MATH 145, DISCRETE MATHEMATICS FOR ENGINEERS, SECTION 1001, SPRING 2008
ANNOUNCEMENTS
This is a page for occasional announcements.
- March 05: Re problem 4.1(7); to show that every integer >7 is
a sum of a nonnegative integer multiple of 5 plus a nonnegative
integer multiple of 3. The base case is n=8, which is 5•1+
3•1;
so this is established. The statement we wish to prove is
∀n≥8 P(n), where P(n) is the formula
∃k∃m(n=5k+3m). We've established P(8); so as our
induction step, we fix n≥8, assume P(n) is true, and try to
prove P(n+1) is true. So assume n=5k+3m for some k,m≥0.
There are two cases to
consider; first where k=0, then where k>0. If k=0, so n=3m, then
we know m≥3 because n≥8. Then we have n+1=1+3m=
1+9+3(m-3)=5•2+3(m-3). Setting k'=2 and m'=m-3 (both nonnegative),
we have n+1=5k'+3m'; so P(n+1) holds in this case. In the other
case, we have k>0, so n+1=1+5k+3m=6+5(k-1)+3m=5(k-1)+3(m+2). Here
we have k'=k-1 and m'=m+2, again both nonnegative, so P(n+1) holds
in this case too.
- February 07: There are sample exam questions--with answers--on
this site; also I plan to be in my office tomorrow morning by 10 for any
pre-exam questions.
- February 05: In the event of a snow day tomorrow, I will be holding
extended office hours on Thursday (1--5pm).
- February 01: There will be tutoring sessions for this course;
sign up in AMU 317.
- January 25: Answers to assigned homework problems will be posted
the day they're due, unless there have been arrangements made to accept
a late assignment. So look for the answers to be posted this afternoon.
- January 18: It turns out that the only time our logic seminar can
be scheduled to everyone's satisfaction is 10am on Fridays. Because of
that I must move the Friday 10am office hour to 2pm. The other 10am
slots remain unaltered--at least for now. Please note this change in the
syllabus.