ArsDigita University
Month 2:
Discrete Mathematics  Professor Shai Simonson
Syllabus
Week 1:
Introduction, Proofs, Logic, Boolean Algebra and applications, Sets and
applications, Basic sums and functions.
Reading:
Rosen 1.11.8, 3.13.2, 5.5, 9.19.3
How to Read Mathematics
(
http://academics.stonehill.edu/compsci/History_Math/mathread.htm
), Polya,
How to Solve It
.
Lecture 1:
What kinds of problems are solved in discrete math?
What are proofs?
Examples of proofs by contradiction, and proofs by induction:
Triangle numbers,
irrational numbers, and prime numbers. (3.13.2)
Lecture 2:
Boolean Algebra and formal logic.
Applications in algorithms, complexity
theory, AI, digital logic design and computer architecture. (1.11.2, 9.19.3)
Lecture 3:
More logic: quantifiers and predicates
.
Sets, operations on sets, using
logic to prove identities on sets. (1.31.5)
Lecture 4:
Sets.
Applications in counting (the inclusionexclusion theorem), theory
of computation and data structures. (5.5)
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 Spring '09
 Combinatorics

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