history and roles of mathematics1

7/29/2019 History and Roles of Mathematics1

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Brief History of Mathematics

2000 BC

Earlier a place value notation number system

had evolved over a lengthy period with a

number base of 60


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1700 BC

i. Phytegores theorem a2+b2 = c2

ii. Linear equations were studied in the context

of solving number problems

iii. Quadratic equations were also studied and

these examples led to a type of numerical

algebra

iv. Geometric problems relating to similar

figures, area and volume were also studiedand values obtained for


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450 BC

i. The Babylon basics of Mathematics was

developed by Greek

ii. Further mathematical discoveries were

driven by the astronomy, for example the

study of trigonometry


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300 BC to 200 AD

i. Major Greek progress in mathematics

ii. After this time progress continued in Islamic

countries


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16th Century

i. Major progress in mathematics in Europe

began again

ii. Algebraic solution of cubic and quartic

equations by Pacioli

iii. Cardan, Tartaglia, Ferrari Copernicusand

Galileo revolutionised the applications of

mathematics to the study of the universe


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17th Century

i. Napier, Briggs and others greatly extend the

power of mathematics and discover the lawof logarithms

ii. Cavalierimade progress towards the

infinitesimal calculusiii. Descartes added the power of algebraic

methods to geometry

iv. Progress towards the calculus continued withFermat, who, together with Pascal, beganthe mathematical study of probability


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18th Century

i Eulerwho, in addition to work in a wide

range of mathematical areas, was to invent

two new branches, namely the calculus of

variations and differential geometry

ii Lagrange was to begin a rigorous theory of

functions and of mechanics


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v. Newton and Barrow(Newtons teacher),

developed the calculus into a tool to push

forward the study of nature. They show theinteraction between mathematics, physics

and astronomy

vi. Newton's theory of gravitation and histheory of light take us into the 18th Century


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19th Century

In geometry Plckerproduced fundamental

work on analytic geometry and Steinerin

synthetic geometry


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The roles of Mathematics

Mathematics as a Language

What is Mathematics?

Often, people equate mathematics with arithmetic

Traditionally, the major emphasis of the K-8mathematics curriculum has been to teach childrenarithmetic

Mathematics involves more than computation

Mathematics should include experiences that helpstudents to shift their thinking about mathematics


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Mathematics as a Language

Blake wrote: "I have heard many People say,

'Give me the Ideas. It is no matter what Words

you put them into.'"

To this he replies, "Ideas cannot be Given but

in their minutely Appropriate Words."

William Blake

(quoted by J. Newman, The World of Mathematics, 1956)


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Mathematicians need to be clear and concisewhen they communicate

Our math education system pays someattention to the idea that math is a language.

For example:

Some math teachers make use ofcooperative learning(an environment thatencourages students to communicatemathematical ideas)

Some math assessment instruments requirethat students explain what it is they aredoing as they solve the math problems in theassessment.


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Mathematics as a Science

generating a formula that describes

some basic tendency of nature

use with existing theory to deduce an

unknown quantity

an analytic tool applied to experimental

data

Mathematics is important in physics and

astronomy


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Mathematics as a Way of Thinking

The process of learning mathematics

necessarily involves learning certain ways ofthinking

One of the reasons to learn problem solving

in our Mathematics curriculumSeeing connections is a big part of

mathematical problem solving and theoremproving

provide powerful support for businessdecision


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Mathematics as the Art of Calculation

Mathematics consists of techniques for

getting answers

Calculation is at the very root of

Mathematics

In China, abacus is the art of calculation.


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Mathematics is a Patterns and Relationships

Patterns and relationships are found in

aspects of math such as counting and

geometry

Number patternssuch as 3, 6, 9, 12are

familiar to us since they are among thepatterns we first learn as young students

Mathematics is especially useful when it

helps you predict, and number patterns areall about prediction


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Recognizing number patterns is also an

important problem-solving skill

If you see a pattern when you look

systematically at specific examples, you can

use that pattern to generalize what you see

into a broader solution to a problem


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Mathematics is a Tool or an instrument

Mathematics can solve abstract problem inthe mathematical problems

It also can solve daily life activities

One of the best examples is when a personis cooking

history and roles of mathematics1

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