COMP280: lectures sketches
Spring 2004
The following notes are my own sketch to myself,
of what topics/examples to cover.
They are not any substitute for lecture,
nor are they even meant to be comprehensible to others.
However, for topics which are not also discussed in the book,
I'll attempt to have my notes be more readable.
Readings refer to sections of Rosen 5ed, unless indicated otherwise.
Future dates are tentative topics,
depending on how much gets covered in particular lectures.
(For past dates, if you notice discrepancies between
the listed topic and the actual topic,
please let me know).
For the first few weeks of class, Logic, the
readings/lecture-notes are from
the on-line
TeachLogic
project.
(Though if you want, you can certainly read Rosen's survey of
topics, sections 1.1-1.4.)
- Jan.13: intro;
logic motivation [archive pdf].
- Jan.15:
propositions [archive pdf],
reasoning with truth tables [archive pdf].
- Jan.20:
Finish
reasoning with truth tables [archive pdf];
start
reasoning with algebra [archive pdf].
Handouts:
boolean algebra laws [archive pdf],
inference rules [archive pdf],
waterworld axioms [archive pdf].
- Jan.22:
Finish
reasoning with algebra [archive pdf];
start
reasoning with inference rules [archive pdf].
- Jan.27:
Finish
reasoning with inference rules [archive pdf].
- Jan.29:
Modeling WaterWorld [archive pdf]
with relations;
interpretations [archive pdf] and
modeling [archive pdf] other
situations.
Begin
quantifiers [archive pdf].
- Feb.03:
First-order logic = propositional logic +
quantifiers [archive pdf];
- Feb.05:
boolean algebra with quantifiers [archive pdf].
-
Feb.10:
inference rules with quantifiers [archive pdf];
-
Feb.12:
sets (Rosen sections 1.6, 1.7).
-
Feb.17:
Finish
sets,
begin
relations and graphs.
-
Feb.19:
relations and graphs;
functions.
-
Feb.24: begin Cardinality
-
Feb.26: finish Cardinality
-
Mar.02, 04:
Spring break!
-
Mar.09:
Induction
-
Mar.11:
Strong Induction
-
Mar.16:
Structural Induction
-
Mar.18:
Finish
Structural Induction,
start Program proofs
-
Mar.23:
Finish
Program proofs.
-
Mar.25:
Algorithm complexity, and big-Oh
-
Mar.30:
modular arithmetic
-
Apr.fo01:
inverses mod n, Fermat's Little Th'm
-
Apr.06:
mod applications: hashing, public key;
-
Apr.08:
Counting
-
Apr.13:
Recurrence relations
-
Apr.15:
Finite State Machines
-
Apr.20:
Complexity: P vs NP
-
Apr.22:
Some cute problems