THE NATURE OF MATHEMATICS
Lesson 1
GEd 102 | GEDR | BSMA 1102
○ applies methods of proof both in
The Nature of Mathematics fashion that is conventional and
unventional
● Stewart, “Nature’s Number”
● study of patterns
○ mathematics is a formal system of
○ allow people to observe,
thought that was gradually developed in
hypothesize, experiment,
the human mind and evolved in the
discover, and recreate
human culture
● language
○ realize the existence of “form” in
○ collective thoughts dealing with
surroundings → a system of thought:
counting numbers→
understanding measures → gradually
■ (now) universal language
develop the science of measures and
dealing with symbols, arts,
gained the ability to count, gauge,
equations,geometric
assess, quantify, and size almost
shapes and patterns.
everything → notice and
● set of problem-solving tools
recognizerudiment hints about
○ answers to existing questions
patterns
○ presents solutions to occurring
○ concept of recognizing shapes made →
problems
classifying contour → using those
○ power to unveil the reasons
designs to build human culture:
behind occurrences & offers
civilization →
explanations
● natural world is embedded in a
● process of thinking
magnanimously mathematical realm of
○ involves reasoning, which can be
patterns
inductive or deductive
○ natural order efficiently utilizes all
mathematical patterns to its advantage
● made use of mathematics to understand the Mathematics is Everywhere
nature by ● daily tasks and activities
○ comprehending the structure of its ● important tool in the field of sciences,
underlying patterns and regularities humanities, literature, medicine, and even in
● Mathematics is present in everything we do music and art
○ building block of our daily activities ● rhythm of our daily activities
● operational in our communities
Mathematics is a Tool ● a default system of our culture
● useful, practical, and powerful. ● cook, shop wisely, read maps, use the
● forming new ways to see problems so we computer, budget
can understand them by combining insights ● cosmic perspective
with imagination ○ mystery can be decoded by
● perceive realities in different contexts seriously observing and studying
● sense to decipher patterns, relationships, their regularities →waiting for the
and logical connections signature of some kind interference
● new way to see and understand the modern ○ some exposed, some not easy to
world discern
● broad and deep discipline
○ deals with the logic of
■ shape The Essential Roles of Mathematics
■ quantity ● allows us to learn and understand the
■ arrangement natural order of the world
● powerful tool in decision-making ● often studied as a pure science but it also
● a way of life finds its place in other areas
Mathematics is a/an ● nothing visual, verbal, or aural come close
illus by Nocon and Nocon to matching the accuracy, economy, power
and elegance of mathematics
● art ● helps us to take the complex processes that
is naturally occuring in the world around us
1
THE NATURE OF MATHEMATICS
Lesson 1
GEd 102 | GEDR | BSMA 1102
○ represents them by utilizing logic ○ with a desire to know the truth
○ more organized and more efficient ○ with trial and error
● facilitate to & control-social, natural, ○ without fear of facing more
statistical, political, or medical questions and problems to solve
● physics, biology, & other sciences
● provides tools for calculations
● in learning and doing mathematics, there will
always be
○ new questions to answer Mathematics is for Everyone
○ new problems to solve ● good math provides utilization and
○ new things to think about usefulness in the order of things
● know the basics of the mathematical
The Mathematical Landscape operations in order to survive daily tasks
● human mind and culture developed a ● for the human society to survive and for the
conceptual landscape human species to persistently exist,
● region in mind → concepts of numbers, humanity needs, beyond rudiment of
symbols, equations, operations calculations, mathematics
abstractions, and proofs ● pure and applied
○ a number is not simply a ● mathematics puts order amidst disorder
mathematical tree of counting ● become better persons and helps make the
○ infinite variables can be world a better place to live in
encapsulate to finite
○ The wind in this landscape is The Importance of Knowing and Learning
unpredictable that the rate of change Mathematics
is known as calculus. ● rules and structures explain what is going on
● proofs, theorems, definitions, and axioms + ● beneficial in generating conclusions and in
reasoning, analytical, critical thinking + predicting events
mathematical logic = precise, exact and ● provide clues
powerful ○ human activities need clues for the
● the numbers in mathematics is not a "thing" human culture to meaningfully work
but a process ● Mathematical training
○ s comfortable on the “thingification” ○ vital to decipher the clues provided
of those processes and we forgot by nature
that 1+1 is not a noun but a verb. ● role of mathematics goes clues and it goes
beyond prediction
● understand how system works→ our goal is
How Mathematics is Done to control it to make it do what we want
● Math is a way of thinking
○ that thinking is going to be ● (Stewart) mathematics is a useful way to
developed rather than just merely think about nature (pattern)
see face value of the results ○ understand how they happen;
● For most, mathematics is just nothing but ○ why they happen
something to survive, rather than to learn. ○ which is different
● abstract and complex-a lot of people adopt ○ organize the underlying patterns and
the belief that they are not math people regularities in the most satisfying
● Mathematics builds upon itself way
○ complex concepts are built upon ○ predict how nature will behave
simpler concepts ○ control nature for our own ends
● the first thing to do is to identify the ○ make practical use of what we have
components or the operations that it wants learned about our world
you to carry out, and everything follows ○ Mathematics helps us to do all
● done with these things, and often, it is
○ curiosity indispensable
○ with a penchant for seeking patterns
and generalities
