MMW 1A - 1

nature

nature

Is mathematics' physical reflection

pattern

A term used to describe repeating objects or events.

ian stewart

In _________ book “Nature’s Numbers”, he stated “by using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature’s patterns are not just there to be admired, they are vital clues to the rules that govern natural processes”.

self-organized patterns

Patterns formed without external intervention.

invoked organized patterns

Patterns formed with external intervention.

fibonacci sequence

Is a sequence of numbers in which terms are obtained by adding the two previous terms in the sequence.

leonardo pisano bigollo

Italian mathematician _______ commonly known as “Leonardo Fibonacci” who discovered the Fibonacci sequence.

organizing patterns and regularities

The numbers present not just in plants but in any other natural objects display mathematical regularities. These regularities give deeper understanding on nature’s phenomenon. Mathematics helps organize these patterns which are clues to uncover the underlying rules and regularities in the world.

predicting behavior of nature and phenomena in the world

It is often desirable to describe the behavior of some real life system or phenomenon, whether physical, sociological, or even economic, in mathematical terms.

mathematical model

The mathematical description of a system of phenomenon

helping control nature and occurrences in the world for our own ends

No one has the power to control natural occurrences in the world. However, experts developed models that will predict natural phenomenon.

has numerous applications in making it indispensable

Mathematics is everywhere. We are living in a world where mathematics is behind every activity.

number

Is a mathematical object used to count, quantify, and label another object.

operation symbols

Include addition (+), subtraction (-), multiplication (x or •), division (÷ or /) , and exponentiation (𝑥𝑛).

relation symbols

Include greater than or equal, less than or equal, equal, not equal, similar, approximately equal, and congruent.

congruent figures

Figures that are the same shape and size.

similar figures

Figures that are the same shape, but not necessarily the same size.

approximately equal

Two quantities when they are close enough in value so the difference is insignificant in practical terms.

grouping symbols

Include parentheses, curly brackets or braces, or square brackets.

variables

These are used when quantities take different values. These usually include letters of the alphabet.

set theory symbols

Are those used in the study of sets. These include subset, union, intersection, element, not element, and empty set.

logic symbols

These symbols include implies, equivalent, for all, there exists, and therefore.

statistical symbols

Include sample mean, population mean, median, population standard deviation, summation and factorial, among others.

mathematical expression

Defined as a mathematical phrase that comprises a combination of symbols that can designate numbers (constants), variables, operations, symbols of grouping and other punctuation. However, this does not state a complete thought.

mathematical sentence

Makes a statement about two expressions. The two expressions either use numbers, variables, or a combination of both. It uses symbols or words like equals, greater than, or less than and it states a complete thought.

open sentence

A sentence that uses variables; thus it is not known whether or not the mathematical sentence is true or false.

closed sentence

A mathematical sentence that is known to be either true or false.

set

A well-defined collection of distinct objects.

element

Each object belonging to a set is called ____.