MATH 100/ MMW

patterns

the most fascinating things we observed in nature

measurement

to construct objects like houses and buildings

time

clocks, calendars, watches, are used to measure it

estimation

how many individuals are present at the events

money

the ability to manage money is crucial

geometry

shapes, lines, and angles in many living creatures

patterns and numbers:

patterns, measurements, time, estimation, money, geometry

symmetry

two sides are identical

fractals

are infinitely self-similar

trees-dendritic

have electrical discharges

spirals

it looks like spinning galaxies

chaos

topological mixing and dense periodic orbit

meanders

a sinuous bends in rivers or other channels

waves

move while carrying energy

dunes

wind movement over huge masses

bubbles/foam

it is feasible for the enclosed area

tessellation

it is repeating tiles on a flat surface

cracks

it is a linear apertus

spots and stripes

numerous animals have these

types of patters:

symmetry, fractals, trees-dendritic, spirals, chaos, meanders, waves and dunes, bubbles/foam, tessellation, cracks, spots and stripes

fibonacci sequence

1,1,2,3,5,8,13,21

constant

represent every single number

variable

represent any unknown number and makes use of letters

term

an expression preceded by an addition pr subtraction sign

open phrase

is a mathematical expression that maybe a number, a variable,

closed sentence

a mathematical sentence that is always true or false

language of sets

a set is a group of unique items collectively referred to as its elements

tabular method

it is done by listing or tabulating the elements of the set

set-builder method

it is done by stating or describing the common characteristics

two ways of describing a set:

tabular method, set-builder method

null set

a set that does not contain any element

singleton set

a set which contains only one element

finite set

a collection with a specific number or elements

infinite set

a set whose elements cannot be listed

cardinal number of a set

the number of distinct elements in a given set

equivalent sets

two sets A and B are said to be equivalent

equal sets

if two sets A and B have the same items

universal set

every other set that is formed has this set as its foundation

power set

it is necessary to comprehend what subsets are

sub set

a set is said to be a subset of another set

types of sets

null set, singleton set, finite set, finite set, infinite set, cardinal number of set, equivalent set, equal set, universal set, power set, sub set

proper subsets

is one that only comprises a small number of the original sets elements

improper subsets

includes all the original sets elements and the null set

types of subsets:

proper subset, improper subset

ordered pair represent as:

input, output

relation

relationship between two sets

domain

equal to all x values

domain

set of all possible input values

range

equal to all y values

range

set of all possible output values

function

relationship between two sets of data

composite function

is when one function is inside of another function

reasoning

thinking logically

inductive

starts w/ specific solutions and uses them to form a general conclusion

deductive

starts w/ general rules or accepted facts and applies them to a specific situation