MA 5401 Syllabus
Fall '04, T. Olson
Instructor:
Tamara Olson
(trolson@mtu.edu)
310 Fisher Hall
487 - 2191
Office Hours:
WF 11:30am-12:30pm
Fri 2-3 pm (Fisher 310 or 331)
and by appointment
Homework assignments
#9 (due F 12/3) Problems 5.14a, 5.14b, 5.19a (p.111),
in-class presentation from section 5.4,
and proof of Lemma 16
#8 (due W 11/17) Problems 5.7 and 5.10 (p.104) and
in-class presentation from section 5.3
#7 (due W 11/10) Problems 5.1 and 5.3 (pp.101-102)
and example of a function f
where strict inequality holds in theorem 5.3 (p.100).
#6 (due W 11/3) Example, problems 4.5 and 4.7 (p.89),
and problem 4.10 (p.93)
#5 (due W 10/13) Cantor function problems and problem 3.28:
- Prove that the Cantor ternary function is continuous
- Prove that the Cantor ternary function is monotone
- Prove that the Cantor ternary function is measurable
- Consider the Cantor ternary function as a mapping from the Cantor set, C,
to the unit interval [0,1].
Does the Cantor ternary function map C onto [0,1]?
Is this mapping one-to-one?
(Justify your claims with proof or counterexample.)
- Problem 3.28 (pp.71-72)
You may assume that the two definitions of the Cantor
ternary function are equivalent,
and that the Cantor ternary function is constant on each interval
Ikj
of the complement of the Cantor set.
#4 (due M 10/4) problems 3.19, 3.22, 3.24 (pp.70-71)
#3 (due M 9/27) problems 3.15, 3.16, 3.17a (p.66) and in-class presentation
(part of problem 3.23)
#2 (due M 9/20) problems 3.5, 3.8 (p.58) and 3.14b (p.64)
#1 (due M 9/13) problems 2.37, 2.38 (p.46) and 3.14a (p.64)
Text:
H.L. Royden, Real Analysis, Third Edition, 1988.
Material in chapters 3-5.
Assessment:
Homework, a midterm exam, and a final exam.
Homework grades will be either ``Good,'' ``O.K.,'' or ``resubmit.''
(``Good'' and ``O.K.'' correspond to ``A'' and ``B''.)
Grade:
Homework: 40%
Mid-term Exam: 30%
Final Exam: 30%
Proof-writing help