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PRE-LIM_MMW Flashcards

1
Q

The study of the relationships among numbers, quantities, and shapes.

A

Mathematics

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2
Q

Study of Math Types

A

arithmetic
algebra,
trigonometry
geometry
statistics
calculus

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3
Q

are visible regularities
found in the natural world.

A

Patterns in Nature

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4
Q

Natural Patterns

A

spirals,
symmetries
mosaics
stripes
spots

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5
Q

explains the pattern through music.

A

Plato

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6
Q

explains the pattern through
geometry.

A

Phythagoras

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7
Q

explains the nature through the
nature of God.

A

Empedocles

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8
Q

Greek Philosophers Studied Patterns

A

Plato
Pythagoras
Empedocles

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9
Q

Other scientist Studied Patterns

A

Joseph Plateau
Ernst Haeckel
D’Arcy Thompson
Alan Turing
Aristed Lindenmayer
Benoit Mandelbrot

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10
Q

Belgian physicist in the 19th
century, who formulated the concept of minimal surface through soap films.

A

Joseph Plateau

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11
Q

a German biologist and artist
who painted hundreds of marine organisms to
emphasize symmetry.

A

Ernst Haeckel

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12
Q

a Scottish biologist who
pioneered the study of growth patterns in both
animals and plants that shows simple equations
could explain spiral growth.

A

D’ Arcy Thompson

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13
Q

a British mathematician in the
20th century who predicted mechanisms of
morphogenesis that give rise to patterns of spots
and stripes.

A

Alan Turing

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14
Q

a Hungarian theoretical
biologist and botanist at the University of Utrecht. Used L-systems to describe the behaviors of plant cells and to model the growth
processes of plant development

A

Aristed Lindenmayer

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15
Q

a Polish-born French-American mathematician and polymath with broad interests in the practical sciences. He labeled “the act of roughness” of physical phenomena and “the uncontrolled element in
life”

A

Benoit Mandelbrot

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16
Q

were the ones who showed how the
mathematics of fractals could create
growth patterns

A

Lindenmayer and Mandelbrot

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17
Q

a never-ending pattern. It is an
infinitely complex pattern that is self-similar across different scales

A

Fractals

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18
Q

adopts eight patterns in
landscape namely scattered, fractured, mosaic,
Naturalistic drift, serpentine, spiral, radial, and
dendritic. Occurs commonly in plants, animals,
rock formations, river flow, stars, and in human
creations.

A

W. Gary Smith

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19
Q

W. Gary Smith 8 patterns

A

scattered
fractured
mosaic,
Naturalistic drift
serpentine
spiral
radial
dendritic

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20
Q

“Fibonacci” means

A

Son of bonacci

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21
Q

Father of Fibonacci sequence. Lived between 1170 and 1250 in Italy.

A

Leonardo Pisano Bogollo

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22
Q

Fibonacci Day

A

November 23

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23
Q

Fibonacci numbers are very close to
Golden Ratio, which is referred to
and represented as phi (ϕ) which is
approximately equal to

A

1.618034.

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24
Q

a logarithmic spiral whose
growth factor is ϕ, the golden ratio.

A

Golden Spiral

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25
Q

a set of numbers or objects in
which all the members are related with each other by a specific rule.

A

Pattern

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26
Q

constitutes between two sets: a
collection of ordered pairs containing one object from each set.

A

Relation

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27
Q

Types of Function

A
  1. One to One - a function.
  2. One to Many - not a function.
  3. Many to One - a function.
  4. Many to Many - not a function.
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28
Q

a type of relation. A relation is
allowed to have the object x in the first set to be related to more than one subject in the second set.

A

Function

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29
Q

a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites,
or generators)

A

Voronoi diagrams

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30
Q

Voronoi diagrams were considered as early as 1644 by philosopher

A

René Descartes

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31
Q

defined and studied the general n-dimensional case in 1908. This type of
diagram is created by scattering points at random on a Euclidean plane

A

Georgy Voronoi

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32
Q

is an attribute of a shape or
relation; the exact reflection of form on opposite sides of a dividing line or plane.

A

Regularities

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33
Q

a period of time it
takes to swing back to its original position is
related to its length, but the relationship is
not linear

A

Motion of Pendulum

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34
Q

an image that is exactly the same size as the object and is far behind the mirror as the object is distant from the mirror.

A

Reflection in the Mirror Plane

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35
Q

any object that is
moving and being acted upon only be the force of gravity is said to be in state of free fall.

A

Free Falling Object

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36
Q

a pair of forces acting on
the two interacting objects.

A

Action-Reaction pair

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37
Q

Three examples of “Simplicity emerging from complexity”

A

Drops, Dynamics, and Daisies

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38
Q

The role of mathematics is to describe symmetry-breaking processes in order to explain in a unified way the fact that the patterns seen in San dunes and zebra’s stripes are caused by processes which, while physically different, are mathematically very similar.

A

Patterns in Nature

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39
Q

Mathematics solves puzzles in nature (such as why planets move in the way that they do), describes changing quantities via calculus, modelling change (such as the evolution of the eye), and predicts and controls physical systems.

A

Puzzles in Nature

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40
Q

Nurses routinely use addition, fractions,
ratios and algebraic equations each
workday to deliver the right amount of
medication to their patients or monitor
changes in their health.

A

Mathematics in Medicine

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41
Q

Political Scientists use mathematics
(statistics) to predict the behavior of group of people.

A

Mathematics in Political Science

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42
Q

Analysis and study in economics help
explain the interdependent relation
between different variables. Economists try to explain what causes rise in prices or unemployment or inflation.

A

Mathematics in Economics

43
Q

Mathematics has enabled farming to be more
economically efficient and has increased productivity.

A

Mathematics in Farming and
Gardening

44
Q
  • Calculating prick per unit
  • Figuring percentage discounts
  • Comparing unit and bulk price of items
  • Estimating total price
  • Etc.
A

Mathematics in Planning a Market
and Grocery Shopping

45
Q
  • Plant pots in the inner garden and even
    restroom fixtures
  • Measuring ingredients
  • Calculating cooking time
  • Making ratios and proportions in baking
A

Mathematics Anywhere in the House

46
Q
  • Fuel required based on distance
  • Total expenses for toll fees
  • Tire pressure check
  • Time allowance to the trip
  • Short-cut routes alternatives
  • Road map reading
  • Speed limits and others
A

Mathematics in Travels

47
Q
  • Making accurate measurements of lengths,
    widths, and angles
  • Projecting detailed material estimate
  • Getting the best value of valuable
    resources
A

Mathematics in Construction

48
Q

It combines mathematical theory, practical engineering and scientific computing to address the fast-changing technology.

A

Mathematics in Engineering

49
Q

Individuals with poor math fundamentals typically make greater financial mistakes like underestimating how quickly interest
accumulates.

A

Mathematics in Investment

50
Q

In a swift changing world, creating and following schedule prove beneficial, but it takes more mathematical skills than
simply using a clock and calendar to
manage time well and be on top of
others

A

Mathematics in Time

51
Q
  • is the system of words, signs and symbols which people use to express ideas, thoughts and feelings.
    -consists of the words, their pronunciation and the methods of combining them to be understood by a community.
    -is a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures or marks having understood meanings
A

Language

52
Q

It is part of the English language used for making formal mathematical statements, specifically to communicate definitions, theorems, proofs and examples.

A

Mathematical English

53
Q

is a special-purpose language. It has its own symbols and rules of grammar that are quite different from those of English.

A

Symbolic Language

54
Q

A complete statement that stands alone as a sentence

A

Symbolic Assertions

54
Q

A symbolic assertion without variables. It is either true or false.

A

Symbolic Statements

55
Q

A symbolic expression that refers to some mathematical object.

A

Symbolic Terms

56
Q

3 Types of symbolic Expressions

A

Symbolic Assertion
Symbolic Statements
Symbolic Terms

57
Q

It is a collection of some rules which gives the procedures to perform first in order to evaluate a given mathematical expressions.

A

Order of operation

58
Q

-is the system used to communicate mathematical ideas.
-has its own grammar, syntax, vocabulary, word order, synonyms, conventions, idioms, abbreviations, sentence structure and paragraph structure.
-also includes a large component of logic. The ordinary language which gradually expands to comprise symbolisms and logic leads to learning of mathematics and its useful application to problem situations.

A

Mathematical Language

59
Q

Four main actions attributed to problem-solving and reasoning

A

Modelling and Formulating
Transforming and manipulating
Inferring
Communicating

60
Q

Creating appropriate representations and relationships to mathematize the original problem.

A

Modelling and Formulating

61
Q

Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions.

A

Transforming and manipulating

62
Q

Applying derived results to the original problem situation, and interpreting and generalizing the results in that light.

A

Inferring

63
Q

Reporting what has been learned about a problem to a specified audience.

A

Communicating

64
Q

is a major contributor to overall comprehension in many content areas, including mathematics.

A

Vocabulary Understanding

65
Q

consist of terms. The terms is separated from other terms with either plus or minus signs. A single term may contain an expression in parentheses or other grouping symbols.

A

Mathematical Expressions

66
Q

Types of Mathematical Expressions

A

Monomial
Binomial
Trinomial
Polynomial

67
Q

State whether the equation is true or false for the given value of the variable.

A

Open sentence

67
Q

is a technique used by mathematicians, engineers, scientists in which each particular symbol has particular meaning.

A

Convention

68
Q

refers to the particular topics being studied, and it is important to understand the ________ to understand mathematical symbols.

A

Context

69
Q

Is a well defined collection of distinct objects

A

Set

70
Q

The objects that make up a set is called

A

Elements

71
Q

The elements in the given set are listed or enumerated, separated by a comma, inside a pair of braces

A

Roster/Tabular

72
Q

The common characteristics of the elements are defined. This method uses set builder notation where x is used to represent any element of the given set.

A

Rule/Descriptive

73
Q

has no element and is denoted by ∅ by a pair of braces with no element inside, i.e. {}

A

Empty/Null/Void Set

73
Q

has countable number of elements, i.e. A = {1, 2, 3, 4, 5}

A

Finite Set

74
Q

has uncountable number of elements, A = {…, -3, -2, -1, 0, …}

A

Infinite Set

75
Q

is the totality of all the elements of the sets under consideration, denoted by U, i.e. U = {…-2, -1, 0, 1, 2,…}

A

Universal Set

75
Q

is a set whose elements are found in A and B or in both. In symbol: 𝐴∪𝐵={𝑥/𝑥 ∈𝐴 𝑜𝑟 𝑥 ∈𝐵}.

A

Union of Sets A and B

75
Q

have been the same elements

A

Equal Sets

76
Q

have the same number of elements

A

Equivalent Sets

77
Q

have at least one common element

A

Joint Sets

78
Q

have no common element

A

Disjoint Sets

79
Q

A friendly reminder na you’re doing your best, Kyle. Just keep up, and continue to pursue your dreams! Aim High!

A

Trust God for all of your plans

80
Q

is a set every element of which can be found on a bigger set. The symbol ⊂ means “a subset of” while ⊄ means “not a subset of”.

A

Subset

81
Q

the set containing all the subsets of the given set with n number of elements.

A

Power Set

81
Q

if the first set equals the second set.

A

Improper Subset (⊆)

82
Q

other than the set itself and the null set, all are considered ___________.

A

Proper Subset (⊂)

83
Q

is a set whose elements are common to both sets. In symbol: 𝐴∩𝐵={𝑥/𝑥” “∈𝐴 𝑎𝑛𝑑 𝑥 ∈𝐵}”. “

A

Intersection of Sets A and B

84
Q

is a set whose elements are found in set A but not in set B. In symbol: 𝐴−𝐵= {𝑥/𝑥∈𝐴 𝑎𝑛𝑑 𝑥∉𝐵}”. “

A

Difference of Sets A and B

85
Q

is a set whose elements are found in the universal set but not in set A. In symbol

A

Complement of Set A

86
Q

The universal set is usually represented by a rectangle while circles with the rectangle usually represent it ___________.

A

Subset

86
Q

(4 August 1834 – 4 April 1923) - an English Logician an Philosopher

A

John Venn

87
Q

The pictorial representation of relationship and operations of set is the so-called

A

Venn-Euler Diagrams or simply Venn Diagrams

88
Q

The ______________ is usually represented by a rectangle while circles with the rectangle usually represent it subsets.

A

Universal Set

89
Q

(15 April 1707– 18 September 1783) – was a Swiss mathematician, physicist, astronomer, logician, and engineer.

A

Leonhard Euler

90
Q

-are mathematical entities that give unique outputs to particular inputs.
-consists of argument (input to a function), value (output), domain (set of all permitted inputs to given function) and codomain (set of permissible outputs).

A

Function

91
Q

is a set of inputs and outputs, oftentimes expressed as ordered pairs (input, output)

A

relation

92
Q

means consisting of two parts. In mathematics, _________ means that it belongs to a number system with base 2 and not base 10. A ________ is made up of 0’s and 1’s.

A

Binary

92
Q

is a single binary digit.

A

bit

93
Q

is a rule of combining two values to produce a new value.

A

Binary Operation

94
Q

is the science of formal principles of reasoning or correct inference. It is the study of principles and methods used to distinguish valid arguments from those that are not valid.

A

Logic

95
Q

is the study of reasoning in mathematics.

A

Mathematical Logic

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