1. MATM111
Our lady of Fatima 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. Nature of 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
Language of 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
Language of 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
7. Nature of Mathematics
Language of 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
Language of 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
Language of 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
Language of 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
Language of 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 to Math 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 to Math 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
Language of 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)
16. Nature of Mathematics
Language of Mathematics
Equals (=)
is, are, was, were, will
be
gives, yields
sold for, cost
Remember this key words!
17. Nature of Mathematics
Sets
A set 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
22. RECITATION
Multiple Choice: Basic concepts: Select the best answer to the following multiple-choice questions about basic concepts of sets.
23. Nature of Mathematics
Elementary Logic
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
Elementary Logic
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
27. Nature of Mathematics
Elementary Logic
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
Elementary Logic
QUANTIFIER
1. Universal Quantifier “for all” or “for every”, denoted by ∀
2. Existential Quantifier “there exists”, denoted by ∃
30. RECITATION
1.) Let’s consider a 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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