Standards - Mathematics

2019 - Mathematics Course of Study Document
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.29

Critically analyze issues related to information processing including accuracy, efficiency, and security.

Unpacked Content

Knowledge

Students know:

  • Electronic transfer of information such as email are susceptible to breaches.

Skills

Students should be able to: Give examples of information processing where accuracy, efficiency or security may be an issue.

Understanding

Students understand that:

  • Cryptography is used in online settings to keep information secure.
  • Error-detecting and error-correcting codes can be used to detect and correct errors that may occur when information is read or transmitted electronically.
  • Data compression methods are used to transmit large amounts of data efficiently.

Vocabulary

  • Cryptography
  • Error-detecting codes
  • Error-correcting codes
  • Data compression
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.30

Apply ciphers (encryption and decryption algorithms) and cryptosystems for encrypting and decrypting including symmetric-key or public-key systems.

Unpacked Content

Knowledge

Students know:

  • How to multiply matrices and find inverses.

Skills

Students are able to:

  • Carry out modular arithmetic procedures.
  • Use a variety of ciphers to encrypt and decrypt moderate-sized messages.

Understanding

Students understand that:

  • Symmetric-key cryptography such as substitution ciphers or public-key cryptosystems can be used to encrypt and decrypt messages.
  • Cryptosystems are used to ensure the privacy and authenticity of information.

Vocabulary

  • Modular arithmetic
  • Cipher
  • Encryption
  • Decryption
  • Symmetric-key cryptography
  • Public-key cryptography
  • RSA cryptosystem
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.31

Apply error-detecting codes and error-correcting codes to determine accuracy of information processing.

Unpacked Content

Knowledge

Students know:

  • How to perform modular arithmetic.
  • Binary numbers

Skills

Students are able to:

  • Determine if a code such as a zip code or a UPC code contains an errors.
  • Determine if a code can be corrected.
  • Identify situations where errors should be corrected or just detected.

Understanding

Students understand that:

  • Data that is transferred can contain errors and codes can be used to detect errors.
  • Error correcting codes can be used to increase the likelihood of accuracy.

Vocabulary

  • Check digits
  • Information digits
  • Barcodes
  • UPC codes
  • Binary digits or bits
  • Substitution error
  • Transposition error
  • Maximum likelihood decoding
  • Hamming distance, minimum distance
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.32

Apply methods of data compression.

Example: Huffman codes

Unpacked Content

Knowledge

Students know:

  • How to construct a binary tree with vertices and edges

Skills

Students are able to:

  • Use variable length codes to recode data with shorter codes for the more frequently used characters.
  • Use a data compression code to decode.
  • Construct a Huffman code for a given set of characters and their frequencies.

Understanding

Students understand that:

  • Data compression is accomplished by using shorter binary strings for commonly used characters.

Vocabulary

  • Variable-length codes
  • Prefix (or prefix-free) codes
  • Huffman codes
  • Huffman trees

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