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45 Cards in this Set
- Front
- Back
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Mathematical Induction |
a way of proving a formula (conjecture) is true for all values in the domain |
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sum of numbers from 1->100 |
n(n+1)/2 |
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Probability |
odds of an even occurring |
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Sample Space |
set of all possible out comes |
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event |
set of desired outcomes |
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Permutation is order important? |
an ordered arrangement of all or some of the elects of a set order is important |
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Formula for a Permutation |
n!/(n-r)! |
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Combinations is order important? |
the number of subsets of a specific size Order is not important. |
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Formula for Combinations |
n!/(r! (n-r)!) |
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Functions |
act on input (x) to produce an output (y) value |
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Domains (x) |
set of independent variables |
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Range (y) |
results |
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Co-Domain |
Domain (where range is contained) set of possible results |
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One-to-One |
function for which every element of the range of the function corresponds to exactly one element of the domain |
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Onto |
every Y is used |
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State Transition Diagram |
shows each state, each input value on each state where it goes (next state etc)
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PigeonHole Principle |
pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item |
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Composition of Functions |
the restate of one function (range ) may be the input (sub of domain) of a second function |
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Graph |
Consists of a finite set of vertices (nodes) and a finite set of edges connecting them |
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Directed graph (di-graph) |
consists of a finite set of vertices (nodes) and a finite set of directed edges each edge is associate3d with an ordered pair of vertices |
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Simple Graph |
a graph that does not have any loops or parallel edges (may have an isolated vertex) |
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Complete graph |
A simple graph where each vertex is connected to every other vertex |
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Degree of a vertex |
Number of edges that connect to it |
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Total degree of graph |
sum of the degrees of all vertexes |
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Walk |
travel from one vertex to another |
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closed walk |
a walk that starts and ends last the same vertex |
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Trail |
a walk that does not repeat any edges |
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Path |
A trail that does not repeat any vertexes |
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Circuit |
A closed walk that does not repeat edges |
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Simple Circuit |
A circuit that does not repeat any vertices |
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Euler Circuit |
starts and stops at the same vertex contains every vertex (at least once ) and every edge only once every vertex must have an even degree graph must be connected then there will be a Euler Circuit |
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Root |
one vertex form which all others hang from "A nicely HUNG tree" |
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Terminal Vertex |
a vertex that does not have any children, Leaf degree of 1 |
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internal Vetex |
a vertex that is not a leaf degree is >1 |
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tree |
a connected graph with no circuits (may be trivial) |
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Binary tree |
a rooted tree where at most each vertex has at most 2 children |
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Full Binary Tree |
if a node has children with has 2 of them |
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Properties of a Binary tree |
K internal vertices K+1 terminal vertices total 2k+1 vertices |
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spaning tree |
a sub graph that contains every vertex (you take away edges till there is not circuits thus creating a tree, while not isolating any vertexes) |
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Minimum Spanning Tree |
Has the least total weight |
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Relation |
An Association between data |
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Reflexive |
Every value relates to its self |
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Symmetric |
if xRy then yRx |
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Transitive |
if xRy and yRz then xRz |
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Cardinality |
the number of elects in a set |
