Discrete math Flashcards Set

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Last updated 6:45 AM on 3/11/25
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21 Terms

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Discrete Math
A branch of mathematics essential for computer science, focusing on counting/combinatorics to discover patterns and understand complexity.
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Graph
A representation of pairwise relations with entities as vertices and relations as edges.
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Euler's formula
For planar graphs, the formula v - e + f = 2 relates vertices (v), edges (e), and faces (f).
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Vertex
An entity in a graph that connects through edges.
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Edge
A relation between two vertices in a graph.
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Face
An area you can move within in a planar graph without crossing any edge.
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Summation notation
A notation used to represent the sum of a sequence of numbers, e.g., Σᵢ₌₀⁹ 2 = 2 + 2 + 2 + ... + 2.
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Distributive property
The property stating that Σ cf(i) = c Σ f(i), allowing the factor to be distributed.
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Permutation
An arrangement of objects in a specific order; the number of permutations on n objects is n!.
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Anagram
A word created by rearranging the letters of another word, accounting for identical elements to avoid overcounting.
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Set
An unordered collection of distinct elements, which can be finite or infinite.
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Cardinality
The number of elements in a finite set, denoted as |S|.
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Subsets
The number of subsets of a set S with n elements is 2ⁿ.
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Function
A relation from a set X to a set Y where each element in X is paired with exactly one element in Y.
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Onto function
A function where for every y in Y, there exists an x in X such that f(x) = y.
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Bijection
A function that is both one-to-one and onto, indicating |X| = |Y|.
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Bijection application
Used for counting the number of elements in a set, particularly useful in combinatorics.
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n-bit words
The total number of binary sequences of length n, calculated as 2ⁿ.
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Contradiction proof
A method of proof where the opposite of a statement is assumed, leading to a contradiction.
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Pascal's Triangle
A triangular array of the binomial coefficients, where each number is the sum of the two directly above.
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Inclusion/Exclusion principle
A principle used in counting to avoid overcounting, especially when elements are not distinct.