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Mathematics in the Modern World > Prelim Lectures > Flashcards

Prelim Lectures Flashcards

Lectures 1-3 Nature by Numbers The Map of Mathematics Mathematical Language and Symbols

1
Q

➭ It is developed by the human mind and culture
➭ It is a formal system of thought for recognizing, classifying, and exploiting patterns
➭ It is the Science of Patterns
➭ All about numbers, symbols, equations, operations, functions, calculations, abstractions, devising proofs

A

Mathematics

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2
Q

Type of Patterns

A

➭ Numeric Patterns

➭ Geometric Patterns

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3
Q

Purpose of Mathematics (6)

A

➭ Making conclusions and/or predictions of events
➭ Describe the natural order and occurrences
➭ Organize patterns, regularities, and irregularities
➭ Help to control epidemics
➭ Provide tools for calculations
➭ Provide new questions

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4
Q

How is Mathematics done (5)

A

➭ with curiosity
➭ with a penchant for seeking patterns and generalities
➭ with the desire to know the truth
➭ with trial and error
➭ without fear of facing more questions and problems to solve

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5
Q

Who uses Mathematics

A

➭ Pure and Applied Mathematicians
➭ Natural and Social Scientists
➭ Everyone

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6
Q

Who was the first to discover about the sequence?

A

Indians

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7
Q

Real name of Fibonacci

A

Leonardo Pisano Bogollo

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8
Q

Fibonacci lived from (year) in (place)

A

1170-1250, Italy

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9
Q

Fibonacci means

A

Son of Bonacci

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10
Q

Leonardo became famous for the

A

Fibonacci Sequence and Hindu-Arabic Numerals

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11
Q

It is the series of numbers

A

Fibonacci Sequence

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12
Q

The value of the Golden Ratio

A

1.618034

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13
Q

True or False

The bigger the pair of Fibonacci numbers, the closer the approximation of the value of the Golden Ratio.

A

True

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14
Q

The Golden Ratio Equation

A

Xₙ = Φⁿ − (1 − Φ)ⁿ / √5

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15
Q

Characteristics of Math Language (5)

A 
➭ Precise
➭ Concise
➭ Powerful
➭ Nontemporal
➭ Has vocabulary and parts of speech
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16
Q

Parts of Speech for Math

Numbers

A

Nouns

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17
Q

Parts of Speech for Math

Operation symbols (+, ÷ ,^ , v)

A

Connectives

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18
Q

Parts of Speech for Math

Relation symbols (=, , ~) for comparison

A

Verbs

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19
Q

Parts of Speech for Math

Grouping symbols such as (), { }, [ ]

A

Associate groups

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20
Q

Parts of Speech for Math

Variables

A

Pronouns

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21
Q

Refers to object of interest acting as the subject in the ordinary language.

A

Mathematical Expression

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22
Q

A sentence with a complete thought, which can be regarded as true or false.

A

Mathematical Sentence

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23
Q

Mathematical Expression/Sentence Example

5 plus 2 is equal to the square root of 49.

A

Sentence, True

5 + 2 = 7

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24
Q

Mathematical Expression/Sentence Example

10 divided by 2 is less than 3.

A

Sentence, False

10/2 = 5

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25
Q

Mathematical Expression/Sentence Example

Manila is the capital of the Philippines.

A

Sentence

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26
Q

Mathematical Expression/Sentence Example

The Province of Cavite.

A

Expression

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27
Q

Mathematical Expression/Sentence Example

The number 5 is a composite number.

A

Sentence, False

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28
Q

Mathematical Expression/Sentence Example

(x + 1)^2

A

Expression

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29
Q

Mathematical Expression/Sentence Example

Square root of x – 1= 3, if x = 10

A

Sentence, True

30
Q

Mathematical Expression/Sentence Example

Pretty girl

A

Expression

31
Q

Mathematical Expression/Sentence Example

3 + 4 = 4 + 3

A

Sentence

32
Q

Mathematical Expression/Sentence Example

5 x 3

A

Expression

33
Q

Mathematical Expression/Sentence Example

The word vowel starts with a consonant.

A

Sentence

34
Q

Mathematical Expression/Sentence Example

You and I

A

Expression

35
Q

Mathematical Expression/Sentence Example

Hayward got injured in the game.

A

Sentence

36
Q

Mathematical Expression/Sentence Example

3x = 3

a. x = 1
b. x = 2

A

Sentence

a. True
b. False

37
Q

Mathematical Expression/Sentence Example

3x +4y

A

Expression

38
Q

Mathematical Expression/Sentence Example

1(5) = 5

A

Sentence

39
Q

Mathematical Expression/Sentence Example

Math is a language.

A

Sentence

40
Q

It is a powerful tool for analysis and communications in mathematics. It represents the natural language and mathematical language with symbols and variables.

A

Logic

41
Q

Not

A

Negation

42
Q

Symbol of Negation

A

~

43
Q

~

A

Negation; Not

44
Q

And / But

A

Conjunction

45
Q

Symbol of Conjunction

A

Ʌ

46
Q

Ʌ

A

Conjunction; And / But

47
Q

Or

A

Disjunction

48
Q

Symbol of Disjunction

A

v

49
Q

v

A

Disjunction; Or

50
Q

Implies; If, then

A

Conditional

51
Q

Symbol of Conditional

A

→

52
Q

→

A

Conditional; Implies; If, then

53
Q

If and only if

A

Biconditional

54
Q

Symbol of Biconditional

A

↔

55
Q

↔

A

Biconditional; If and only if

56
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

Today is Sunday and Harry is not happy.

A

s ˄ h

57
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

Today is Sunday and Harry is not going to watch a volleyball game.

A

s ˄ ̴ v

58
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

If it is going to rain, then Harry is not going to watch a volleyball game.

A

r → ̴ v

59
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

Harry is going to watch a volleyball game if and only if he is happy.

A

v ↔ ̴ h

60
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

Harry is happy only if it is not going to rain.

A

̴ h → ̴ r

61
Q

h: Harry is not happy
v: Harry is going to watch a volleyball game
r: It is going to rain
s: Today is Sunday

Harry is going to watch a volleyball game or it is going to rain.

A

V v r

62
Q

p: Gian plays volleyball
q: Lanz plays basketball

̴ p

A

Gian does not play volleyball.

63
Q

p: Gian plays volleyball
q: Lanz plays basketball

p ˄ q

A

Gian plays volleyball and Lanz plays basketball.

64
Q

p: Gian plays volleyball
q: Lanz plays basketball

p → ̴ q

A

If Gian plays volleyball, then Lanz does not play basketball.

65
Q

p: Gian plays volleyball
q: Lanz plays basketball

P v ( ̴ P → Q)

A

Gian plays volleyball, or if Gian does not play volleyball, then Lanz plays basketball.

66
Q

P: Adele is a singer
Q: Adele is a songwriter
R: Adele is an actress

(P ˄ Q) → ̴ R

A

If Adele is a singer and Adele is a songwriter, then Adele is not an actress.

67
Q

P: Adele is a singer
Q: Adele is a songwriter
R: Adele is an actress

R → ( ̴ P ˄ ̴ Q)

A

If Adele is an actress, then Adele is not a singer and Adele is not a songwriter.

68
Q

p ̴ p
T
F

A

̴ p
F
T

69
Q 
p   q   p ˄ q
T   T
T   F
F   T
F   F
A 
p ˄ q
T
F
F
F
70
Q 
p   q   p v q
T   T
T   F
F   T
F   F
A 
p v q
T
T
T
F
71
Q 
p   q   p → q
T   T
T   F
F   T
F   F
A 
p → q
T
F
T
T
72
Q 
p   q   p ↔ q
T   T
T   F
F   T
F   F
A 
p ↔ q
T
F
F
T

Mathematics in the Modern World (1 decks)

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