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Answers 1) .20(84)=16.8 2) a) 987.4 b) 987.44 3) 54 4) a) 86 b) 74

Warm Up 1/22/2013 1) What is 20% of 84? 2) Round 987.435 a) to the nearest tenth. b) to the nearest hundredth 3) Truncate 54.89 4) Find the mean a) 60, 80, 90, 100, 100 b) 0, 80, 90, 100, 100. Answers 1) .20(84)=16.8 2) a) 987.4 b) 987.44 3) 54 4) a) 86 b) 74.

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Answers 1) .20(84)=16.8 2) a) 987.4 b) 987.44 3) 54 4) a) 86 b) 74

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  1. Warm Up 1/22/20131) What is 20% of 84?2) Round 987.435a) to the nearest tenth.b) to the nearest hundredth3) Truncate 54.894) Find the mean a) 60, 80, 90, 100, 100b) 0, 80, 90, 100, 100

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

  3. Two minutes:1) 58% of 1292) Round 93.652a) nearest wholeb) nearest tenthc) nearest hundredth3) Find the mean: x f 0 2 100 6

  4. Hello Bingo • Directions: 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.

  5. What is Discrete Math?

  6. 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.

  7. 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

  8. Set Theory • Set Notation • Venn Diagrams

  9. 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

  10. Election Theory • Preference Schedules • Plurality • Majority • Condorcet • Runoff • Paradoxes • Arrow’s Conditions • Approval Voting

  11. 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)

  12. Matrices • Basic Operations • Using a matrix for inventories • The Leslie Model

  13. Probability • Counting Methods (Permutations and Combinations) • Independent and Dependent Events • Using tables and trees • Expected Value • The Fair Bet

  14. 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

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

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

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