GEC104 Video Lecture 1 Mathematics in our World Part 1
Summary
TLDRMahid Mahmudaram from the Mathematics Department at Mindanao State University explores the multifaceted nature of mathematics, drawing an analogy with John G. Saxe's poem 'The Blind Men and the Elephant' to illustrate its diverse aspects. The lecture delves into how mathematics reveals patterns in nature, influences daily life, and is integral to various professions. It emphasizes the importance of understanding and appreciating mathematics for its role in unraveling nature's mysteries, predicting outcomes, and contributing to a better world.
Takeaways
- 📚 Mathematics is a diverse discipline that encompasses more than just arithmetic and geometry; it also includes data, measurement, inference, deduction, proof, and mathematical models of natural phenomena, human behavior, and social systems.
- 🐘 The poem 'The Blind Men and the Elephant' by John G. Sachs is used as an analogy to illustrate the different perceptions of mathematics based on the area one focuses on, emphasizing the importance of seeing the whole picture.
- 🔍 Mathematics helps reveal hidden patterns in nature, the world, and the universe, aiding in our understanding of these complex systems.
- 🎶 Mathematics is described as a language expressed in various forms including patterns, shapes, and music, and is part of what we see and hear in our environment.
- 🌐 Ian Stewart defines mathematics as a formal system of thought for recognizing and exploiting patterns, suggesting that these patterns are clues to the rules governing natural processes.
- 🔢 Common notions associated with mathematics include numbers and counting, numeric and geometric patterns, and patterns of movement.
- 🏠 Mathematics is present in everyday life, from setting alarms to making purchasing decisions, and is used by everyone from students to professionals.
- 🌳 Nature displays mathematical patterns in ripples, land formations, lightning, and even in the shapes and colors of animals.
- 🏆 The importance of mathematics extends to various professions, including teaching, aviation, navigation, accounting, economics, and manufacturing.
- 🧩 Mathematics plays a crucial role in understanding the human body, managing populations, and predicting outcomes in sports, arts, and other events.
- 🛠 Mathematics is often underappreciated, but it is essential for unraveling the puzzles of nature, making predictions, understanding weather conditions, and controlling the spread of epidemics.
- 🤔 The process of doing mathematics involves curiosity, seeking patterns, a desire for truth, enduring trials and failures, and not fearing more questions and problems.
Q & A
What is the main theme of the lecture by Mahid Mahmudaram?
-The main theme of the lecture is the diverse nature of mathematics and its relevance in understanding the world around us.
What poem is used as an analogy to describe the perception of mathematics?
-The poem 'The Blind Men and the Elephant' by John Godfrey Saxe is used as an analogy.
What does the poem 'The Blind Men and the Elephant' illustrate about the perception of mathematics?
-The poem illustrates that depending on which part of mathematics one studies, one gets a very different idea of what mathematics is, similar to how each blind man perceived the elephant differently.
What are the various aspects of mathematics mentioned in the lecture?
-The lecture mentions arithmetic, geometry, data and measurement, inference, deduction, proof, and mathematical models of natural phenomena, human behavior, and social systems.
What does Ian Stewart define mathematics as in his book 'Nature's Numbers'?
-Ian Stewart defines mathematics as a formal system of thought for recognizing and exploiting patterns.
How does the lecture relate mathematics to the patterns found in nature?
-The lecture suggests that nature's patterns are vital clues to the rules that govern natural processes, and mathematics helps us recognize these patterns.
What are some common notions associated with mathematics mentioned in the script?
-The common notions include numbers and counting, numeric and geometric patterns, and patterns of movement.
How is mathematics used in everyday life according to the lecture?
-Mathematics is used in everyday life in activities such as setting alarms, buying groceries, budgeting, making schedules, and even in professions like teaching, piloting, and accounting.
What role does mathematics play in understanding the human body and managing populations?
-Mathematics helps in understanding the physical attributes and cellular formations of the human body, and it is used in managing populations and predicting the likelihood of different communities.
Why is mathematics considered underappreciated according to the lecture?
-Mathematics is considered underappreciated because many people are still unaware of the need for every individual to know and appreciate the roles of mathematics in understanding nature, making predictions, and solving problems.
How does the lecture describe the process of doing mathematics?
-The lecture describes the process of doing mathematics as being driven by curiosity, seeking patterns, desiring to know the truth behind phenomena, undergoing trials and failures, and not fearing more questions and problems.
Who are the main users of mathematics according to the lecture?
-The main users of mathematics include mathematicians, scientists studying natural or social sciences, and practically everyone in their everyday life activities.
What are some reasons why mathematics is important to know as cited in the lecture?
-Reasons include putting order in disorder, helping to become better persons through better decision-making, and making the world a better place by understanding and explaining natural phenomena.
Outlines
📚 Mathematics: Perception and Perceptions
The script begins with an introduction to the speaker, Mahid Mahmudaram, and the topic of mathematics in our world. It uses the analogy of 'The Blind Men and the Elephant' to illustrate the diverse nature of mathematics, which encompasses more than just arithmetic and geometry. The poem highlights how focusing on a single aspect can lead to a limited understanding of the whole. The speaker emphasizes that mathematics is about recognizing patterns in nature, the universe, and human-made systems, and it serves as a language expressed through numbers, shapes, and even music. The importance of understanding the broader concept of mathematics is stressed, including its role in revealing hidden patterns and its definition by Ian Stewart as a system of thought for exploiting patterns.
🌿 Mathematics in Nature and Daily Life
This paragraph explores the omnipresence of mathematics in nature and everyday activities. It provides examples such as ripples in water, land formations, and patterns in animals' scales, which all exhibit mathematical patterns. The script discusses how mathematics is used in daily routines, from setting alarms to buying groceries, and in various professions, including teaching, piloting, and accounting. The importance of mathematics in understanding the human body, managing populations, and predicting outcomes in sports and other events is highlighted. The paragraph concludes by emphasizing the underappreciated role of mathematics and lists several reasons why it is essential for individuals to understand and appreciate its various roles in unraveling nature's mysteries, making predictions, and solving problems.
🔍 The Essence and Application of Mathematics
The final paragraph delves into the common perceptions of mathematics as numbers, symbols, and notations, and the deeper understanding that it involves studying processes and proving theorems. It outlines how mathematics is conducted with curiosity, a penchant for patterns, and a desire to uncover truths. The script mentions the iterative process of trials and errors in mathematical discovery and the continuous pursuit of questions and problems. It identifies mathematicians, scientists, and everyday individuals as users of mathematics, each with different tools and attitudes. The paragraph concludes by citing reasons why mathematics is important, such as bringing order to chaos, aiding in personal decision-making, and contributing to a better understanding of the world, ultimately making the world a better place.
Mindmap
Keywords
💡Mathematics
💡Analogy
💡Patterns
💡Perception
💡Natural Phenomena
💡Inference
💡Proof
💡Mathematical Models
💡Language
💡Unreal Reality
💡Daily Routine
Highlights
Mathematics is a diverse discipline that encompasses more than just arithmetic and geometry, including data, measurement, inference, and mathematical models of natural phenomena and social systems.
The poem 'The Blind Men and the Elephant' by John G. Sachs is used as an analogy to explain the different perceptions of mathematics based on the area of study.
Mathematics reveals hidden patterns that help us understand nature, the world, and the universe.
British mathematician Ian Stewart defines mathematics as a formal system of thought for recognizing and exploiting patterns.
Nature's patterns are vital clues to the rules that govern natural processes, emphasizing the importance of mathematics in understanding the world.
Mathematics is expressed in various forms, including patterns, shapes, and music.
Mathematics is present in our daily routines, from setting alarms to making purchasing decisions.
Different professions, including teachers, pilots, and accountants, utilize mathematics in their work.
Mathematics plays a crucial role in understanding the human body, managing populations, and predicting outcomes in various events.
Mathematics is often underappreciated, with many unaware of its importance in unraveling the puzzles of nature and serving as a useful way to think about it.
Mathematics helps in making arrangements and understanding patterns of various behaviors, which is essential for organizing regularities and irregularities.
Mathematical tools enable the prediction of future outcomes based on previous occurrences.
Meteorologists use mathematical concepts to study the atmosphere and prevent disasters.
Mathematics is known for calculations, which are fundamental in various fields and daily life activities.
Mathematics provides new questions to think about, especially in the context of research.
Mathematics is conducted with curiosity, a penchant for seeking patterns, and a desire to understand the truth behind phenomena.
Mathematics is done without fear of facing more questions and problems to solve.
Mathematicians, scientists, and practically everyone uses mathematics in their everyday life activities.
Mathematics is important for putting order in disorder, making better decisions, and helping to make the world a better place to live.
The lecture concludes by emphasizing the importance of mathematics in various aspects of life and its role in understanding and improving the world.
Transcripts
[Music]
good day everyone
my name is mahid mahmudaram from the
mathematics department
of the mindanao state university main
campus in marawi city
today we are going to discuss
mathematics in our world
we will start our lesson with a brief
discussion about the famous poem titled
the blind man and the elephant written
by john g
sachs this poem has a great analogy
with how we perceive mathematics
the poem is about six blind men who were
eager to learn what an elephant is
the first man who happened to stumble to
the side of the elephant
said that it is like a wall the second
who touched the tip of its tusk
said that the elephant is like a spear
when the third approached and happened
to take the trunk
he concluded that the elephant is like a
snake
the fort then reached out his hand and
touched the leg
and then said that the elephant is like
a tree
the fifth who by chance touched the ear
said that the elephant is like a fan
lastly the sixth blind man grabbed the
swinging tail
and said that the elephant is like a
rope
the six blind men continued to dispute
and though each was partly right all
were actually wrong
mathematics is a diverse discipline that
deals not only with arithmetic and
geometry
but also with data and measurement with
inference deduction and proof
and with mathematical models of natural
phenomena
of human behavior and of social systems
mathematics is like the elephant in the
poem
in the sense that depending on which
part of mathematics you study
you get a very different idea of what
mathematics is
because there are different aspects and
representations in mathematics
it is not difficult for students and
even teachers
to be so focused on a particular area in
mathematics
and failed to see the whole picture
the study of mathematics reveals hidden
patterns that help us
understand nature the world around us
and the universe in general in this
lecture
we will learn more about what
mathematics is
to help us understand the world of
mathematics
we need to first understand its meaning
mathematics is all about the
unbelievable patterns of numbers
formed by nature and by the universe it
is
all about language that is expressed in
different forms
including patterns shapes and music
among others in a sense mathematics is
all about what our eyes can see
what our ears can hear and even what we
can perceive
in our physical environment lastly
it is a language that we understand
aside from this british mathematician
and writer
ian nicola stewart defines mathematics
in his book
nature's numbers the unreal reality
of mathematical imagination as a formal
system of thought
for recognizing and exploiting patterns
combining these ideas led us to believe
that nature's patterns are not just
there to be admired
they are vital clues to the rules that
govern natural processes
here are some common notions associated
with mathematics
number one numbers and counting
people easily recognize mathematics
through numbers and operations
number two numeric and geometric
patterns
these refer to patterns observed from
geometric figures or from
a sequence of numbers and number 3
patterns of movement since moving bodies
that follow a certain pattern
can be represented mathematically
any person can recognize the beauty of
nature's mathematical patterns
even without any mathematical training
moreover in order to understand the
rules that govern
nature we may use mathematics to
recognize the clues of the patterns
observed in nature
mathematics is indeed everywhere if we
look close enough
we can see hints or clues of it in
nature
let us consider as an example the
ripples
formed when an object interacts with a
body of water
at rest these are composed of circles
with center fixed at a point
patterns of movements in water surface
in land formation and even in lightnings
and in trees we also see that there are
mathematical patterns
in the shapes and colors of animals
including their scales or
first
we also see mathematics in our daily
routine
at home some people are not even out of
bed
when encountering mathematics for
instance
when setting an alarm and hitting the
snooze button
they quickly calculate the new time they
will arise
we use mathematics in counting and
especially when buying simple things
like groceries or expensive ones like a
car
basic principles of mathematics are in
play
when making purchasing decisions that
require
cost and affordability of items
for students they use mathematics in
simple activities like
budgeting their allowance and making
schedules for studying
during exams
the use of mathematics is not only
limited
to the works of mathematicians and
mathematics educators
it can also be used in other professions
for example all teachers make use of
basic mathematics in preparing lessons
and computing grades
pilots and captains require some
knowledge
in computation algebra and even calculus
and statistics
in order to properly operate and
navigate
accountants economists and now even
factory workers need to understand basic
algebra and trigonometry to operate
complex manufacturing electronic
equipment
most people do not realize how
mathematics play
an important role in their life it is
very useful
in understanding various features of the
human body
its physical attributes and cellular
formations
also managing populations and likelihood
of different communities
involve a lot of mathematics
mathematics can also be seen in
different events
like in sports we also have mathematics
that helps in creating
arts music and dance it helps us
understand
past and present events so that we may
be able to predict possible outcomes
this is particularly important in
preventing calamities
mathematics is on the list of
underappreciated disciplines
by most people many are still unaware of
the need for every individual
to know and appreciate the roles of
mathematics
some of which are listed as follows
number one
to help us unravel the puzzles of nature
and to serve as a useful way to think
about nature
with the help of mathematics we have a
chance to understand the mysteries
surrounding nature
we are also able to make mathematical
representations of our oceans
forests the human body and the world
this is important in our attempt in
preserving them
and taking care of ourselves
number two with mathematics we are able
to make arrangements
and understand patterns of various
behaviors
this enables us to organize patterns
regularities
and irregularities number three by
examining previous occurrences
we are able to predict future outcomes
using various mathematical tools
number four meteorologists make use of
mathematical concepts
in studying the atmosphere in order to
understand
weather conditions and prevent disasters
mathematics also help provide effective
solutions
in controlling the widespread of
epidemics
number five everyone is aware that
mathematics is best known for
calculations
and number six mathematics provides new
questions to think about
especially when you conduct researches
when people are asked what mathematics
is all about
they usually say numbers symbols and
notations
which is partially correct second
people easily recognize mathematics when
looking at
expressions involving operations
mathematical equations
and functions third a few people with
adequate knowledge in mathematics
say that it is all about the study of
certain processes
and giving concrete representations to
concepts that are usually
abstract in form lastly mathematics is
all about
proving theorems principles and
mathematical laws
how mathematics is done number one
with curiosity the need to find answers
to questions
pushes mathematicians to dig deeper and
conduct more studies
number two with a penchant for seeking
patterns and generalities when
conducting a study
mathematicians seek patterns and combine
pieces of
information to make generalizations of
particular cases
number three one major factor for the
continuous development of mathematics
is the desire of individuals to know the
truth behind various phenomena
number four like in other sciences there
are times when mathematics requires
us to undergo numerous trials and
experience failure
before arriving at a successful end
number five mathematics is done without
fear of facing more questions
and more problems to solve
as to who uses mathematics first in the
list are mathematicians
mathematicians can actually be
classified according to whether they
study pure mathematics or
applied mathematics second mathematics
is being used by scientists
who are studying either natural sciences
or social sciences
and third practically everyone uses
mathematics in their
everyday life activities in conclusion
every individual uses different
mathematics
at different times for different
purposes
using different tools with different
attitudes
at this point we will cite some reasons
why mathematics is important to know
number one it puts order in disorder
with the help of mathematics we can
organize
well there are available methods in
mathematics that can be utilized in
assigning courses to teachers
arranging schedules deciding where to
build
hospitals finding strategic areas to put
cctvs
and more when faced with this array one
may look at mathematics
for possible solutions number two
it helps us become better persons
adequate knowledge in mathematics
may help make us better persons since it
can be used as a guide
in making better decisions in life
number three it helps make the world a
better place to live
in mathematics help explain everything
in nature
which in return help people build a
stronger relationship
with their surroundings
thank you very much for listening and i
hope you enjoyed watching
see you again for more discussions on
mathematics in our world
[Music]
[Applause]
[Music]
[Applause]
[Music]
you
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