurable functions, simple functions,
                prelude to the Lebesgue integral



May 1       Final Exam: 3:30p - 5:30p 

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