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 7 study guide (note quizzes are cumulative):**

Define the following properties: closure under composition, associative property, identity, closure under inverses, commutative property

Define group, permutation group, symmetry group, group action (an action of a group G on a set X is a ...), coloring, permutation acting on a coloring, equivalent colorings, G(c) -- the stabilizer of the element c with respect to the group G is ..., C(f) -- the set of all coloring in C fixed by f is ...,

Calculate something related to the above.

Define linear function.

Determine if a function is linear or not.

Define linear recurrence relation.

Define homogeneous recurrence relation.

Solve simple linear homogeneous recurrence relation.

Given general solution to linear recurrence relation, determine solution satisfying initial conditions.

Find the generating function of a sequence and simplify (See Monday's 11/16 lecture).

Define Fibonacci sequence via (1) give first several terms of sequence, (2) by stating the homogeneous linear recurrence relation plus initital conditions.

Define geometric sequence.

State the formula for the partial sums of a geometric sequence.

Define derangement.

Calculate D_n.

State the inclusion-exclusion theorem.

Problem similar to: How many terms are in the sum ∑ | A_{i} ∩ A_{j} ∩ A_{k}|?

State Pascal's formula.

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