North Carolina: Discrete Mathematics for Computer Science Math Standards

33 standards · 5 domains

FUNCTIONS

DCS.F.1.1 Implement procedures to find the nth term in an arithmetic or geometric sequence using spreadsheets.
DCS.F.1.2 Represent the sum of a sequence using sigma notation.
DCS.F.1.3 Implement procedures to find the sum of a finite sequence.
DCS.F.1.4 Implement procedures to find the sum of an infinite sequence and determine if the series converges or diverges.
DCS.F.1.5 Interpret the solutions to arithmetic and geometric sequences and series problems, in context.

DCS.GT.1.1 Represent real world situations with a vertex-edge graph, adjacency matrix, and vertex-edge table.
DCS.GT.1.2 Test graphs and digraphs for Euler paths, Euler circuits, Hamiltonian paths, or Hamiltonian circuits.
DCS.GT.1.3 Interpret a complete digraph to determine rank.
DCS.GT.2.1 Implement critical path analysis algorithms to determine the minimum project time.
DCS.GT.2.2 Implement the brute force method, the nearest-neighbor algorithm, and the cheapest-link algorithm to find solutions to a Traveling Salesperson Problem.
DCS.GT.2.3 Implement vertex-coloring techniques to solve problems.
DCS.GT.2.4 Implement Kruskal and Prim’s algorithms to determine the weight of the minimum spanning tree of a connected graph.

DCS.L.1.1 Construct truth tables that encode the truth and falsity of two or more statements.
DCS.L.1.2 Critique logic arguments (e.g., determine if a statement is valid or whether an argument is a tautology or contradiction).
DCS.L.1.3 Check 1s and 0s to determine whether a statement is true or false using Boolean logic circuits.
DCS.L.1.4 Judge whether two statements are logically equivalent using truth tables.

DCS.N.1.1 Implement procedures of addition, subtraction, multiplication, and scalar multiplication on matrices.
DCS.N.1.2 Implement procedures of addition, subtraction, and scalar multiplication on vectors.
DCS.N.1.3 Implement procedures to find the inverse of a matrix.
DCS.N.2.1 Organize data into matrices to solve problems.
DCS.N.2.2 Interpret solutions found using matrix operations including Leslie Models and Markov Chains, in context.
DCS.N.2.3 Represent a system of equations as a matrix equation.
DCS.N.2.4 Use inverse matrices to solve a system of equations with technology.
DCS.N.3.1 Recognize sets, subsets, and proper subsets.
DCS.N.3.2 Implement set operations to find unions, intersections, complements and set differences with multiple sets.
DCS.N.3.3 Represent properties and relationships among sets using Venn diagrams.
DCS.N.3.4 Interpret Venn diagrams to solve problems.
DCS.N.4.1 Use the Euclidean Algorithm to determine greatest common factor and least common multiple.
DCS.N.4.2 Use the Fundamental Theorem of Arithmetic to solve problems.
DCS.N.4.3 Conclude that sets are equal using the properties of set operations.
DCS.N.4.4 Explain theorems related to greatest common factor, least common multiple, even numbers, odd numbers, prime numbers, and composite numbers.