MATHEMATICS: Its meaning and its Characteristics

What is Math?

Who said “The laws of nature are but the mathematical thoughts of God."

Euclid

Who affirmed, stating that “Mathematics is the language in which God has written the Universe.”

Galileo Galilei

which means “to learn”

manthanein

• Greek root word for Math

• Ancient Greek language, means what one learns or what one gets to know

máthēma

“knowledge, study, learning”

máthēma

mathematique

• Old French term for “mathematics”

Latin term for “mathematics”

mathēmatica

• Two Ancient Greek terms

• “fond of learning

”mathēmatikós, or mathemata

Is a science of:

• Calculation

• Numbers and space

• measurement, quantity and magnitude

Mathematics

It constitutes a body of established facts, achieved by a reliable method, verified by practice, and agreed on by a consensus of qualified experts

Mathematics

Is a science because:

• the development of all types of formal deductive reasoning

Mathematics

Old standard dictionary definition is “the study of the properties of numbers and geometrical figures.”

Mathematics

True or False:

• Today, mathematics includes abstract algebra, logic, and probability, none of which is part of traditional arithmetic or geometry.

True

Who said:

• A desire for a particular kind of knowing; knowing that is self-contained on the individual or may be seen as an autonomous thinking

(Schaaf, 1963)

A desire for a particular kind of knowing;

Mathematics

knowing that is self-contained in the individual or may be seen as autonomous thinking

Mathematics

The science of numbers and their operations, interrelations, combinations, generalizations, and abstractions, and of space configurations of their structure, measurement, transformations, and generalizations.

Mathematics

study of patterns and relations

Mathematics

“Way of thinking”

Math

An art characterized by order and internal consistency.

Mathematics

Math is a language that uses carefully defined terms and symbols. Thus, mathematics is a tool.

True

• “Science of patterns”

• “the science of order, patterns, structure, and logical relationships”

• Mathematics

“Approximation”

Calculate

Cum

“With”

Putare

“reason, thinking”

What is Compute?

With reason

The ultimate goal of calculating and computing.

Decision making

T of F: There are five characteristics of Math.

t

What are the 5 characteristics of Math?

Precision, Definition, Reasoning, Coherence, Purposefulness

It is precise in the sense that mathematical statements are clear and unambiguous. It is clear what is known and what is not known

Precision

Abound in mathematics. It is the bedrock of mathematical structure and the platform that supports reasoning

Definitions

Is the lifeblood of mathematics. It is the engine that drives proving and problem-solving. Its absence is the root cause of the learning-by-rote approach

Reasoning

Concepts and skills are interwoven in mathematics

Coherence

Mathematics is goal-oriented, and for every concept or skill there is a purpose for it

Purposefulness

There are 9 mathematics as a tool. What are those?

• Data management

• Geometric Designs

• Codes

• Linear Programming

• The Mathematics of Finance

• Apportionment and Voting

• Logic

• The Mathematics of Graphs

• Mathematical System

What is Mathematics for? Give three.

• Helps unravel the puzzles of nature.

• Helps organize patterns and regularities as well as irregularities in the world.

• Helps predict the behavior of nature and phenomena.

• Helps control nature and occurrences such as epidemics.

• Provides tools for calculations.

• Provides new questions to think about.

Who uses Math?

Everyone

Who stated that mathematics is a formal system of thought that was gradually developed in the human mind and evolved in the human culture.

Stewart

It is a formal system of thought that was gradually developed in the human mind and evolved in human culture

mathematics

True of false: Schools of thought realize the existence of “figure” to which they gave meaning to it.

False, “form” not figure

What is the essence of Math according to Des Cartes?

“I think … therefore I am”

What ar ethe two kinds of Math that Mathematicians uses?

Pure and applied

What are the two sciences that scientists uses but is applied to Mathematics?

natural and social

True of false: different people use different mathematics at different times for different purposes using different tools

True

Give thre reasons why is Mathematics important to know?

• It puts order in disorder

• It helps us to become a better person’

• It helps make the world a better place to live in