IXL Skill Plan | North Carolina Standard Course of Study: Discrete Math for Computer Science

North Carolina Standard Course of Study: Discrete Math for Computer Science

Skills available for North Carolina Discrete Math for Computer Science math standards

Section

Number and Quantity
Functions
Statistics and Probability
Graph Theory
Logic

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DCS.N	Number and Quantity
DCS.N.1 Apply operations with matrices and vectors.
DCS.N.1.1 Implement procedures of addition, subtraction, multiplication, and scalar multiplication on matrices.		Introduction to matrices 1. Matrix vocabulary 2. Matrix operation rules Matrix operations 3. Add and subtract matrices 4. Multiply a matrix by a scalar 5. Add and subtract scalar multiples of matrices 6. Multiply two matrices 7. Simplify matrix expressions 8. Properties of matrices
DCS.N.1.1 Implement procedures of addition, subtraction, multiplication, and scalar multiplication on matrices.
Introduction to matrices 1. Matrix vocabulary 2. Matrix operation rules Matrix operations 3. Add and subtract matrices 4. Multiply a matrix by a scalar 5. Add and subtract scalar multiples of matrices 6. Multiply two matrices 7. Simplify matrix expressions 8. Properties of matrices

DCS.N.1.2 Implement procedures of addition, subtraction, and scalar multiplication on vectors.		Introduction to vectors 1. Find the magnitude of a vector 2. Find the component form of a vector 3. Find the direction angle of a vector 4. Find the component form of a vector from its magnitude and direction angle Triangle and parallelogram methods 5. Graph a resultant vector using the triangle method 6. Graph a resultant vector using the parallelogram method Vector operations 7. Add vectors 8. Subtract vectors 9. Multiply a vector by a scalar Linear combinations of vectors 10. Linear combinations of vectors
DCS.N.1.2 Implement procedures of addition, subtraction, and scalar multiplication on vectors.
Introduction to vectors 1. Find the magnitude of a vector 2. Find the component form of a vector 3. Find the direction angle of a vector 4. Find the component form of a vector from its magnitude and direction angle Triangle and parallelogram methods 5. Graph a resultant vector using the triangle method 6. Graph a resultant vector using the parallelogram method Vector operations 7. Add vectors 8. Subtract vectors 9. Multiply a vector by a scalar Linear combinations of vectors 10. Linear combinations of vectors

DCS.N.1.3 Implement procedures to find the inverse of a matrix.		Determinant of a matrix 1. Determinant of a matrix Inverse of a matrix 2. Is a matrix invertible? 3. Inverse of a 2 x 2 matrix 4. Inverse of a 3 x 3 matrix 5. Identify inverse matrices
DCS.N.1.3 Implement procedures to find the inverse of a matrix.
Determinant of a matrix 1. Determinant of a matrix Inverse of a matrix 2. Is a matrix invertible? 3. Inverse of a 2 x 2 matrix 4. Inverse of a 3 x 3 matrix 5. Identify inverse matrices
DCS.N.2 Understand matrices to solve problems.
DCS.N.2.1 Organize data into matrices to solve problems.		1. Solve a system of equations using augmented matrices: word problems
DCS.N.2.1 Organize data into matrices to solve problems.
1. Solve a system of equations using augmented matrices: word problems

DCS.N.2.2 Interpret solutions found using matrix operations including Leslie Models and Markov Chains, in context.
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.2.3 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.2.4 Use inverse matrices to solve a system of equations with technology.

DCS.N.3 Understand set theory to solve problems.
DCS.N.3.1 Recognize sets, subsets, and proper subsets.		1. Sets, subsets, and complements 2. Set-builder notation
DCS.N.3.1 Recognize sets, subsets, and proper subsets.
1. Sets, subsets, and complements 2. Set-builder notation

DCS.N.3.2 Implement set operations to find unions, intersections, complements and set differences with multiple sets.		1. Sets, subsets, and complements 2. Unions and intersections of sets
DCS.N.3.2 Implement set operations to find unions, intersections, complements and set differences with multiple sets.
1. Sets, subsets, and complements 2. Unions and intersections of sets

DCS.N.3.3 Represent properties and relationships among sets using Venn diagrams.
DCS.N.3.3 Represent properties and relationships among sets using Venn diagrams.


DCS.N.3.4 Interpret Venn diagrams to solve problems.		1. Use Venn diagrams to solve problems
DCS.N.3.4 Interpret Venn diagrams to solve problems.
1. Use Venn diagrams to solve problems
DCS.N.4 Understand statements related to number theory and set theory.
DCS.N.4.1 Use the Euclidean Algorithm to determine greatest common factor and least common multiple.
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.4.2 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.4.3 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.
DCS.N.4.4 Explain theorems related to greatest common factor, least common multiple, even numbers, odd numbers, prime numbers, and composite numbers.

DCS.F	Functions
DCS.F.1 Apply recursively-defined relationships to solve problems.
DCS.F.1.1 Implement procedures to find the nth term in an arithmetic or geometric sequence using spreadsheets.
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.		1. Introduction to sigma notation
DCS.F.1.2 Represent the sum of a sequence using sigma notation.
1. Introduction to sigma notation

DCS.F.1.3 Implement procedures to find the sum of a finite sequence.		1. Find the sum of an arithmetic series 2. Find the sum of a finite geometric series
DCS.F.1.3 Implement procedures to find the sum of a finite sequence.
1. Find the sum of an arithmetic series 2. Find the sum of a finite geometric series

DCS.F.1.4 Implement procedures to find the sum of an infinite sequence and determine if the series converges or diverges.		1. Convergent and divergent geometric series 2. Find the value of an infinite geometric series
DCS.F.1.4 Implement procedures to find the sum of an infinite sequence and determine if the series converges or diverges.
1. Convergent and divergent geometric series 2. Find the value of an infinite geometric series

DCS.F.1.5 Interpret the solutions to arithmetic and geometric sequences and series problems, in context.
DCS.F.1.5 Interpret the solutions to arithmetic and geometric sequences and series problems, in context.

DCS.SP	Statistics and Probability
DCS.SP.1 Apply combinatorics concepts to solve problems.
DCS.SP.1.1 Implement the Fundamental Counting Principle to solve problems.		1. Counting principle
DCS.SP.1.1 Implement the Fundamental Counting Principle to solve problems.
1. Counting principle

DCS.SP.1.2 Implement procedures to calculate a permutation or combination.		1. Combinations and permutations 2. Find probabilities using combinations and permutations 3. Combinations and permutations: word problems
DCS.SP.1.2 Implement procedures to calculate a permutation or combination.
1. Combinations and permutations 2. Find probabilities using combinations and permutations 3. Combinations and permutations: word problems

DCS.GT	Graph Theory
DCS.GT.1 Understand graph theory to model relationships and solve problems.
DCS.GT.1.1 Represent real world situations with a vertex-edge graph, adjacency matrix, and vertex-edge table.
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.1.2 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.1.3 Interpret a complete digraph to determine rank.

DCS.GT.2 Apply graph theory to solve problems.
DCS.GT.2.1 Implement critical path analysis algorithms to determine the minimum project time.
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.2.2 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.2.3 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.GT.2.4 Implement Kruskal and Prim's algorithms to determine the weight of the minimum spanning tree of a connected graph.

DCS.L	Logic
DCS.L.1 Evaluate mathematical logic to model and solve problems.
DCS.L.1.1 Construct truth tables that encode the truth and falsity of two or more statements.		1. Truth tables
DCS.L.1.1 Construct truth tables that encode the truth and falsity of two or more statements.
1. Truth tables

DCS.L.1.2 Critique logic arguments (e.g., determine if a statement is valid or whether an argument is a tautology or contradiction).		1. Truth values
DCS.L.1.2 Critique logic arguments (e.g., determine if a statement is valid or whether an argument is a tautology or contradiction).
1. Truth values

DCS.L.1.3 Check 1s and 0s to determine whether a statement is true or false using Boolean logic circuits.
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.L.1.4 Judge whether two statements are logically equivalent using truth tables.