MTH 355
Symbolic Logic
This course meets from 10:50 AM  12:05 PM TTh in Business 110.
The
syllabus
will be available in LaTeX,
DVI, and
Postscript, and
HTML.
A schedule of lectures tells
what I plan to talk about, and what I expect you to have read, by each
class meeting.
Textbook
We're using the textbook
The
Language of FirstOrder Logic, by Jon Barwise and John Etchemendy.
This book comes with a floppy disk in the back, either for Macintosh or
Windows. You may buy and use whichever you prefer: the Macintosh
edition has a red cover, while the Windows edition has a blue cover.
The authors have set up an
online
errata page for the textbook.
I used this textbook a year ago for the MTP
course in Mathematical Logic, and was quite happy with it. It comes
with a computer program named "Tarski's World" which allows the user to
experiment with logical sentences interpreted in an onscreen "world".
Some of your homework assignments will be turned in on floppy disk,
while others will be turned in on paper (or, if you prefer, by email).
Homework assignments
 Homework 1, assigned 16 Sept, due 30 Sept, extended to 9 Oct
because the book hadn't come in yet
 Problems from chapter 2 of the textbook:
3,4,5,19 (to be turned in on floppy disk)
6,8,9,10,17,18,21,22,24 (to be turned in on paper or by email)
Note: some of the statements in problem 2.9
cannot be translated; your job is to translate the ones that
can, and give some explanation of why the others can't.
 Homework 2, assigned 21 Oct, due 4 Nov

Problems 3.9,3.17*,3.18,3.20,3.26* (paper or email)
Problems 3.30,3.31,3.34 (informal proofs on paper or email;
counterexamples on disk)
Problems 3.43 (formal proof, paper or email)
Problem 3.60* (paper or email)
Problems 4.4,4.5 (on disk)
Problems 4.11 (paper or email)
Problem 4.14 (informal proofs, paper or email; counterexamples on disk)
Problems 4.25 (formal proofs, paper or email)
 Homework 3, assigned 6 Nov, due 25 Nov

Problems 5.18, 5.23, 5.24, 5.25, 6.9, 6.26, 6.37, 6.52 (paper or email)
Problems 6.19, 6.20, 6.23, 6.50 (on disk)
 Homework 4, aka takehome final exam,
assigned 25 Nov, due at the scheduled exam time, 10:30 AM, 16 December.

Problems 7.2, 7.3, 7.4, 7.9, 7.10, 7.25, 7.27, 7.28, 7.29, 7.30, 7.31,
Problems 8.16, 8.17, 8.18, 8.19, 8.25, 8.26, 8.34, 8.35
And on mathematical induction, the following three:
 Prove that there exists a real number x>1 such that for all
sufficiently large n,
F_{n} >= x^{n},
where F_{n} indicates the nth Fibonacci number,
defined by
F_{0} = F_{1} = 1 and
for n > 1, F_{n} = F_{n1} + F_{n2}.
Hint: You'll need to use a base case larger than
1. How much larger depends on what value of x you choose.
Extra credit: What is the smallest value of x for
which you can't make your proof work, even by picking a large base
case?
 Prove that for every natural number n, and every square on a
2^{n} x 2^{n} checkerboard, there is a way to tile
the checkerboard using 3square, Lshaped tiles, leaving out only
the specified square and not overlapping any tiles.
 Prove the "Pigeonhole Principle": that for any finite set S
and any function
g : S > S, if g is not onto, then g is not onetoone.
("g is onto" would mean
that for every element x of S, there is a y in S such that g(y)=x.
"g is onetoone" would mean that
for every elements x and y of S, if g(x)=g(y) then x=y.)
Reading assignments
By Tuesday, 16 Dec, you should have read through chapter 9
of the textbook.
Last modified:
Thu Dec 11 15:45:33 EST 1997
Stephen Bloch / sbloch@boethius.adelphi.edu