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FEMALE VOICE:
UNSW Australia

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[MUSIC PLAYING]

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NORMAN WILDBERGER:
We live in a highly complex

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and interconnected world.

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Making sense of it
can be a challenge,

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but looking closer
we can find

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simple connections

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that can be understood
using high school mathematics.

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Hi, I'm Norman Wildberger
and we're here

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at the University
of New South Wales.

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This course will show you
how to use mathematics

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to explore relationships
and answer questions

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about the real world.

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How much longer does it take
to download a movie in HD?

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Does your city have
enough gas stations?

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What's the connection between
how much you exercise

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and your life expectancy?

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These questions are
about relationships

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between variable
quantities in our world.

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Some relationships are very
familiar from everyday life,

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such as how the price
of a pork chop

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depends on its weight.

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Others express important
physical or mathematical laws,

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like the fact that the
acceleration of an object

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is directly proportional
to the force on it.

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Or that the area
of a planar figure

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scales quadratically
with its size.

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And some correspondences
surprise us,

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such as how populations of cities
are distributed in a given country.

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Historically, these ideas rest
on 17th century discoveries

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of Fermat and Descartes:

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that mathematical relations

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can be modelled
with algebraic equations

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and visualised with
a sheet of graph paper.

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These insights brought
together Greek geometry

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and Arabic algebra

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and set the stage for calculus
and the Newtonian revolution

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in physics.

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In this course,
we'll look at understanding

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linear, quadratic and
inverse functions

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and their graphs,

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with applications to
a wide variety

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of real life situations.

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You'll strengthen your skills
in algebra and geometry,

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connect with science
and economics,

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and solve a wide variety
of interesting, fun

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and sometimes challenging
problems.

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Finishing this course
will be valuable

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to senior high school

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and incoming college
and university students

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wanting to review an
essential pre-calculus topic.

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It'll be useful to
high school teachers

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and to anyone
with an interest

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in how the remarkable
power of mathematics

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helps us understand
the world around us.