Exploring the world of mathematics kust

Dr. Farhana Shaheen
EXPLORING THE
WONDERFUL WORLD OF
MATHEMATICS

Mathematics: Comes from the
Greek word “Mathema” meaning
“Science, Knowledge, or
Learning”
• The study of Figures and Numbers.
• The study of Patterns of Structure, Change
and Space.
• The language of Sciences
• A Science dealing with the Logic of Quantity,
Shape and Arrangement.
• The Science that deals with Numbers,
Quantities, Shapes, Patterns, Measurement
and the concepts related to them.

Math THE QUEEN OF ALL
SCIENCES
• Why is mathematics called ''the queen
of all sciences‘’?
• Math is both the science and the art of
tackling complicated challenges.

Maths is the language of the
universe
• If there is any subject that can be used to
understand the complexity and intricacy of
nature, it is Maths.
• Maths takes us to a world of perfectness
and infinitude.
• It is the world of fact and reason and that
is the only thing that matters.

MATH IS THE BUILDING
BLOCK OF ALL SCIENCES
• It is the building block for everything in
our daily lives, including mobile
devices, architecture (ancient and
modern), art, money, engineering, and
even sports,
astronomy
and what not.
11

Maths is ALL AROUND
US
• Mathematics is the science that deals
with the logic of shape, quantity and
arrangement. Math is all around us, in
everything we do.

Passion for Math?
• It is often said that math is the queen of all
sciences, but the truth is that it is also
known as a subject that complicates the
lives of many students, being the most
difficult to learn.
• The passions aroused by this science
are extreme: either you love it, or you
hate it.

The Importance of Studying
Mathematics and the Benefits it brings
to our Brain.

BUT THE FACT IS…
MATH IS UNAVOIDABLE

Learning Disability
• A learning disability is a condition that
produces a gap between someone's ability
and his or her performance.
• Typical learning difficulties include
•Dyslexia,
•Dyscalculia, and
•Dysgraphia –

DYSLEXIA
• A specific learning disability in reading.
Kids with dyslexia have trouble reading
accurately and fluently. They may also
have trouble with reading comprehension,
spelling and writing.

Dyscalculia
• Resources: http://www.dyscalculia.org/
• The word "dyscalculia" means difficulty
performing math calculations.
• In other words, it just means
“Math difficulty".
• And specifically, it means
a learning disability which affects Math.

Dyscalculia is not a disease
• It’s a simple learning disability that can
be treated by just following some
simple and easy steps and giving some
extra time along with the routine of
those students.

DYSCALCULIA
• A specific learning disability in Math.
• Kids with dyscalculia may have difficulty
understanding number-related concepts or
using symbols or functions needed for
success in mathematics.

DYSGRAPHIA
• A specific learning disability in writing.
• Kids with dysgraphia may have difficulty
writing legibly and at age-appropriate
speed. Many children with dysgraphia also
struggle to put their thoughts down on
paper.
• This is sometimes called a disorder of
written expression.

Learning Math Issues:
Many students claim that there are too
many mathematics formulas to
remember. This can be a contributing
factor to students' lack of interest in
classroom mathematics.

Strategy for memorizing
Formulae?/?/?

Try-
• They enhance the storage and recall of
information contained in the memory.
• It can be an ACRONYM-
• e.g. VIBGYOR:
• Violet; Indigo; Blue; Green; Yellow;
Orange; Red.

(Memory devices)
• LIATE:
• Log; Inverse; Algebraic;
Trigonometric; Exponents

Give More Importance
Towards Applications of
Maths
• https://www.youtube.com/watch?v=sBF
cX2KWScI

Life Without Maths- is
NOTHING
39

• In shopping… In baking, cooking
40

The Power of Mathematical
Visualization
• Mathematical visualization is an aspect
of geometry which allows one to
understand and explore mathematical
phenomena via visualization.
• A new, visual way to think about Math.

Visual Math
• https://www.youtube.com/watch?v=TyO
dLqHJqRY&pbjreload=10
• These animations will help you understand
the math concepts you never got in high
school

The Power of Visualization in
Mathematics
• Creating Visual representations for Math
students can open up their understanding.
• Geogebra
• Youcubed
• Desmos

The Power of Visualization in
Mathematics
• Animations
• Visual Patterns
• Graphs
• Number Lines
• Tape Diagrams
• Duda Maths
• Area Models

Math and Movies
• (Animation at Pixar) – Numberphile
• https://www.youtube.com/watch?v=mX
0NB9IyYpU
•

Math in Music
• Donald Duck Donald In Mathmagic
Land
• https://www.youtube.com/watch?v=Pvc
eKeHl0Sg
• An Adventure in Color/Mathmagicland
(1961)
• https://www.youtube.com/watch?v=yLffxw
RlXcc

Music and Math
• The Genius of Beethoven –
Natalya St. Clair
• https://www.youtube.com/watch?v=zAxT0
mRGuoY

The Maths of Music
• Ratios of Frequencies of Musical Notes
• https://www.youtube.com/watch?v=rTT1X
HJKKug

Cryptography with Matrices
• This tutorial will show you how to
encode and decode messages using
matrices.
• https://www.youtube.com/watch?v=hlYAC
o8c4bc

Applications of Matrix in Real
Life
• 1976 Matrix Singular Value Decomposition
Film
• https://www.youtube.com/watch?v=R9
UoFyqJca8
• https://www.youtube.com/watch?v=jzHb1
R5wWYU

The True Power of the Matrix
• (Transformations in Graphics) -
Computerphile
• https://www.youtube.com/watch?v=vQ60r
Fwh2ig

• Fibonacci Numbers in Nature
• Golden Ratios in Nature
• Fractals in Nature

Importance of
GOLDEN RATIO
• Makkah The Miraculous Golden Ratio City
The Secret Of Kaaba
• https://www.youtube.com/watch?v=19zU
WMCJTnE
• Why is 1.618034 So Important?
• https://www.youtube.com/watch?v=keLN8
9CWZ-A

FRACTALS
• The Mandelbrot Set -
• “How to transform in my mind, Formulas
into Geometrical Shapes”
• https://www.youtube.com/watch?v=56gzV
0od6DU

Fibonacci Sequence in Music
• https://www.youtube.com/watch?v=2pb
Earwdusc
• The Magic of Fibonacci numbers | Arthur
Benjamin

Let’s Visit the Wonderful
World of Mathematics

Mathemagician Arthur Benjamin
• Math is logical, functional and just ...
awesome. Mathemagician Arthur
Benjamin explores hidden properties of
that weird and wonderful set of
numbers, the Fibonacci series. (And
reminds you that mathematics can be
inspiring, too!)
• https://www.youtube.com/watch?v=SjS
HVDfXHQ4

Mathemagician Arthur Benjamin
• We spend so much time on learning
about Calculations- we should Not
forget about Applications-
• The MOST IMPORTANT application of
Math is LEARNING HOW TO THINK
• Mathematics is Not just solving for “x”,
it’s Also figuring out “WHY”

Math isn’t hard-It’s a
Language
• “The Laws of Nature are written in the
Language of Mathematics”
• Galileo
• https://www.youtube.com/watch?v=V6yix
yiJcos
• TEACH MATHS AS A HUMAN LANGUAGE

The Surprising Beauty of
Mathematics
• | Jonathan Matte |
TEDxGreensFarmsAcademy
• https://www.youtube.com/watch?v=SEiSlo
E1r-A

Real life Applications of
Trigonometry
• Trigonometry - Easy to Understand 3D
Animation
• https://www.youtube.com/watch?v=ovL
bCvq7FNA&t=185s
• https://www.youtube.com/watch?v=1ok
hBnvuuck

RECREATIONAL MATHS &
MATHEMATICAL PUZZLES
• Mathematics is not only a language of
tough equations and logic, it has a real
beauty of thinking, and Puzzles and
Recreational Mathematics is the best
way to explore the deepness of
Mathematics.

GEOGEBRA
• THE GRAPHING CALCULATOR FOR
FUNCTIONS, GEOMETRY, ALGEBRA,
CALCULUS, STATISTICS AND 3D
MATH!
• It makes a link between Geometry and
Algebra, in a unique Visual way.

GEOGEBRA
• GeoGebra is an interactive geometry,
algebra, statistics and calculus application,
intended for learning and teaching
mathematics and science from primary
school to university level.

• Discover Math with GeoGebra
• Solve equations, graph functions, create
constructions, analyze data, explore 3D
math!
• https://www.geogebra.org/

https://www.youcubed.org/
• Watch this video:

YOUCUBED- MISSION
• Our main goal is to inspire, educate and
empower teachers of Mathematics,
transforming the latest research on math
into accessible and practical forms.
• We know from research how to teach
math well and how to bring about high
levels of student engagement and
achievement but research has not
previously been made accessible to
teachers.

TAPE DIAGRAM
• A tape diagram, also known as a bar
model, is a pictorial representation of
ratios.
• In mathematics education, it is used to
solve word problems.

DUDAMATH
• http://www.dudamath.com/
• DUDAMATH is an integrated environment
for interactive exploration of mathematical
concepts and problem solving.

For Kids: Bedtime Math
• Parents know to read to their kids at night,
but what about Math?
• Our mission is simple: to make math a fun
part of kids' everyday lives, as beloved as
the bedtime story.
• https://parents.bedtimemath.org/home/
data-center#tab=account

Trigonometry - Easy to
Understand 3D animation
https://www.youtube.com/watch
?v=PF2nmCVSUEs
•

Trick for doing trigonometry
mentally!
https://www.youtube.com/watch?v=jI81WXy
FrL0

Super Hexagon for
Trigonometric Identities
• https://www.youtube.com/watch?v=T7D
1W1oD8wo

What if they spent the time on
studying- what they spend on
Chatting?

Watch this!
• https://www.khanacademy.org/partner-
content/pixar/start/introduction/v/pipeline-video
content/pixar/environment-modeling-2/mathematics-
of-parabolas2-ver2/a/parabolas-lesson-brief
content/pixar/environment-modeling-2/animating-
parabolas-ver2/v/overview-parabolic-arcs
content/pixar/environment-modeling-2/animating-
parabolas-ver2/v/environment-modeling2

MATHIGON
• WORLD OF MATHEMATICS
• http://world.mathigon.org/

List of Free Math softwares
http://listoffreeware.com/list-of-best-
free-math-software/

Euler Math Toolbox
• Euler Math Toolbox is a free math
software for your PC. With the help of this
software you can carry out various
calculations in mathematics such as
subtraction, addition, calculus
problems, algebra, matrices, functions
and complex equations. This freeware is
very useful for math students as they can
solve nearly all types of mathematics
problems by using this freeware.

xFunc
• Xfunc is a free math software for your
computer. With the help of this freeware
you can solve math problems easily. By
using this software you can write various
types of equations in mathematics
solve them and also see their solutions.
You can utilize various functions to make
different mathematical expressions with
the help of Xfunc.

QMentat
• QMentat is a free software for practice and
learning mental mathematics. Mental
mathematics means performing mathematical
calculations in your mind. There is no need to
use calculators, pencil and pen in mental
mathematics. With the help of this freeware
you can quickly develop skills for mental
mathematics. This freeware can perform
various types of math operations such as roots,
powers, divisions, multiplication, subtraction and
addition.

TalkingMath
• TalkingMath is a free math software for your
children. With the help of this freeware your
kids can learn mathematics easily and quickly.
This freeware also supports audio mode.
TalkingMath works in 3 different modes such as
timer, standard and interactive mode.
TalkingMath lets you perform various types
of mathematical calculations such as
division, multiplication, subtraction and
addition.

JXCirrus Maths
• JXCirrus Maths is a free math software to learn
mathematics. This freeware is specially created
for small children to learn math in a exciting
and fun way. With the help of this freeware you
can easily create easy and basic exercises in
math for your children. JXCirrus Maths teaches
your children basic math operations such as
division, multiplication, subtraction and addition.

SpeQ Mathematics
• SpeQ Mathematics is a free math software for
your computer. With the help of this freeware
you can easily learn math and solve complex
problems in mathematics. It has inbuilt support
for a wide variety of variables, constants and
mathematical functions. SpeQ Mathematics also
lets you define functions and custom variables.
You can also solve problems of trigonometry by
using this freeware.

Math Editor
• Math Editor is a free math software. With the
help of this freeware you can create
mathematical equations with various symbols
such as Cyrillic, alpha, beta, Greek symbols,
square root, integrate easily and quickly. It
supports TIFF, GIF, BMP, JPEG and PNG
formats. This freeware is very useful for creating
mathematical equations on your PC.

Microsoft Mathematics
• Microsoft Mathematics is a free math software
for your computer. With the help of this freeware
math students can solve complex math
problems easily. It basically helps math students
to solve problems in algebra. Apart from that you
can also draw 3D and 2D images with the help
of this utility. The main objective of this freeware
is to teach students the basic of math, physics
and chemistry.

CompliCalc
• CompliCalc is a free mathematical software.
With the help of this freeware you can solve
complex mathematical problems easily and
quickly. This freeware also includes various
functional and algebraic calculators. CompliCalc
lets you perform a wide variety of operations
such as calculate square root, factorial, discount
and distance. To use this freeware you need to
specify the task you want to perform on the main
interface of this freeware.

DESMOS GRAPHING
CALCULATOR
• https://www.desmos.com/calculator

'Geometry' means
'Earth Measuring'.
• Initially, as with the Egyptians,
geometry originated from practical
necessity and the need to measure
land; the word 'Geometry' means 'Earth
Measuring'.
• The Babylonians were certainly skilled
geometers, and the Egyptians developed a rich
and complex mathematics based around
surveying. Both of these cultures would pass
their information on to the Greeks.

GEOGEBRA
• Geogebra is a free math software. With the help
of this freeware math teachers can teach
mathematics and math students can learn
mathematics. This freeware provides a sound
platform to math students to learn math and
solve mathematical problems of various topics
such as linear programming, complex numbers,
vectors, probability, discrete mathematics,
calculus, statistics, algebra, functions and
graphs, geometry etc.

GEOGEBRA
• http://web.geogebra.org/chromeapp/
3D Grapher is a feature-rich yet
easy-to-use graph plotting and
data visualization software suitable
for students, engineers and
everybody who needs to work with
2D and 3D graphs.
With 3D Grapher you can easily
plot the equation and table-based
graphs, zoom them, rotate, view at
any angle and even animate. You
can draw the unlimited number of
graphs in one coordinate system
to visualize and analyze the
domains of functions and their
intercepts.

GeoEnzo
• GeoEnzo is a math software specially
build for mathematics teachers. With the
help of this freeware mathematics teacher
can teach geometry to math students. This
freeware lets you easily draw various
types of geometrical shapes such as cone,
triangle, circle, cube, line and many more.
This freeware is very useful for teaching
geometry to math students.

INTRODUCING
PREALGEBRA FOR
FOUNDATION YEAR
• http://www.xyzsolve.com/PreAlgebra/in
dex.aspx

Math-Shortcut-Tricks.Com
• Square and Square Root Tricks
• Cube and Cube root Tricks
• BODMAS Rules
• Fraction Tricks
• Knowing Basic Maths

Calculator for kids
• Calculator for Kids is a basic math application
specially build for your children. With the help of
this freeware kids can learn the basic math and
carry out simple mathematical operations such
as division, subtraction, multiplication, addition
etc. Your kids can learn basic functions of math
with a simple approach by using this freeware.
Calculator for Kids is a portable application.

ATHLETICS vs
Mathletics has evolved… right into your
hands. The multi award-winning e-learning
platform is available on iPad.
Use in the classroom, at home – or
anywhere. Use online or offline - Mathletics
can be accessed ANYWHERE!

It can be a sentence-
• Like- King Harry Doesn’t Usually Drink
Chocolate Milk

MATH Mnemonics- Example
• Some People Have Curly Brown Hair
Through Proper Brushing
• Now you look yourself on the Capital
Letters
Sin x = P/H
Cos x = B/H
Tan x = P/B

• Is there any simple way to remember
the Trigonometry formulas?
• SOH-CAH-TOA

Or-It can be a poem?
Like in Statistics-

(Memory devices)
• It can be any physical action-

Finding SLOPE of a line
• Mnemonics can be a picture-

Mnemonics-
Example: To find slopes
• For horizontal lines:
• Slope=0
• Z for zero
• For vertical lines:
• Slope is undefined
• N for No slope

To determine the concavity of a
function using second derivative
Concave upward Concave downward
Think of
some
examples …

Memorizing the formula
(a+b)^n:
• Use- Pascal’s Triangle

Go for Mental Maths- It
sharpens your mind- and
saves your time
•
• Avoid using Calculator

Let’s try making Math
EeeZeee

Let’s see how fast we are in
mental Maths- ;)
• Think of a number- ???
• Double it---
• Add 6 to it
• Divide it into half
• Deduct your number-
• And- the Answer is ???

Let’s see how fast we are in
Maths symbols ;)

Mathinglish
• M
• A
• T
• H
• INGLISH

Which strategy would you use
here?

• 5 + 3 = 28
9 + 1 = 810
8 + 6 = 214
5 + 4 = 19
Then 7 + 3 = ??

Solve the puzzle-
• 11 x 11 = 4
• 22 x 22 = 16
• 33 x 33 = 18
• 44 x 44 = ??

CHALLENGE:
Complete the third box

Prove that 2 = 1
• Find the flaw!

Exploring the world of mathematics kust

Recommended

Recommended

More Related Content

Similar to Exploring the world of mathematics kust

Similar to Exploring the world of mathematics kust (20)

More from Farhana Shaheen

More from Farhana Shaheen (20)

Recently uploaded

Recently uploaded (20)

Exploring the world of mathematics kust