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2-3. MATHEMATICS AS A LANGUAGE.pptx
- 1. MATM111 Our lady ofFatima university COLLEGE OF ARTS AND SCIENCES Pampanga Campus Math and Physics Department NATURE OF MATHEMATICS: Mathematical Language and Symbols Jerica Nicole R. Flores, MAEd Lecturer
- 2. Learning Outline I. Natureof Mathematics: Mathematical Language and Symbo 2.1. Language of Mathematics 2.2. Sets 2.3. Elementary Logic
- 3. Discuss the language,symbols, and conventions of mathematics Learning Outcomes II. Nature of Mathematics: Mathematics in Our World Explain the nature of Mathematics as a Language. At the end of the chapter the students are expected: Perform operations on Mathematical Expressions completely.
- 4. Nature of Mathematics Languageof Mathematics Language, a system of conventional spoken, manual (signed), or written symbols by means of which human beings, as members of a social group and participants in its culture, express themselves.
- 5. Nature of Mathematics Languageof Mathematics Language itself is: PRECISE It can make very fine distinctions among set of symbols CONCISE It can briefly express long sentences POWERFUL It gives upon expressing complex thoughts
- 6. Nature of Mathematics Languageof Mathematics Symbols commonly used in Mathematics are:
- 7. Nature of Mathematics Languageof Mathematics ENGLISH Language vs. MATHEMATICS Language: English Mathematics SYMBOLS English Alphabet and punctuation English Alphabet, Numerals, Greek Letters, Grouping Symbols, Special Symbols Name Noun Expressions Complete Thought Sentence Equation Action Verbs Operations and other actions (simplify, rationalize) What is in a sentence Verbs Equality, inequality, membership in a set
- 8. Nature of Mathematics Languageof Mathematics Comparison: English VS Mathematics Language I. Name Example: a. Carol English Example: a. 5 b. 1.2 + 6 c. 3x – 3 d. ordered pair (x,y) e. a function f(x) Mathematics
- 9. Nature of Mathematics Languageof Mathematics Comparison: English VS Mathematics Language II. Complete Thought Example: a. He loves Mathematics. English Example: a. x = 5 b. 1 + 3 = 4 c. 3x – 3 = 9 d. 2x ≠ 8 Mathematics
- 10. Nature of Mathematics Languageof Mathematics Comparison: English VS Mathematics Language III. Synonyms Example: a. Group is to Association English Example: a. 1 + 2 + 3 + 5 and 8 b. 1 = 1 c. ½ + ½ Mathematics
- 11. Nature of Mathematics Languageof Mathematics Difficulties in the Math Language 1. Different meaning or use of words in Math and English. “and” is equivalent to plus “is” may have different meaning 2. The different uses of numbers: cardinal, ordinal, or nominal. “cardinal numbers” ones used for counting “ordinal numbers” ones used for telling positions “nominal numbers” used only as a name to identify something
- 12. RECITATION Translation: English toMath Language and vis a vis 1. English to Math Six less than twice a number is forty-five 2x - 6 = 45 A number minus seven yields ten – 7 = 10 A total of six and some number 6 + x Twelve added to a number x + 12 Eight times a number is forty-eight 8x = 48 The produce of fourteen and a number 14x
- 13. RECITATION Translation: English toMath Language and vis a vis 2. English to Math Twice a number minus eight 2x – 8 The quotient of a number and seven is two x/7 = 2 Three-fourths of a number ¾ x The product of a number and ten is eighty 10x = 80 Eight less than a number is five x – 8 = 5 . How many times does five go into twenty? 20/5 = x
- 14. Nature of Mathematics Languageof Mathematics Translation: English to Math Language and vis a vis 2. Mathematics to English Choose a quantity to be represented by a variable, then write the mathematical expression for each number. a. A three-digit numbers whose hundreds digit is half the tens digit, and the tens digit is 2 more than the unit's digit. ½ (x + 2) (x + 2) (x)
- 15. Nature of Mathematics Languageof Mathematics Remember this key words!
- 16. Nature of Mathematics Languageof Mathematics Equals (=) is, are, was, were, will be gives, yields sold for, cost Remember this key words!
- 17. Nature of Mathematics Sets Aset in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics
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- 22. RECITATION Multiple Choice: Basicconcepts: Select the best answer to the following multiple-choice questions about basic concepts of sets.
- 23. Nature of Mathematics ElementaryLogic Logic serves as a set of rules that govern the structure and presentation of mathematical proofs. It allows us to determine the validity of arguments in and out of mathematics.
- 24. Nature of Mathematics ElementaryLogic A proposition is a statement that is, by itself, either true or false. They can be expressed in symbols P, Q, R, or p, q, r. a. Simple – means single idea statement b. Compound – conveys two or more ideas
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- 27. Nature of Mathematics ElementaryLogic STATEMENTS CONNECTIVES SYMBOLIC FORM TYPE OF STATEMENTS Not P Not ~ P Negation P and Q And P ∧ Q Conjunction P or Q Or P ∨ Q Disjunction If P, the q If…Then P → Q Conditional P if and only if q If and only if P ↔ Q Bi-conditional Logical Connectives
- 28. Nature of Mathematics ElementaryLogic QUANTIFIER 1. Universal Quantifier “for all” or “for every”, denoted by ∀ 2. Existential Quantifier “there exists”, denoted by ∃
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- 30. RECITATION 1.) Let’s considera propositional language where: • p means “Paola is happy”, • q means “Paola paints a picture”, 2.) Let: A =“Aldo is Italian” B =“Bob is English”. Formalize the following sentences: 1. “Aldo isn’t Italian” 2. “Aldo is Italian while Bob is English” 3. “If Aldo is Italian then Bob is not English” 4. “Aldo is Italian or if Aldo isn’t Italian then Bob is English” 5. “Either Aldo is Italian and Bob is English, or neither Aldo is Italian nor Bob is English”
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