Mathematics-as-a-Language Mathematics-as-a-LanguageMathematics-as-a-LanguageMathematics-as-a-Language.pptx

math as language

1. Mathematics as a language Mathematics in the Modern World

2. Mathematics as language A LANGUAGE is a systematic means of communicating by the use of sound or conventional symbols . It is the code we all use to express ourselves and communicate to others.

3. Components of a language: Vocabulary of symbols or words Grammar or rules of how these symbols are used Community of people who use and understand these symbols Range of meanings that can be communicated with these symbols.

4. ENGLISH LANGUAGE Symbols: English Letters Vowels and Consonants Words Phrases Sentences MATHEMATICAL LANGUAGE Symbols: English Letters/ Arabic Numerals Variables and Constants Term Algebraic Expressions Mathematical statements: Equations, Inequalities, etc

5. Elements of the mathematical language  

6. The Language of Mathematics was designed so we can write about: Things like Numbers, Sets, Functions, etc. What we Do with those things (add, subtract, multiply, divide, join together, etc.)

7. symbols Mathematics uses symbols instead of words: There are the 10 digits: 0, 1, 2, ... 9 There are symbols for operations: +, −, ×, /, ... And symbols that "stand in" for values: x, y, ... And many special symbols:  π , =, <, ≤, ...

8. Letter Conventions Often (but not always) letters have special uses: Those are  not rules , but they are often used that way. Examples What they usually mean Start of the alphabet: a, b, c, ... constants (fixed values) From i to n: i, j, k, l, m, n Positive integers   (for counting) End of the alphabet: ... x, y, z variables (unknowns)

9. Example: y = ax + b People will  assume  that a and b are fixed values, And that x is the one that changes, which in turn makes y change.

10. Nouns, Verbs, Sentences Even though we don't use the words "noun", "verb", or "pronoun" in Mathematics, you can imagine these  similarities to English : Nouns  could be fixed things, such as numbers, or expressions with numbers: The  Verb  could be the equals sign "=", or an inequality like < or > 15 2(3-1/2) 4 2

11. Nouns, Verbs, Sentences Pronouns  (things like  it ,  he ,  you , etc.) could be variables like  x  or  y : And they could be put together into a  Sentence  like this: 3x + 7 = 22 5x-7 xy 2 -3/x