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COMP280 Syllabus
Spring 2005
The following notes are my own sketch to myself,
of what topics/examples to cover.
They are no substitute for lecture.
Suggested strategy:
between each class, after you review the previous lecture's notes,
print and scan the upcoming notes.
In class you're then freed up to
follow along in the hardcopy, annotating as needed.
- Logic (a language for reasoning, and for interfaces)
- Jan.13: intro: 90=100;
logic
motivation,
and
what is a proof?.
- Jan.18:
propositions
,
and
well-formed formulas.
Reference:
waterworld axioms.
- Jan.20:
reasoning with truth tables,
limitations of truth tables;
reasoning with algebra ,
normal forms.
Handouts:
boolean algebra laws,
inference rules,
- Jan.25:
reasoning with inference rules.
- Jan.27:
Inference rules
and sub-proofs.
- Feb.01:
Modeling WaterWorld
with relations;
interpretations,
modeling
other
situations,
and
quantifiers.
- Feb.03:
First-order logic = propositional logic +
quantifiers (cont.)
- Feb.08:
boolean algebra with quantifiers.
- Feb.10:
inference rules with quantifiers
- Sets and Functions (a language for data)
- Feb.15:
sets (Rosen sections 1.6, 1.7)
- Feb.17:
relations and graphs
-
Feb.22:
functions
-
Feb.24:
wrap up functions,
most of Cardinality.
-
Mar.01:
wrap up Cardinality,
begin Induction.
Exam 1 released (take-home)
- Reasoning about {data, programs} x {recursive, iterative}
-
Mar.03:
Induction
Mar.04 17:00: Exam1 take-home due
-
Mar.08, 10:
Spring brrreak!
-
Mar.15:
Finish Induction, and cover
Strong Induction
-
Mar.17:
Structural Induction
-
Mar.22:
Program proofs
-
Mar.24:
Program proofs (cont.)
- Arithmetic
-
Mar.29:
Algorithm complexity, and big-Oh
-
Mar.31:
Recurrence relations
-
Apr.05:
modular arithmetic
-
Apr.07:
Spring rrRecess!
-
Apr.12:
inverses mod n, Fermat's Little Th'm
-
Apr.14:
mod applications: hashing, public key
-
Apr.19:
Counting
- Computing with Restrictions (a smattering)
-
Apr.21:
Finite State Machines
-
Apr.26:
Complexity: P vs NP
-
Apr.28:
Some cute problems
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 everything but Logic, readings can be found in Rosen.
For the first Logic portion, the
above 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.)
Some things I wish I'd said:
Digressions on
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