MA 4450
Fall '06, T. Olson

NEW: Final Exam (postscript) and ``Tips on Writing Proofs''
Final Exam (pdf)

Instructor: Tamara Olson (trolson@mtu.edu)
310 Fisher Hall
487 - 2191

Office Hours: MW 2:00-3:30pm, F 11am-noon, and by appointment
(In addition, I am almost always free immediately after class each day.)

Prerequisites: One semester of undergraduate real analysis (for example, the topics covered in "Elementary Analysis: The Theory of Calculus" by Kenneth A. Ross) and one semester of linear algebra.
(MA 3450 and (MA 2320 or MA 2321 or MA 2330))

Text: Real Analysis by N.L. Carothers
The bookstore does not carry this text, so you must purchase a copy through Amazon.com or another source. The first 11 pages are available online from Cambridge University Press. View the ``Excerpt'' at http://www.cambridge.org/us/ .

Homework writeups:

  1. Chapter 1 problems: #(14 or 15), 21 (with p=3), 25, 46, part of 47
    due Monday 9/18
  2. Chapter 2 problems: #22, 29, 33
    due Wednesday 9/27
  3. Chapter 16 problems:
    #4 and 2 counterexamples
    #9, 16, 42
    due Monday 10/9
  4. Chapter 16 (part II):
    #40, 58, 61
    due Monday 10/16
  5. Chapter 17:
    #1,4,6
    due Monday 10/30
  6. Chapter 3 :
    #2,15,18,44
    due Monday 11/6
  7. Chapter 4 :
    #15,17,20,22
    due Monday 11/13
  8. Chapter 4 (part II):
    #46a, 46d, and critique of a ``proof''
    (some subset of #46,48,49,50)
    due Monday 11/27
  9. Chapter 7 (pp.94-95):
    #16,18,19 (some subset of 12, 13, 14, 16, 18, 19, 25)
    due Monday 12/4
  10. Fourier series stuff
    due Monday 12/11

Tentative schedule:

Week(s) Text Topics
1-2 Ch.1 (review) real numbers, limits, continuity
3-4 Ch.2 countability, Cantor set, monotone functions
5-6 Ch.16 Lebesgue measure
7 Midterm Exam  
8 Ch.17-18 (parts) measurable functions and integration
9-10 Ch.3 (plus L2 theory) vector spaces: metrics and norms, limits
11 Ch.4 open and closed sets in a metric space
12 Ch.7 Completeness
13   L2 and inner products
14   Fourier series
14.5 Final Exam  

Your comments are solicited on these
Possible topics for last three weeks:

Assessment: Written homework assignments will be collected regularly (weekly) and there will be a midterm exam and a final exam. Occasionally, you may be required to make an in-class presentation as part of a homework assignment or an exam.

Grade: Homework: 40%
Mid-term Exam: 30%
Final Exam: 30%


Proof-writing help



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trolson@mtu.edu
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