Transcript History of Mathematics

Introduction to Mathematics
Paolo Lorenzo Bautista
Special thanks: Pauline Mangulabnan
De La Salle University
Short Exercise. TRUE or FALSE
1. The symbols + and – were introduced
before the 1200s.
2. It is possible to count without numbers.
3. The multiplication symbol was introduced
by William Oughtred in the 1400s.
4. There were already evidence of counting
during the time of Christ.
5. Famous mathematicians believed that
mathematics is never spiritual.
6. Animals can count.
Short Exercise. TRUE or FALSE
1. The symbols + and – were introduced
before the 1200s.
2. It is possible to count without numbers.
3. The multiplication symbol was introduced
by William Oughtred in the 1400s.
4. There were already evidence of counting
during the time of Christ.
5. Famous mathematicians believed that
mathematics is never spiritual.
6. Animals can count.
There were already evidence of
counting during the time of Christ.
•
Among the oldest direct evidence
of human counting is a baboon’s
thigh bone marked with 29
notches. (150,000 years ago)
•
They used different sort of
things to count like pebbles,
scratches, tallies, straight
segments, curves, etc.
• Famous Hindu Numerals
The symbols + and – were
introduced before the 1200s.
•
The symbols for addition and
subtraction first appeared in
1465 in Robert Muller’s paper.
•
However, the downward stroke of
addition is not so vertical.
The multiplication symbol was introduced
by William Oughtred in the 1400s.
•
In 1631, the
multiplication symbol
(x) was introduced by
William Oughtred in
his book, Keys to
Mathematics.
•
He invented the slide
rule (early form of a
calculator)
Famous mathematicians believed that
mathematics is never spiritual.
•
Srinivasa Ramanujan (INDIAN)
– An equation means nothing to me
unless it expresses a thought of God
•
Carl Friedrich Gauss
– I proved a theorem not by dint of
painful effort but by the grace of
God
•
George Cantor, Blaise Pascal,
John Littlewood, etc.
Animals can
count.
H. Kalmus (1964)
Tetsuro Matsuzawa (Kyoto)
Michael Beran (2003)
•
Counting facilities are
found in animals like
squirrels, rats,
chimpanzees, and other
pollinating insects.
•
They can distinguish
numbers through visual
patterns and can
produce signals, react
to rewards and match
dots with numbers to
show such recognition.
HOW CAN YOU COUNT
WITHOUT NUMBERS?
Without counting or simply using
your fingers, represent quantities
from zero to fifty using your body.
How are you going to represent
each quantity? Your system must be
possible even for counting until a
thousand.
How can you represent the time of
the day without using numbers?
How will you show 3:00 pm? 7:00
pm? 2:00 am? It does not have to be
exact to the last minute. What
materials will you be using?
Reflection:
• Why do you think people study mathematics?
• Why do we need people to study
mathematics?
Mathematics
WHAT HAS MATH BROUGHT TO
THE WORLD TODAY?
The hypercube: fictional? What is it? Does
it exist?
Logic and the mathematical imagination
has given a product of the mind a
(palpable) reality of its own!
‘True facts about imaginary things’
5-dimensional hypercube
9-dimensional hypercube
What is a 248-dimensional object?
The Lie group E8
In 2006, a physicist proposed that the 248-dimensional E8 is the fabric of the universe.
From a beautiful idea, math
transcends our understanding of
the universe.
Mathematicians enjoy the activity of
the mind which leads to the most
breathtaking realities of today.
“imagination is more
important than knowledge”
Math is found everywhere! It runs many
aspects of our living.
Cars run on engines that
run on the principles of
calculus.
CD players, audio and video players,
digital cameras and your cell phones
use coding theory, linear algebra and
geometry.
Internet routing protocols and search engines
use graph theory and linear algebra
to manage and efficiently access information
on the web.
GPS: Algebra, geometry, trigonometry,
statistics and linear algebra
Fractals and Partial
Differential Equation
Animated characters are
usually constructed
from a grid of points
with a means to
interpolate between the
grid points and produce
a natural, smooth
appearance.
HARMONIC
FUNCTIONS
Mathematicians like Stanley Osher, Yves Meyer, Daniel
Spielman and Alberto Adrego Pinto are examining areas
of life where maths can find applications, including
modelling of human behaviour.
Number theory, coding
theory and cryptography