MAA
3200 –
INTROD TO ADV
MATH
FLORIDA INT'L UNIV.
PROJECTS #1 and #2
(Sept. 7th,
2008)
FALL 2008
TEXTBOOKS: 1.
"How to Prove it" (2nd edition) by Daniel J. Velleman (2006)
and
2. "Introduction to Analysis" (5th edition) by E.D. Gaughan
(1998)
The questions
below are for credit - so you are not allowed to share your solutions
or discuss the
problems with your classmates. You can use books and on-line sources
but you must
indicate this in your solutions. You are not allowed to ask any
professors,
tutors, or
other students for assistance with these problems but if the questions
are not
clear you can
ask me in class. Always justify your answers and provide all the
details.
Most of
the questions in Project #1 ask what is supposedly wrong with a
putative
proof. You must point
out exactly where are all the
errors and if possible fix them.
Each of
the projects must be done in a BLUE EXAM BOOKLET (size: 8"x
11")
BEGIN EACH QUESTION ON A
SEPARATE PAGE, por favor.
PROJECT
#1 (50 points) - DUE in class on 10-07-08 by 10:45 am
From:: "How to
Solve It" (2nd edition) by Daniel Velleman
A1
Chapter 3 Sec.
1 Nos.
16
(5 points)
A2
Chapter 3 Sec. 2 Nos.
12
(5 points)
A3-5 Chapter 3
Sec. 3
Nos. 21, 23, 24
(5
points each)
A6
Chapter 3 Sec. 4
Nos.
11
(5 points)
A7
Chapter 3 Sec.
5 Nos. 30
(5 points)
A8
Chapter 3
Sec. 6
Nos.
12
(10 points)
A9
Chapter 3 Sec. 7 Nos.
9
(5 points)
PROJECT #2 (50
points)
- DUE in class on 11-20-08 by 10:45 am.
From: "How to Solve It" (2nd edition)
by
Daniel Velleman
B1 Chapter
4
Sec.
1 Nos.
12
(5 points)
B2
Chapter 4 Sec. 3
Nos.
22
(5 points)
B3
Chapter 5 Sec. 1
Nos.
19
(5 points)
B4
Chapter 5 Sec. 4
Nos.
6
(5 points)
B5
Chapter 6 Sec. 1
Nos.
16
(5 points)
B6
Chapter 6 Sec. 3
Nos.
20
(5 points)
B7. Let f(x)
= 4-x and g(x) = (x-7)/(x-3). Find all the set of all
functions that can be
generated by starting with {f,g}and repeatedly using
compositions. (10 points)
B8. Let s(1) =
c and
s(n+1) = square_root [c + 2.s(n)] for
n>0. For which values
of c will the
sequence s(n) converge and to what limit. Give proof. (10
points)
(Hints for B7-8: See
Projects0.4 (p.31) & 1.3 (p.59) and Sol.
to Projects 0.4&3.1
from
"Introduction to Analysis" by
E. Gaughan.)
BONUS
PROJECT (10 points) - DUE in class on 11-20-08 by
10:45 am.
C1. Go to the site Magic
Gopher Puzzle. Your task is to figure out how
the Magic
Gopher gets the correct answer. Prove any mathematical statements
you make.