Final Review
MA 114-004
Fall 2015
The Final will cover will cover sections 1.1-1.4, 2.1-2.5, 3.1-3.2, 4.1-4.3, 4.5, 5.1-
5.7, 6.1-6.5 and 8.1-8.2 in Finite Mathematics and its Applications, Goldstein,
Schneider, and Siegel, 11th Edition.
Topics
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Equations of lines
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Graphing lines
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Graphing linear inequalities
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Finding feasible set of a system of linear inequalities
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Finding the intersection point of a pair of lines
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Addition Method
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Substitution Method
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Gaussian and Gauss-Jordan elimination
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Solving systems of at least 2 variables using the Gauss-Jordan method.
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Matrix inverse
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Finding inverse of
2
×
2
matrix
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Finding inverse of larger dimension using the Gauss-Jordan method
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Determining if an inverse exists
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Linear Programming
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Finding optimal solution using the steps outlined in class
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Definition of a simplex tableau
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Introduction of slack variables
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Solving optimization problems using the Simplex Method
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For problems in standard form
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For maximum problems
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For minimum problems
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Duality
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Union and intersection of a sets
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Listing all subsets of a set
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Complement of a set
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The inclusion-exclusion principle
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DeMorgan’s Laws
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Venn diagram representation of sets
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The Multiplication Principle
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Permutations and combinations
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Formulas
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In applications
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Problems counting possible combinations with ‘or’
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The Binomial Theorem
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Formula for a binomial coefficient
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Probability definitions
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experiment
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outcome
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sample space
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event
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mutually exclusive
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Determining a sample space
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Probability rules
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Computing probability when outcomes are equally likely
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Inclusion-Exclusion Rule
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Conditional probability
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Independence
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Tree Diagrams
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Constructing
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Computing conditional probability and probability of an intersection
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Markov processes
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Transition stochastic matrices
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Properties of stochastic matrices
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Transition diagrams
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Computing probability distribution for all states
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Regular stochastic matrices
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Properties of the stable matrices
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Finding the stable matrix/distribution.
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Some Practice Problems