MATH (LESSON 1 AND 2) Flashcards
a science or study of pattern and order
MATH
relies on logic
rather than on observation as its
standard of truth, yet employs
observation, simulation, and even
experimentation as means of
discovering truth.
MATH
MATH IN DAILY LIFE 5 (PMEPPFT)
PATTERNS, MEASUREMENT, ESTIMATION, RPOBLEM SOLVING, PROBABILITY, FRACTIONS, TIME
MATH IS FUNDAMENTAL TO THE (PBS,EIT,E,SS)
PHYSICAL AND BIOLOGICAL SCIENCES, ENGINEERING AND INFO TECH, ECONOMICS, SOCIAL SCIENCES
MATH IS A USEFUL WAY TO…
THINK ABOUT NATURE AND OUR WORLD
MATH IS A TOOL TO (Q,OCW,PP,MLE)
TO QUANTIFY
ORGANIZE AND CONTROL WORLD
PREDICT PHENOMENA
MAKE LIFE EASIER
4 ROLES OF MATH (HELPS OPCH)
ORGANIZE PATTERNS AND REGULARITIES IN OUR WORLD
PREDICT THE BEHAVIOR OF NATURE AND PHENOMENA IN THE WORLD
CONTROL NATURE AND OCCURRENCES IN THE WORLD FOR OUR OWN ENDS
HAS NUMEROUS APPLICATIONS IN THE WORLD MAKING IT INDISPENSABLE
VISIBLE REGULARITIES
PATTERNS IN NATURE
VITAL CLUES TO THE RULES
NATURE PATTERNS
REGULAR, REPEATED, RECURRING FORMS OR DESIGNS
PATTERN
EX OF PATTERN (FSWI)
FISH PATTERNS
STARS
WEATHER SEASON CYCLE
INTRICATE WAVES
ITALIAN MATHEMATICIAN THAT DISCOVERED A VERY SPECIAL SEQUENCE OF NUMBERS
LEONARDO FIBONACCI
FIBONACCI WHOLE NAME
LEONARDO PISANO BOGOLLO
HE LIVED FROM
1170 AND 1250 IN ITALY
FIBONACCI MEANS
SON OF BONACCI
HE ALSO HELPED SPREAD
HINDU-ARABIC NUMERALS
AN INTEGER IN THE INFINITE SEQUENCE
FIBONACCI NUMBER
FS WAS DISCOVERED AFTER AN
INVESTIGATION ON THE REPRODUCTION OF RABBITS
THE FS IS A RULE
TRUE!
FIRST TERM IS
0
RATIO BETWEEN 2 NUMBERS
GOLDEN RATIO
GOLDEN RATIO VALUE
1.618034
OTHER TERM FOR GOLDEN RATIO
GOLDEN:
SECTION
MEAN
NUMBER
PROPORTION
DIVINE:
PROPORTION
SECTION
EX OF GOLDEN RATIO
MONA LISA
NOTRE DAME CATHEDRAL
PARTHENON
RECITATION
TTTT
“Mathematics, as much
as music or any other art, is one of the means by which we rise to a complete self-consciousness.
The significance of mathematics resides precisely in the fact that it is an art: by informing us of
the nature of our own minds, it informs us of much that depends on our minds.”
John William Navin Sullivan, a famous science writer
“Father of Numbers,”
PHYTHAGORAS
means that which is learnt.” or “lesson”
MATHEMA
Mathema is derived
from
MANTHANO
MANTHANO MEANS
to learn
was especially useful during the
development of agriculture when surpluses in food
allowed trade.
RUDIMENTARY MATH
math exists objectively and independent of human thought.
REALISM
holds that mathematics is a
product of the human imagination and is carefully engineered to make formal statements about
nature in order to aid our understanding of the behavior of the universe.
anti-realism or idealism
the branch of
mathematics that are involved in the
study of the physical, biological, or
sociological world.
APPLIED MATH
driven by
abstract problems, rather than real world problems.
PURE MATH
6 THINGS ABOUT YOU AND MATH
Learning math is good for your brain.
Math helps you with your finances
Math helps us have better problem-solving skills.
Practically every career uses math in some way
Math is all around us and helps us understand the world better.
Math is a universal language.
indicates
that you can draw
an imaginary line
across an object and
the resulting parts
are mirror images
of each other.
Symmetry
3 TYPES OF SYMMETRY (BRS)
BILATERAL
RADIAL
SPHERICAL
indicates
that if you draw a
line across an object,
the left portion of
that object will be
the mirror reflection
of right portion.
BILATERAL
indicates
that if you rotate an
object by several
degrees you can still
achieve the same
appearance as the
original position
RADIAL
indicates that if you
cut a certain object
along its center it
will generate two
identical halves.
SPHERICAL
focuses on solving real-world problems in various fields, such as physics, biology, sociology, and engineering
APPLIED MATHEMATICS
need expertise in multiple areas of math and science, as well as collaboration and physical intuition
APPLIED MATHEMATICS
deals with abstract problems rather than concrete real-world issues. While some of these abstract problems may have their roots in practical matters, pure mathematicians delve deeper to explore technicalities and theoretical challenges
PURE MATHEMATICS
Pure and applied mathematics are not mutually exclusive;
they coexist and serve distinct purposes within the realm of mathematics
are focused on proving theorems, while applied mathematicians aim to construct theories that address practical problems
PURE MATHEMATICS
are considered the first kind of abstract numeral system
TALLYING SYSTEMS
is the oldest in the world
Babylonian number system
USE OF MATH IN OUR LIVES (BFPUUU)
- BRAIN HEALTH
- FINANCIAL MANAGEMENT
- PROBLEM-SOLVING
- UNIVERSAL CAREER RELEVANCE
- UNDERSTANDING THE WORLD
- UNIVERSAL LANGUAGE
the study of pattern and structure
MATHEMATICS
Many patterns and occurrences exists in ________, in our _______, in our ________
NATURE, WORLD, LIFE
are visible regularities of form found in the natural world and can also be seen in the universe.
PATTERNS IN NATURE
which are not just to be admired, they are vital clues to the rules that govern natural processes.
NATURE PATTERNS
- Regular
- Repeated
- Recurring forms or designs
- Identify relationships
- Find logical connections to form generalizations
PATTERN
EXAMPLES OF PATTERNS
EXAMPLES OF PATTTERNS:
1. Patterns can be observed even in stars which move in circles across the sky each day.
2. The weather season cycle each year. All snowflakes contains sixfold symmetry which no two are exactly the same.
3. Patterns can be seen in fish patterns like spotted trunkfish, spotted puffer, blue spotted stingray, spotted moral eel, coral grouper, redlion fish, yellow boxfish and angel fish. These animals and fish stripes and spots attest to mathematical regularities in biological growth and form.
4. Zebras, tigers, cats and snakes are covered in patterns of stripes; leopards and hyenas are covered in pattern of spots and giraffes are covered in pattern of blotches.
5. Natural pattems like the intricate waves across the oceans; sand dunes on deserts; formation of typhoon; water drop with ripple and others. These serves as clues to the rules that govern the flow of water, sand and air.
, a system of conventional spoken, manual (signed), or written symbols by means of which human beings, as members of a social group and participants in its culture, express themselves
LANGUAGE
may refer to a system of communication using symbols or sounds.
LANGUAGE
defined language as a set of sentences constructed using a finite set of elements.
Linguist Noam Chomsky
The language of mathematics makes it easy to express the kinds of thoughts that mathematicians like to express. It is:
- PRECISE: It can make very fine distinctions among set of symbols
- CONSISE: It can briefly express long sentences
- POWERFUL: It gives upon expressing complex thoughts
refer to numbers or values that are manipulated in a mathematical sentence.
MATHEMATICAL NOUNS
are symbols that show the relationship of at least two expressions.
MATHEMATICAL VERBS
are the basic mathematical operations.
Addition, subtraction, multiplication and division
the capacity of consciously making sense of things, applying logic, and
adapting or justifying practices, institutions, and beliefs based on new or existing information.
REASON
type of reasoning that forms a conclusion based on the examination of specific
examples is called
INDUCTIVE REASONING
examples. The conclusion formed by using inductive reasoning
is called a
CONJECTURE
It can only become a ________ once a
proof of the conjecture is established.
THEOREM
A ___________is a demonstration, or argument, that shows
beyond a shadow of a doubt that a given assertion is a logical consequence of our axioms and
definitions.
PROOF
_________________ (1564-1642) used
inductive reasoning to discover that the time required for a pendulum to complete one swing,
called the ________________________, depends on the length of the pendulum.
Galileo Galilei, period of the pendulum
A statement is a true statement if and only if it is true in all cases. If you can find one case
for which a statement is not true, called a _________________________, then the statement is a false
statement.
COUNTEREXAMPLE
____________ reasoning is
distinguished from inductive reasoning in that it is the process of reaching a conclusion by
applying general assumptions, procedures, or principles.
DEDUCTIVE
may be a system of words or codes used within a discipline.
LANGUAGE
POLYA’S FOUR-STEP PROBLEM-SOLVING STRATEGY
- UNDERSTAND THE PROBLEM
- DEVISE A PLAN
- CARRY OUT THE PLAN
- REVIEW THE SOLUTION
may refer to a system of communication using symbols or sounds.
LANGUAGE
There must be a ________________of words or symbols.
VOCABULARY
__________________must be attached to the words or symbols.
MEANING
A language employs _____________, which is a set of rules that outline how vocabulary is used
GRAMMAR
A ____________organizes symbols into linear structures or propositions.
SYNTAX
A ___________ or discourse consists of strings of syntactic proposition.
NARRATIVE
There must be (or have been) a group of people who use and understand the symbols.
There must be (or have been) a group of people who use and understand the symbols.
is a name given to some mathematical object of interest.
- A Number
- A Set
- A Function
( 1, 2, 3…, a, x, t, α, β, σ, A, B, C, etc.)
MATHEMATICAL EXPRESSION
analogue of an English sentence; it is a correct arrangement of Mathematical Symbols that states a complete thought.
MATHEMATICAL SENTENCE
