Hlavní obsah
Math
Virginia Math
Discrete Mathematics: Computational Methods
Select and apply a sorting algorithm, such as a bubble sort, merge sort, or network sort.
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Describe the advantages and disadvantages of various sorting algorithms.
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Analyze the knapsack and bin-packing problems.
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Select and apply search algorithms to analyze problems.
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Determine the average, best-case, and worst-case reasoning for different searches.
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Compare and contrast iterative and recursive processes.
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Use recursive processes to model growth and decay.
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Use recursive processes to create fractals.
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Use recursive processes to generate the Fibonacci sequence.
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Determine if a recursive solution is more efficient than an iterative solution.
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Compare and contrast ciphers and codes.
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Describe the evolution of cipher systems.
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Identify the Fundamental Theorem of Arithmetic.
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Describe how the complexity of prime factorization is used in cryptography.
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Describe modular arithmetic in context (e.g., clocks, days of the week, measures of time).
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Analyze the relationship between divisibility and modulus.
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Determine congruence within modular arithmetic.
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Perform operations within modular arithmetic.
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Apply modular arithmetic to problems in context (e.g., cryptography, International Standard Book Number (ISBN), International Bank Account Number (IBAN)).
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Describe maximum complexity of an algorithm using Big O notation.
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Describe Turing machines and how they are used to test the limits of computation.
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Describe the halting problem and explain how it characterizes the fundamental limitations of computation and undecidability.
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Explain the P versus NP problem and defend a justification for equality, inequality, or undecidability.
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Analyze how the equivalence of P- and NP-class problems might impact society.
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