GEC104 Video Lecture 1 Mathematics in our World Part 1

Summary

Mahid 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

00:00

📚 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.

05:01

🌿 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.

10:01

🔍 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.

Keywords

💡Mathematics

Mathematics is a field of study that involves the properties and relationships of numbers, quantities, shapes, and patterns. In the video, it is presented as a diverse discipline that extends beyond arithmetic and geometry to include data analysis, measurement, inference, and proof. The script uses the analogy of the blind men and the elephant to illustrate the multifaceted nature of mathematics, where each part represents a different aspect of the discipline.

💡Analogy

An analogy is a comparison between two things that are different in most respects but alike in some way, used to explain a concept or idea. The video uses the poem 'The Blind Men and the Elephant' as an analogy to explain how different people may perceive mathematics differently, depending on their exposure to its various branches.

💡Patterns

Patterns in the context of the video refer to the regularities and repetitions found in mathematics, nature, and the universe. They are vital clues to understanding the underlying rules of natural processes. The script mentions that mathematics is about recognizing and exploiting these patterns, such as the ripples in water or the branching patterns in trees.

💡Perception

Perception is the process of interpreting and organizing sensory information to give meaning to the environment. The video discusses how different people's perceptions of mathematics can vary widely, depending on which 'part' of the discipline they have encountered, similar to how each blind man perceived the elephant differently.

💡Natural Phenomena

Natural phenomena are observable events or facts that occur in the natural world and can be explained by natural laws. The script explains that mathematics helps in understanding these phenomena by revealing hidden patterns and providing a formal system of thought to recognize and exploit these patterns.

💡Inference

Inference is the process of deriving logical conclusions from premises known or assumed to be true. In mathematics, inference is used to deduce theorems and proofs, which is an essential part of the discipline as discussed in the video.

💡Proof

A proof in mathematics is a logical argument that establishes the truth of a statement or mathematical proposition. The video mentions proof as one of the integral components of mathematics, which helps in validating mathematical theorems and principles.

💡Mathematical Models

Mathematical models are abstract representations of real-world phenomena, used to understand and predict the behavior of these phenomena. The script refers to mathematical models as tools that help in representing natural phenomena, human behavior, and social systems.

💡Language

In the video, language is used metaphorically to describe mathematics as a means of expression that includes not only numbers but also patterns, shapes, and music. It emphasizes that mathematics is a universal language that can be 'spoken' and understood through various forms.

💡Unreal Reality

The term 'unreal reality' as used by Ian Stewart in his book 'Nature's Numbers' refers to the abstract nature of mathematical imagination. The video explains that mathematics, while seemingly detached from the physical world, is deeply connected to the reality of natural processes and patterns.

💡Daily Routine

Daily routine in the context of the video refers to the everyday activities where mathematics plays a role, often without people realizing it. Examples from the script include setting alarms, budgeting, making schedules, and even the patterns seen in nature, which are part of our daily experiences.

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]

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