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Page 1: Title and Author

  • Title: Mathematical Language and Symbols

  • Author: Prof. Liwayway Memije-Cruz

Page 2: Importance of Language

  • Language facilitates communication and clarifies meaning.

  • It allows individuals to express themselves and maintain their identity.

Page 3: Characteristics of the Language of Mathematics

  • The language of mathematics is designed to express mathematicians' thoughts clearly and succinctly:

    • Precise: Makes very fine distinctions.

    • Concise: Communicates ideas briefly.

    • Powerful: Accurately conveys complex thoughts.

    • Examples include mathematical representations like k=0, mc², and A = r².

Page 4: English Language Structure

  • In English, nouns name entities (people, places, things), while sentences express complete thoughts.

    • Example: "Anne hates mathematics."

    • Nouns: "Anne, mathematics"; Verb: "hates."

Page 5: Mathematics Structure

  • Mathematical analogue of a noun is an expression: names a mathematical object.

  • The analogue of a sentence in mathematics is a sentence, which, like English, must convey a complete thought.

Page 6: Comparing English and Mathematics

  • English vs. Mathematics:

    • Noun (English) corresponds to Expression (Mathematics):

      • Examples: Carol, Idaho, book vs. 5, 2+3, 1/2.

    • Sentence (English) corresponds to Sentence (Mathematics):

      • Examples: "The capital of Idaho is Boise." vs. "3+4=7."

Page 7: Multiple Representations of Numbers

  • Various expressions can represent the same number:

    • Examples: 5, 2+3, -10 ÷ 2, (6-2)+1, 1 + 1 + 1 + 1 + 1.

Page 8: Exercises

  1. Generate synonyms for "similarity."

  2. Provide various expressions for the number three:

  • Standard name: Three.

  • Plus sign: 1+2.

  • Minus sign: 5-2.

  • Division sign: 6÷2.

Page 9: Truth in Mathematical Language

  • Sentences can be classified as true or false; truth is fundamental in mathematical language.

    • Exercises include identifying verbs and determining the truth value of sentences about the capital of Idaho and mathematical statements.

Page 10: Fill in the Blanks

  • Fill in sentences with relevant nouns, verbs, or mathematical expressions and highlight verbs.

Page 11: Examples of Mathematical Sentences

  • Sentences covering various operations:

      1. t + 3

      1. T + 3 = 3 + t

      1. This sentence is false.

      1. X + 0 = x

      1. 1.x = x

      1. Hat sat bat.

Page 12: Mathematical Symbols

  • Overview of mathematical symbols.

Page 13: Common Mathematical Symbols

  • List of symbols with meanings:

    • Equals sign: Indicates equality (e.g., 5 = 2 + 3).

    • Not equal sign: Expresses inequality (e.g., 5 ≠ 4).

    • Greater than: e.g., 5 > 4.

    • Less than: e.g., 4 < 5.

    • Inequality symbols for greater than or equal to, and less than or equal to.

Page 14: Set Theory Notations

  • Overview of notations used in set theory:

    • {}: Encloses elements in a set.

    • | : Indicates membership in a set.

    • Proper subset, superset, and cardinality symbols.

Page 15: References

  • Useful resources for further study:

    • http://www.onemathematicalcat.org

    • https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf

    • https://byjus.com/maths/math-symbols/