Section 1: Mathematical Language and Symbols

• Characteristics of the Language of Mathematics

  • Precise - Able to make fine distinctions of definitions among a set of math symbols
  • Concise - Explain long sentences briefly using math language
  • Powerful - One can express complex thoughts with relative ease
• Expressions of Mathematics

  • Number
  • Set
  • Function
  • Matrix
• Expressions are the mathematical analogue of an English noun. Correct arrangement of mathematical symbols used to represent a mathematical object of interest.
• Expressions does not state a complete thought, it does not make sense to ask an expression is true or false.
• Mathematical Sentence is an analogue of an English sentence. Correct arrangement of mathematical symbols that states a complete thought.
• Mathematical Sentences can be:

  • (Always) true
  • (Always) false
  • Sometimes true / Sometimes false
• Expression or Sentence: 2

  Expression
• Expression or Sentence: 1 +1

  Expression
• Expression or Sentence: 1 + 1 = 2

  Sentence, True
• Expression or Sentence: 1 + 1 = 3

  Sentence, False
• Expression or Sentence: x + 1 = 3

  Sentence, ST/SF
• Expression or Sentence: x

  Expression
• Expression or Sentence: 1 + 2 = 4

  Sentence, False
• Expression or Sentence: $(a+b)^2$


  Expression
• Expression or Sentence: 2x + 1 = 0

  Sentence, ST/SF
• Expression or Sentence: $(a+b)^2 =$$a^2+$$2ab+$$b^2$


  Sentence, True
• Expression or Sentence: 3t < 2

  Sentence, ST/SF
• Expression or Sentence: y + y + y

  Expression
• Expression or Sentence: y + y + y = 3y

  Sentence, True
• Expression or Sentence: $1+$$√2$


  Expression