Always subject to change, correction, and updates during the term.

MA 4450
Fall '10, T. Olson

Homework:

  1. (due W 9/8) Chapter 1 problems # 4, 13
  2. (due W 9/15) Chapter 1 problems # 15, 25, 21 with p=3, 45, 46
  3. (due F 10/1) (3 examples) plus Chapter 2 problems # 21,22,24,34
    -- problems 21,22,24 collected on Friday, 9/24
    -- 3 examples and problem 34 collected Monday, 9/27
  4. (due F 10/8 ) Chapter 3 problems # 2,14,15,18,30
    -- problems 2,14,15 collected Monday
    -- problems 18,30 collected Wednesday

  5. (due F 10/15 ) Chapter 3 problems # 23,27,31,36,44
    -- problems 23,27,31, and convergent-implies-Cauchy collected Monday
    -- problems 36, 44 collected Wednesday

  6. Chapter 4 problems # 2,15,19,20,22,"problem 34" handout
    -- problems 2,15,19 collected Wednesday
    -- "problem 34" (again!) collected Friday

  7. Chapter 16 problems # 16,18,20,24, and border examples for Heine-Borel theorem

  8. (due W 12/8) Chapter 5 problems 2, (8), 19, 30, 48
Cantor Function Notebooks: Instructor: Tamara Olson (trolson at mtu.edu)
310 Fisher Hall
487 - 2191

Office Hours: Tu/Th 10am-noon and by appointment

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 first 11 pages are available online from Cambridge University Press. View the ``Excerpt'' at http://www.cambridge.org/us/ .

We will cover most of chapters 1-8, plus an introduction to Lebesgue measure and Fourier series (parts of chapters 16-18).

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

Extra homework problems.

"Three examples" homework: Your examples do not have to be written as a formula; a graph is fine.

  1. Give an example of a function mapping [0,1] to [0,1] which is increasing and continuous, but not onto.
  2. Give an example of a function mapping [0,1] to [0,1] which is onto and continuous, but not monotone.
  3. Give an example of a function mapping [0,1] to [0,1] which is increasing and onto, but not continuous.


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