CS 173, Spring 2009: Skills list for third quiz
The second midterm will cover the material presented in lectures 1-35.
It will focus on the material since lecture 27 (the last lecture covered
on the second midterm).
Since you have not yet had time to do homework problems on the
material from lectures 33-35, only more basic aspects of this material
will be tested. The corresponding sections of Rosen are listed on the
Lectures web page.
- Everything on the skills lists for the previous quizzes and midterms.
- Structural and tree induction
- You should know how to simple structural and tree induction
proofs, like those on homework 8. We can't ask you to write such a
proof on a short quiz, but we might ask you something simpler e.g.
to write the inductive hypothesis for such a proof.
- Counting
- Know the formulas for counting permutations, combinations,
combinations with repetition, permutations with indistinguishable objects.
- Know the Binomial Theorem, Pascal's Identity, Vandermonde's Identity.
- Know the formula for a binomial distribution, and for the
expected value of a binomial random variable.
- Apply these formulas to solve word problems.
- Discrete Probability
- Calculate probabilities by comparing often an event occurs to
the size of the sample space.
- Define conditional probability, compute the conditional probability
of two specific events.
- Define what it means for two events to be independent.
Decide whether two specific events are independent
- Know the formula for Bernoulli trials. Apply the formula to word
problems.
- Define a (discrete) random variable. Compute the expected value of a
random variable.
- Compute that expected value of a sum of random variables is the sum
of their expected values (linearity of expectation).
- Relations
- Define a relation on a set A.
- Represent a relation as a set of pairs or a directed graph, convert
between the two representations.
- Define reflexive, irreflexive, symmetric, anti-symmetric, transitive.
For any of these problems, determine if a specific relation has the property
and prove that your answer is correct.
- Define an equivalence relation, partial order, strict partial order.
- Graphs
- Define a graph (set of vertices plus a set of edges), simple graph.
- Understand terminology: directed vs. undirected graph,
adjacent/neighboring vertices, endpoints of an edge, edge connecting
(incident with) two vertices, self-loop, subgraph, path
- Define: degree of a vertex, in-degree and out-degree (directed graphs).
- State the Handshaking theorem. Know that a graph has an even number of
vertices of odd degree.
- Define special graphs Kn, Cn, Wn,
Qn, Kn,m and know their full names (e.g. "complete bipartite graph").
Beware: Wn contains n+1 vertices.
- Give the degree sequence of a graph.
- Define: Euler circuit, Euler path, Hamilton circuit, Hamilton path
- Recognize when two graphs are isomorphic. Identify features which
show that two graphs are not isomorphic (e.g. different vertex degrees).
- State the Euler circuit theorem and Euler path theorem.