Mathematics in The Modern World - Prelims

Patterns

sequences or designs that are orderly and that repeat.

Symmetry

when different sides of something are alike

Fractals & Spirals

the 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale.

Fibonacci Patterns

the sequence of numbers that goes 1, 1, 2, 3, 5, 8, 13, 21

Tessellations

patterns that are formed by repeated cubes or tiles

Technology

Modern technology depends on basic research to advance,

Engineering

math is used to design and develop new components or products

Media

Mathematical concepts and themes can be found everywhere in the media

Medicine and Health

Advanced medical devices rely on studies supported by statistics

Finance and Business

Business ownership requires more than skill in creating a product or talent at providing a service.

Language

complex system of words and symbols, either spoken or written

Language of Mathematics

Every language has its vocabulary (the words) and its rules for combing these words into complete thoughts (the sentences).

Characteristics of the language of mathematics

Precise, Concise, Powerful

Precise

able to make very fine distinctions

Concise

able to say things briefly

Powerful

able to express complex thoughts with relative ease

nouns

used to name things we want to talk about (like people, places, and things)

sentences

are used to state complete thoughts. A typical English sentence has at least one noun, and at least one verb

expression

a name given to a mathematical object of interest, mathematical analog of an English noun, does not state a complete thought

Sets

is a collection of objects, and in mathematical discourse, these objects are mathematical ones such as numbers, points in space, or other sets

Functions

Focusing on the phrase "the square root of" in a sentence, a mathematical transformation of such a kind.

Relations

the grammar of the phrase "less than" in a sentence, it demands to be followed by a mathematical object

logical connective (logical operator)

is a symbol or a word which is used to connect two or more sentences.

Logical connectives

Negation, Conjunction, Disjunction, Implication

Negation

Symbol (~) - is the opposite of a statement, usually employing the word not

Conjunction

Symbol (∧) - is a compound sentence formed by using the word "and" to join two simple sentences

Disjunction

Symbol (⋁) - is a compound sentence formed by using the word "or" to join two simple sentences

Implication

Symbol (⇒) - is a type of relationship between two statements or sentences