Essential Ideas

Section 5.6: Groups, Fields, and Real Numbers

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5.6 Outline

  1. Definition of real numbers
    1. definition
    2. decimal representation
      1. terminating decimal
      2. repeating decimal
      3. change fractional form to decimal form
      4. change terminating decimal form to fractional form
    3. real number line
      1. unit distance
      2. number line
      3. dense set
    4. classifications within the set of
… See the whole entry

Section 5.7: Discrete Mathematics

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5.7 Outline

  1. Definition
  2. Clock arithmetic
    1. addition of a 12-hourclock
    2. elementary operations
      1. subtraction
      2. multiplication
      3. zero multiplication
      4. division
  3. Modulo five arithmetic
    1. addition of a 5-hour clock
    2. congruence modulo m
    3. solving modular equations
  4. Group properties for a modulo system
    1. testing group properties
    2. testing
… See the whole entry

Section 5.4: Rational Numbers

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5.4 Outline

  1. Introduction
    1. definition of a rational number
    2. numerator
    3. denominator
    4. classification
      1. proper fraction
      2. improper fraction
      3. whole number
  2. Fundamental property
  3. Operations with rationals
    1. addition
    2. subtraction
    3. multiplication
    4. division

5.4 Essential Ideas

This section, which may be review, is concerned with the rational … See the whole entry

Section 5.3: Integers

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5.3 Outline

  1. Introduction
    1. zero
    2. whole numbers
    3. opposites
    4. integers
    5. absolute value
  2. Addition of integers
    1. procedure
    2. flowchart
  3. Multiplication of integers
    1. procedure
    2. flowchart
  4. Subtraction of integers
  5. Division of integers
    1. definition
    2. procedure
    3. NEVER DIVIDE BY ZERO

 

5.3 Essential Ideas

This section, which may … See the whole entry

Section 5.2: Prime Numbers

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5.2 Outline

  1. Divisibility
    1. definition
      1. divisor
      2. factor
      3. divides
      4. multiple
    2. number of divisors
      1. divisibility rule for 2
      2. divisibility rule for 3
      3. rules of divisibility for 1-12
    3. finding primes
      1. definitions
        1. prime number
        2. composite number
      2. sieve of Eratosthenes
    4. prime factorization
      1. factoring
      2. prime factorization
      3. fundamental
… See the whole entry

Section 5.1: Natural Numbers

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5.1 Outline

  1. Basic concepts
    1. counting numbers
    2. natural numbers
    3. addition
  2. Closure property
    1. definition
    2. closed/not closed
  3. Commutative and associative properties
    1. commutative property for addition
    2. associative property for addition
    3. definition of multiplication
    4. closure for multiplication in the set of natural numbers
    5. commutative property
… See the whole entry