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.
GRAPH THEORY
- 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.
LOGIC
- 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.
NUMBER AND QUANTITY
- 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.
STATISTICS AND PROBABILITY
- DCS.SP.1.1 Implement the Fundamental Counting Principle to solve problems.
- DCS.SP.1.2 Implement procedures to calculate a permutation or combination.