GEC104 Video Lecture 1 - Mathematics in our World (Part 1)
Summary
TLDRIn this enlightening lecture, Mahid Mahmudaram from Mindanao State University explores the multifaceted nature of mathematics, drawing an analogy with the poem 'The Blind Men and the Elephant' to illustrate its diverse aspects. Mathematics is presented as a universal language of patterns, crucial for understanding nature, predicting phenomena, and solving everyday problems. The speaker emphasizes the importance of recognizing and appreciating the role of mathematics in various disciplines and daily life, highlighting its significance in shaping a better understanding of the world.
Takeaways
- 📚 Mathematics is a diverse discipline encompassing arithmetic, geometry, data, measurement, inference, deduction, proof, and mathematical models of natural phenomena and social systems.
- 🐘 The poem 'The Blind Men and the Elephant' illustrates the different perceptions of mathematics, emphasizing that focusing on a single aspect can lead to an incomplete understanding.
- 🔍 Mathematics reveals hidden patterns in nature and the universe, helping us understand the world around us through its various aspects and representations.
- 🎼 Mathematics is expressed in different forms, including numbers, patterns, shapes, and music, and is a language that we can perceive through our senses.
- 🌿 Nature's patterns are not just aesthetic; they are clues to the rules governing natural processes, as suggested by Ian Stewart in 'Nature's Numbers'.
- 🔢 Common notions of mathematics include numbers and counting, numeric and geometric patterns, and patterns of movement.
- 🏠 Mathematics is integral to daily life, from setting alarms to making purchasing decisions, and is used by everyone, not just mathematicians and educators.
- 🛫 Various professions, such as teaching, piloting, accounting, and economics, rely on mathematical knowledge for computation, navigation, and operation of complex systems.
- 🎭 Mathematics plays a role in arts, music, and dance, and helps us understand and predict past and present events, including in sports and preventing calamities.
- 🧩 Mathematics is underappreciated, with many unaware of its importance in unraveling nature's puzzles, understanding behaviors, predicting outcomes, and controlling the spread of epidemics.
- 🤔 The process of doing mathematics involves curiosity, seeking patterns, pursuing truth, enduring trials and failures, and embracing questions and problems.
Q & A
What is the main theme of the lecture given by Mahid Mahmudaram?
-The main theme of the lecture is to discuss the diverse nature of mathematics and its presence in our world, using the analogy of the poem 'The Blind Men and the Elephant' to illustrate how different aspects of mathematics can be perceived.
What is the analogy of 'The Blind Men and the Elephant' used to represent in the context of mathematics?
-The analogy represents how different people may perceive mathematics differently based on their exposure or focus, similar to how each blind man perceived the elephant differently based on the part they touched.
According to the lecture, what are the various aspects of mathematics that one might focus on?
-The various aspects include arithmetic, geometry, data and measurement, inference, deduction, proof, and mathematical models of natural phenomena, human behavior, and social systems.
How does the study of mathematics help us understand the world around us?
-The study of mathematics helps us reveal hidden patterns that aid in understanding nature, the world around us, and the universe in general.
What does Ian Nicola Stewart define mathematics as in his book 'Nature's Numbers'?
-Ian Nicola Stewart defines mathematics as a formal system of thought for recognizing and exploiting patterns.
What are some common notions associated with mathematics mentioned in the lecture?
-The common notions include numbers and counting, numeric and geometric patterns, and patterns of movement.
How is mathematics used in everyday life activities?
-Mathematics is used in everyday life activities such as setting alarms, budgeting, making schedules, and making purchasing decisions.
In what ways does mathematics play a role in various professions?
-Mathematics is used by teachers in preparing lessons and computing grades, by pilots and captains in computation and navigation, and by accountants, economists, and factory workers in operating complex equipment.
Why is mathematics considered underappreciated by many people?
-Mathematics is considered underappreciated because many people are not aware of the extent to which it plays a vital role in understanding nature, making predictions, and solving problems in various fields.
What are some of the roles of mathematics listed in the lecture?
-Some roles include unraveling the puzzles of nature, making arrangements and understanding patterns of behaviors, predicting future outcomes, helping in meteorology and epidemic control, and providing new questions for research.
How is mathematics done according to the lecture?
-Mathematics is done with curiosity, a penchant for seeking patterns and generalities, a desire to know the truth behind phenomena, and without fear of facing more questions and problems.
Who are the main users of mathematics as mentioned in the lecture?
-The main users of mathematics include mathematicians, scientists studying natural or social sciences, and practically everyone in their everyday life activities.
Why is mathematics important to know according to the lecture?
-Mathematics is important to know because it puts order in disorder, helps us become better persons by making better decisions, and helps make the world a better place to live by explaining everything in nature and building a stronger relationship with our surroundings.
Outlines
📚 Mathematics: Perception and Its Diverse Disciplines
In the first paragraph, Mahid Mahmudaram from the Mathematics Department at Mindanao State University introduces the topic of mathematics in our world. The analogy of the blind men and the elephant is used to illustrate the diverse nature of mathematics, which encompasses more than just arithmetic and geometry. It includes data, measurement, inference, and proof, as well as mathematical models of natural phenomena and human behavior. The paragraph emphasizes that the perception of mathematics can vary greatly depending on the area studied, and it encourages a broader understanding of the subject. The importance of recognizing patterns in nature and the universe is highlighted, as is the role of mathematics as a language expressed through numbers, shapes, and music.
🌿 Ubiquity of Mathematics in Nature and Daily Life
The second paragraph delves into the omnipresence of mathematics in nature, using ripples in water as an example of natural patterns that can be mathematically described. It extends this concept to land formations, lightning, and even the patterns found in trees and animals. The discussion then moves to the application of mathematics in everyday life, from setting alarms to making purchases, and its importance in various professions such as teaching, navigation, and manufacturing. The paragraph underscores the underappreciated role of mathematics in understanding the human body, managing populations, and predicting outcomes in sports and other events. It concludes by listing the roles of mathematics, including unraveling the mysteries of nature, understanding patterns of behavior, predicting future outcomes, and providing solutions to complex problems.
🔍 The Essence of Mathematics and Its Practical Applications
In the final paragraph, the script discusses common misconceptions about mathematics, focusing on its true essence as a tool for curiosity, pattern recognition, and truth-seeking. It outlines the process of doing mathematics, which involves curiosity, pattern-seeking, and a willingness to face challenges and questions. The paragraph identifies mathematicians, scientists, and everyday individuals as users of mathematics, each employing it for different purposes and with different tools. The importance of mathematics is reiterated through its ability to bring order to chaos, improve decision-making, and contribute to a better understanding of the world. The script concludes by emphasizing the significance of mathematics in making the world a better place and encouraging further discussions on the topic.
Mindmap
Keywords
💡Mathematics
💡Analogy
💡Patterns
💡Perception
💡Natural Phenomena
💡Language
💡Ian Stewart
💡Numeric and Geometric Patterns
💡Daily Routine
💡Professionals
💡Underappreciated
Highlights
The poem 'The Blind Man and the Elephant' serves as an analogy for how people perceive different aspects of mathematics.
Mathematics is a diverse discipline that deals not only with arithmetic and geometry, but also with data, measurement, and mathematical models of natural phenomena.
Mathematics is compared to the elephant in the poem, emphasizing that depending on which part of mathematics you study, you get a different idea of what it is.
The study of mathematics reveals hidden patterns that help us understand nature, the world around us, and the universe in general.
Mathematics is about recognizing and exploiting patterns, as defined by British mathematician Ian Stewart in his book 'Nature's Numbers'.
Common notions associated with mathematics include numbers and counting, numeric and geometric patterns, and patterns of movement.
Mathematics is present in our daily routines, such as setting an alarm, budgeting, and making purchasing decisions.
Different professions, including teaching, piloting, accounting, and factory work, require mathematical knowledge for effective performance.
Mathematics plays an important role in understanding the human body, managing populations, and predicting outcomes in various fields.
Mathematics helps in creating arts, music, and dance, and in understanding past and present events to predict future outcomes.
Meteorologists use mathematical concepts to study the atmosphere, understand weather conditions, and prevent disasters.
Mathematics is essential for unraveling the puzzles of nature and serves as a useful way to think about natural processes.
The continuous development of mathematics is driven by the desire to understand the truth behind various phenomena.
Mathematics can organize disorder, providing solutions for complex problems like scheduling and strategic planning.
Adequate knowledge of mathematics can help make better decisions in life and contribute to making the world a better place to live.
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 5 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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