Prelim Lectures Flashcards by Jef L

➭ 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

Mathematics

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Type of Patterns

➭ Numeric Patterns

➭ Geometric Patterns

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Purpose of Mathematics (6)

➭ 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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How is Mathematics done (5)

➭ 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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Who uses Mathematics

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

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Who was the first to discover about the sequence?

Indians

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Real name of Fibonacci

Leonardo Pisano Bogollo

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Fibonacci lived from (year) in (place)

1170-1250, Italy

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Fibonacci means

Son of Bonacci

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Leonardo became famous for the

Fibonacci Sequence and Hindu-Arabic Numerals

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It is the series of numbers

Fibonacci Sequence

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The value of the Golden Ratio

1.618034

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True or False

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

True

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The Golden Ratio Equation

Xₙ = Φⁿ − (1 − Φ)ⁿ / √5

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Characteristics of Math Language (5)

➭ Precise
➭ Concise
➭ Powerful
➭ Nontemporal
➭ Has vocabulary and parts of speech

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Parts of Speech for Math

Numbers

Nouns

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Parts of Speech for Math

Operation symbols (+, ÷ ,^ , v)

Connectives

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Parts of Speech for Math

Relation symbols (=, , ~) for comparison

Verbs

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Parts of Speech for Math

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

Associate groups

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Parts of Speech for Math

Variables

Pronouns

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

Mathematical Expression

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

Mathematical Sentence

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Mathematical Expression/Sentence Example

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

Sentence, True

5 + 2 = 7

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Mathematical Expression/Sentence Example

10 divided by 2 is less than 3.

Sentence, False

10/2 = 5

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Mathematical Expression/Sentence Example Manila is the capital of the Philippines.

Sentence

Mathematical Expression/Sentence Example The Province of Cavite.

Expression

Mathematical Expression/Sentence Example The number 5 is a composite number.

Sentence, False

Mathematical Expression/Sentence Example (x + 1)^2

Expression

Mathematical Expression/Sentence Example Square root of x – 1= 3, if x = 10

Sentence, True

Mathematical Expression/Sentence Example Pretty girl

Expression

Mathematical Expression/Sentence Example 3 + 4 = 4 + 3

Sentence

Mathematical Expression/Sentence Example 5 x 3

Expression

Mathematical Expression/Sentence Example The word vowel starts with a consonant.

Sentence

Mathematical Expression/Sentence Example You and I

Expression

Mathematical Expression/Sentence Example Hayward got injured in the game.

Sentence

Mathematical Expression/Sentence Example 3x = 3 a. x = 1 b. x = 2

Sentence a. True b. False

Mathematical Expression/Sentence Example 3x +4y

Expression

Mathematical Expression/Sentence Example 1(5) = 5

Sentence

Mathematical Expression/Sentence Example Math is a language.

Sentence

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

Logic

Not

Negation

Symbol of Negation

Negation; Not

And / But

Conjunction

Symbol of Conjunction

Conjunction; And / But

Disjunction

Symbol of Disjunction

Disjunction; Or

Implies; If, then

Conditional

Symbol of Conditional

→

Conditional; Implies; If, then

If and only if

Biconditional

Symbol of Biconditional

↔

Biconditional; If and only if

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.

s ˄ h

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.

s ˄ ̴ v

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.

r → ̴ v

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.

v ↔ ̴ h

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.

̴ h → ̴ r

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.

V v r

p: Gian plays volleyball q: Lanz plays basketball ̴ p

Gian does not play volleyball.

p: Gian plays volleyball q: Lanz plays basketball p ˄ q

Gian plays volleyball and Lanz plays basketball.

p: Gian plays volleyball q: Lanz plays basketball p → ̴ q

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

p: Gian plays volleyball q: Lanz plays basketball P v ( ̴ P → Q)

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

P: Adele is a singer Q: Adele is a songwriter R: Adele is an actress (P ˄ Q) → ̴ R

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

P: Adele is a singer Q: Adele is a songwriter R: Adele is an actress R → ( ̴ P ˄ ̴ Q)

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

p ̴ p T F

̴ p F T

``` p q p ˄ q T T T F F T F F ```

``` p ˄ q T F F F ```

``` p q p v q T T T F F T F F ```

``` p v q T T T F ```

``` p q p → q T T T F F T F F ```

``` p → q T F T T ```

``` p q p ↔ q T T T F F T F F ```

``` p ↔ q T F F T ```

Prelim Lectures Flashcards

Lectures 1-3 Nature by Numbers The Map of Mathematics Mathematical Language and Symbols (72 cards)