Essential Ideas

Section 4.5: History of Calculating Devices

by

4.5 Outline

  1. First calculating tool
  2. Early calculating devices
    1. abacus
    2. Napier’s rods
    3. slide rule
  3. Mechanical calculators
    1. Pascal’s calculator
    2. Babbage’s calculating machine
  4. Hand-held calculators
  5. First computers
    1. ENIAC
    2. UNIVAC I
  6. Present-day computers
    1. Cray supercomputer
    2. Tianhe-2 supercomputer
    3. minicomputers
    4. history of the internet
    5. personal computers
… See the whole entry

Section 4.1: Early Numeration Systems

by

4.1 Outline

  1. Basic ideas
    1. number
    2. counting number
    3. numeral
    4. numeration system
  2. Egyptian numeration system
    1. simple grouping system
    2. hieroglyphic symbols
    3. addition principle
    4. repetitive system
  3. Roman numeration system
    1. Roman numerals
    2. subtractive principle
    3. multiplicative principle
  4. Babylonian numeration system
    1. positional system
    2. cuneiform symbols
    3. properties of
… See the whole entry

Section 3.4: The Nature of Proof

by

3.4 Outline

  1. Introduction
    1. theorem
    2. syllogism
  2. Direct reasoning
    1. definition
    2. modus ponens
    3. law of detachment
    4. assuming the antecedent
  3. Indirect reasoning
    1. definition
    2. modus tollens
    3. denying the consequent
  4. Transitive reasoning
    1. definition
    2. formulate a conclusion
  5. Logical proof
  6. Fallacies
    1. fallacy of the converse
      1. also called fallacy
… See the whole entry

Section 3.3: Operations and Laws of Logic

by

3.3 Outline

  1. Biconditional, implication, and logical equivalence
    1. definition of biconditional
    2. verifying tautologies
    3. implication
    4. equivalence
  2. Laws of logic
    1. law of double negation
    2. law of contraposition
    3. De Morgan’s laws
  3. Negation of a compound statement
    1. negation of a conditional
    2. language analysis
  4. Miscellaneous operators
… See the whole entry