Warm Up 1/22/20131) What is 20% of 84?2) Round 987.435

a) to the nearest tenth.b) to the nearest hundredth

3) Truncate 54.894) Find the mean

a) 60, 80, 90, 100, 100b) 0, 80, 90, 100, 100

Answers1) .20(84)=16.82) a) 987.4 b) 987.443) 544) a) 86 b) 74

Two minutes:1) 58% of 1292) Round 93.652

a) nearest wholeb) nearest tenthc) nearest hundredth

3) Find the mean:

x

0

100

2

6

f

Hello BingoDirections: Collect the names of classmates or the teacher that satisfy the condition.

You may only use a person once and you may not use yourself.

Winning: A five box line has been formed down, across, or diagonally with names. Take your paper to the front to be verified.

B I N G O

Can find the mean of 0, 100, 100, 100

Plays on the basketball team.

Has never been on Facebook

Sings in the RHS chorus.

Can draw a diagram for“All squares are rectangles”

Was born in Plans to enter the military

Is a vegetarian

Brought a calculator to class today.

Is on the track team

Has an after school job

Has been in a school play

Free Space

Is in ROTC Has been skydiving

Can name the 5 points of PRIDE from memory

Has someone under 3 living at their place.

Has someone over 65 living at their place.

Has more than three pieces of jewelry on today.

Has over a dollar in change on them.

Was born in a different country.

Can graph x<3

Has a journalism pass

Has helped with Service Learning

Has broken three or more bones.

What is Discrete Math?

For the world…

•Discrete mathematics includes sets, functions and relations, matrix algebra, combinatorics and finite probability, graph theory, finite differences and recurrence relations, logic, mathematical induction, and algorithmic thinking. Other topics often considered part of discrete mathematics are Boolean algebra, the mathematics of social choice, linear programming, and number theory.

More simply…

• Because of this diversity of topics, it is perhaps preferable to view discrete mathematics simply as the mathematics that is necessary for decision making in noncontinuous situations

Set Theory

• Set Notation• Venn Diagrams

Recursion and Mathematical Patterns

• Sigma Notation• Arithmetic Sequences and Series• Arithmetic Means of a Sequence• Geometric Sequences and Series (finite and

infinite)• Factorial• Pascal’s Triangle• The Binomial Theorem

Election Theory

• Preference Schedules• Plurality• Majority• Condorcet• Runoff• Paradoxes• Arrow’s Conditions• Approval Voting

Apportionment and Fair Division

• Estate Division• Rounding & Truncating• The Ideal Ratio• Quotas• Adjusted Ratios• Constituency• Absolute Unfairness• Relative Unfairness• Hamilton• Jefferson• Webster• Mean• The Geometric Mean• Hill• The Continuous Case (Moving Knife, Inspection, Cut & Choose)

Matrices

• Basic Operations• Using a matrix for inventories• The Leslie Model

Probability

• Counting Methods (Permutations and Combinations)

• Independent and Dependent Events• Using tables and trees• Expected Value• The Fair Bet

Graphs• Circle• Stem and Leaf• The Five Number Summary• Box and Whisker• Fences, Outliers and Extremes• Box plot• Bar Graph• Pareto Graph• Classes• Histogram• Uniform, skewed, symmetric distributions• Relative Frequency Histogram• Cumulative Frequency• Ogive• Frequency Polygon

Statistics

• Mean, Median, Modes• Deviations and Variance• Standard Deviation• The Standard Normal Curve• Z scores• The Empirical Rule• Normalcdf• Invnorm• Warrantees

Graph Theory

• Connected Coloring• Chromatic Number DegreeEven and Odd• In and Out Adjacency Matrix• Complete Tournaments• Set Notation Bridges• Bipartite Hamilton• Euler Paths and Circuits• Brute ForcePrim’s & Kruscal’s• Nearest Neighbor Shortest Path• Spanning Trees Critical Path & PERT• EST/LST Binary Trees• RPN Transverse a tree