Discrete Structures Fall 2008

92.322

Schedule

 

 

If a problem in ``Assigned on this date"

column is underlined, click on it to see a solution.

 

All problems are due in one week unless stated otherwise.

 

 

 

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Practice Test for First Midterm

Practice Test for Second Midterm

Material for the Final

Class Number

Topics / Reading

Assigned on this date

1, Sep. 3

Sets, lists. Permutations. Factorials. Stirling formula. Number of k-element subsets of an n-element set. Binomial coefficients. Binomial formula. Pascal’s triangle. Combinations with repetitions started.

 

2, Sep. 5

Combinations with repetitions continued. Distributing identical gifts to distinguishable children. Fair distributions (each child gets at least one gift) – method of separators.

3, Sep. 8

General distributions – method of borrowing and returning. Counting the number of monomials of degree d that can be constructed from n variables.

1.8.26, 1.8.33 and the problem given in class

4, Sep. 10

Counting the number of monomials of degree at most d that can be constructed from n variables. Notion of Probability Space.

 

 

5, Sep. 12

 

Notion of Probability Space. Notion of measure. Finite Probability Spaces. Birthday Paradox.

 

 

6, Sep. 15

 

Formulation of Inclusion-Exclusion Principle. Notion of disjoint union. Proof of I-E Principle based on the idea of canonical partition induced by the covering of the union by individual sets.

2.5.6

 

7, Sep. 17

 

 

 

 

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