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MATHEMATICAL LANGUAGE AND SYMBOLS part1 | Darwin Ong | YouTubeToText
YouTube Transcript: MATHEMATICAL LANGUAGE AND SYMBOLS part1
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Summary
Core Theme
Mathematical language is a precise, concise, and powerful system for communicating mathematical ideas, distinct from ordinary language due to its non-temporal, emotionless, and context-devoid nature.
okay
let's continue our lesson so
we're going to discuss the mathematical
language in symbols
so i have a questions to you i hope you
will answer that
and then another question is is mathematics
mathematics
a universal language so
very tricky so
as a good gen i
another question this is the truth of
false if mathematics
is a universal language then mathematics
i hope you will answer your question my questions
questions
okay mathematical language in the
so language is systematic means of the
communicating ideas or feelings by the
use of
conventional signs sounds gestures
marks having understood meanings
according to webster
miriam webster of 2017.
but mathematical language system used to communicate
communicate
mathematical ideas it has its own grammar
grammar
syntax vocabulary word order
synonyms negotiations conventions
idioms abbreviations sentence structure
and paragraph structure
so the language of in mathematics differs
differs
from the language of ordinary speech in
three important ways
according to jamison 2000 so now we have
non-temporal which is
not past present or future or
devoid of emotion context and last we
have precise
but according to dr carol burns mathematics
mathematics
language is precise because it enables
to make very fine distinction it is also
concise because it enables
to say things briefly and lastly we have
powerful according to dr burns
because it's able to express complex
thought with relative ease
so we have two comparisons regarding
mathematical language versus ordinary language
language
so all we know that mathematical
language it has a highly
compact and focus because
it had a compact conveying a lot of
information and ideas
in a very little space and it focused
because it convey the important
information for the
current situation and omitting the rest
while for the ordinary language
it is full of ambiguities
and you know
innuendos hidden agenda and unspoken
cultural assumption according to jamison 2000
math words expressions and sentences
can help students explain what they think
think
it's precise math terms and symbols are
needed to achieve
better understanding and deeper appreciation
appreciation
and then we have the operation terms and
symbols so all we know that
elementary addition subtraction
multiplication and division
symbols and then as for the
mathematical expressions so one or more
numbers in order one
or variables that are connected by the
four fundamental operations raising the
powers and extracting roots
uh for example we have three x plus two
y minus
negative five or pi r squared or square
root of x squared plus b squared
so where the variable that represents
the unknown and makes
use of letters we have example x y z
a b c r or etcetera
where the constant represents any single
number so 0 1 103 pi
etc so we have the term expression
preceded by
the addition or subtractions
well for the literary coefficients that
is the unknown quantity in terms of variable
variable
but numerical coefficient is the
constant which determines
the number of times a variable is to be
multiplied for example we have 2 pi r
plus 1 all we know that 2 pi is our
numerical coefficient
and r is the literal coefficient this is
the variable
so we have also the here 3x
is one term monomial
2x plus 2y that is binomial
three x plus two y minus five that's three
three
trinomial and then five x plus six a six y
y
okay so it represents the given or
presses in symbols
so the sum of two numbers is five oh so
for example let x be the first number
and then the x minus five equals the second
second
number as another example for number two
the two more
than twice a certain number so let
x be the certain number then three
x plus two the required
number so
number we have number three ten less
than twice a certain number
all we know that x be the certain number
so savian
ten less than twice a certain number and
i'm not in an exactly certain number
gallons in avian twice so we have two x
minus 10
so that is the required number
the difference of two numbers is five so
let me the x be the first
number or the larger than the x minus
five the second number the smaller casing
casing
the difference of two numbers is five so
we are looking for the
uh two numbers is uh the difference of
two numbers is five
so let me the x be the first number
and then the x minus five will be the
second number
and then next we have the three
consecutive integers so
let x be the first integer then x plus
one the second integer the x plus two is
the third integer
on the three consecutive integers even
now we are
looking for the event so we have the let
x be the first
integer second the x plus two integer
and then
x plus four will be the third even integer
while for the add integer so we have the
let x be the
first add in the year then x plus 4 to
the second integer and then lastly we
have the x
plus four the third add integer
so next i hope that anything then you
attend a governation
so it represents in the given word
appraisal symbol
in symbols so number eight we have 10
exceeds a given number so we have
another note that
let x be the given number and then 10
exceeds a given number so
10 minus x the excess of a number the
back has a 10 exceeds
a given number now next
the square of sum of a
and b so let a plus b
is the sum of a and b but the question
is this
the given word is the square of the sum
so we have to square the a plus b
though that will be the square of the
sum of a and b
next the sum of squares of a
and b it means a squared will be the
square of a and then b squared will be
the square of b
and then a squared plus b squared is the
sum of the squares of
is twice as old as ken and ken
is three times as old as ian express
of each age in terms of x so do i remember
remember
10 is three times old as e and also
and then mark is twice as old as ken so
we have
twice the old of ken's so we have six x
next the sum of x and y subtracted from
the sum of a and b
so a plus b will be the sum of a and b
x plus y will be the sum of x and y so the
the
the the the pressure is impossible
nothing is
quantity of a plus b minus the quantity
of x plus a causing a habit
the sum of x y plus y will be subtract
from the sum of the a and b so granular engine
engine
so the perimeter of isosceles triangle
is the base
is two centimeters less than the two
equal sides so let's be the x will be
the length of
one side so one way perimeter in a
the the if the base is 2
centimeters less than the two equal
sides oh
so x minus 2 will be the length of the base
base
and then the perimeter is x plus x
so x x x equal so next
jet is four years younger than his
brother jeff
four years younger than his brother jeff
so but let nathan and x will be the age
of jeff
and sabijan the aids of jet will be
younger four years younger than his
brother so
x minus four diva tanda see
jeff so
the age of jeff a jet i mean is x
minus four so find the difference of
squares of their age
so let x squared be the squares of
so x minus four quantity places where it
will be the age
of jet's h and then looking at equation on
on
x squared minus x minus four
quantity squareds will be the difference
of their square x squared will
union hd jeff diba and then
x minus four it is knee yeah cause it is a
okay next we have the difference between
the squares of two consecutive odd integers
integers
let x be the first part in the years
then x
plus four two will be the second integer
and then
x squared will be the square of the
first integer
and then x plus 2 raised to the square
root with the square root of the second integer
integer
so the x squared minus quantity of x
plus 2
this squared will be the difference
between the square of two constants
and then lasts we have curl and has two
times as many 10 pairs as
you know carl has two times as many 10
peso points than
five pairs of points so we'll let x be the
the
number of five peso coins and then
sabi jan twice as many so we have two x
see you again thank you ciao
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