MATM Flashcards
is the study of pattern and structure.
Mathematics
is fundamental to the physical and biological sciences, engineering and information technology, to economics and increasingly to the social sciences.
Mathematics
is a useful way to think about nature and our world.
Mathematics
is a tool to quantify, organize and control our world, predict phenomena and make life easier for us.
Mathematics
helps make sense of these patterns and occurrences.
MATHEMATICS
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
he lived between 1170 and 1250 in Italy.
●”Fibonacci” was his nickname, which roughly means “Son of Bonacci”.
Leonardo Pisano Bogollo
is an integer in the infinite sequence 1, 1, 2, 3, 5, 8, 13, … of which the first two terms are 1 and 1 and each succeeding…
Fibonacci number
●It displays unique mathematical properties that make it useful in fields as diverse as astronomy (distances between planets and the sun, and the shape of galactic spirals), botany (growth patterns of plants and trees), and financial markets (price movements of securities).
Fibonacci number
was discovered after an investigation on the reproduction of rabbits
Fibonacci sequence
can be written as a “Rule“
●First, the terms are numbered from 0 onwards like this:
Fibonacci Sequence
can be expresses as the ratio between two numbers
Golden ratio
a/b= a+b/a
golden ratio
is also sometimes called the golden section, golden mean, golden number, divine proportion, divine section and golden proportion.
Golden Ratio
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
ones used for counting
cardinal numbers
ones used for telling positions
ordinal numbers
used only as a name to identify something
nominal numbers
in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. _______ are one of the most fundamental concepts in mathematics
set
a well-defined collection of distinct objects.
set
(true or false)
The objects of a set are separated by commas.
true
true or false
• The objects that belong in a set are the elements, or members of
the set.
true
t or f
• It can be represented by listing its element between braces. • A set is said to be well - defined if the elements in a set are
specifically listed.
true
serves as a set of rules that govern the structure and presentation of mathematical proofs. It allows us to determine the validity of arguments in and out of mathematics.
logic
a statement that is, by itself, either true or false. They can be expressed in symbols P, Q, R, or p, q, r.
proposition
means single idea statement
Simple
conveys two or more ideas
Compound
a declarative sentence (that is, a sentence that declares a fact) that
is either true or false, but not both.
proposition
for all” or “for every
Universal Quantifier
is a statement requiring a solution, usually by means of mathematical operation / geometric construction
problem
means the ways or techniques use to get answer which will usually involved one ormore problem solving strategies
method
is a process an ongoing activity in which take what we know to discover what we don’t know
problem solving
is a true statement provided that is true in all cases
statement
statement is not true
counterexample
is a process of reaching a conclusion by applying general; assumptions procedures, or principles
deductive reasoning
the reason or reasons offered for or against something
argument
Minor or major propositions or assertions that serve as the bases for an argument. It can be an assumption, law, rule, idea, or observation.
PREMISES
An argument composed of two statements or premises followed by a conclusion.
SYLLOGISM
The last step in a reasoning process
CONCLUSION
Named after George Polya (1887-1985). It is a four-step problem solving strategy that are deceptively simple.
POLYA’S STRATEGY
