Thus for each quiz, make sure you study the basics as outlined in each quiz study guide (click on SG for the appropriate quiz for the Study guide.

You will have more time on exams, so exam questions can be more challenging (so practice more than just the basics).

Quiz 4 study guide (note quizzes are cumulative):

Define inversion, disorder, even permutation, odd permutation.

Problems similar to HW ch4: 1, 7, 10, 11, 12, 15.

Define: relation, reflexive, irreflexive, symmetric, anti-symmetric, transitive, partial order, total order, equivalence relation, equivalence class, partition.

Give an example of a relation that satisfies (and/or does not satisfy) some of the above properties.

Prove a relation is reflexive, irreflexive, symmetric, anti-symmetric, or transitive.

Define complete graph.

Draw K1, K2, K3, K4, K5.

Find a coloring of K5 that does not contain a blue K3 or a red K3

Define ramsey number r(3, 3).

Define ramsey number r(s, t).

Define: 1:1, onto, bijection.

Prove a function is not 1:1 or not onto.

Section 3.1: State what are the objects and what are the boxes for Application 1, 2, 6; solve application 2

Section 3.2: State what are the objects and what are the boxes and/or solve Application 7

Define: P(n, r), C(n, r) both mathematically and in words:

Mathematically: P(n, r) = n!/(n-r)!, C(n, r) = n!/[r!(n-r)!]

In words:

P(n, r) = the number of r-permutations of a set S where |S| = n

C(n, r) = the number of subsets with r elements from set set with n elements.

Define: r-permutation, r-subset, multiset.

OR

Calculate simple problems such as number of subsets, P(n,r), C(n, r), permutations of multisets including unlimited repeats, limited repeats, and determining number of non-negative integral solutions to x1 + x2 + ... + xk = r.

OR

Solve a problem (almost) identical to one of your shorter HW problems: 1, 4, 17, 19a, 20, 39a