Chapter 1 Flashcards
Math Foundations
What is math considered?
independent scientific discipline:
-analysis of geometric shapes & arithmetic of numbers
-analysis of certain conditions, characteristics and patterns
What are the two types of math?
-pure math
-applied math
What is pure math?
-focus on abstract, theoretical concepts, no practical applications
What is applied math?
-application of math in physics, medicine, computer science and economics
What is the math called used in economics?
business math
What are the different subfields in business math
-functions theory
-differential calculus
-optimization
-financial math
How are numbers used in business math?
to quantify their economic quantities and relationships
What are the sets of numbers
-real numbers
-natural numbers
-integers
-rational numbers
-irrational numbers
What is a natural number?
sign N:
from 0, 1, 2, 3 - etc.
What is an integer?
sign Z:
numbers with minus sign -3, -2, 1, 0,
What is a rational number
sign Q:
fractions, decimals, with negative
-2/3, -0.45, 1/2
What is a finite and infinite number in rational numbers?
finite: 2.4
infinite number: 1/3 = 3.33333333333
What is a real number
sign: R
all numbers in the number line
What is an irrational
sign Q:
infinite number of decimal places, that cannot be represented as fraction
What is algebra?
symbolic calculation, using letters as placeholders for real numbers
What are the basic rules of algebra
-commutative law of addition & multiplication
-associative law of addition and multiplication
-distributive law
What are summands
two numbers added together
what are factors
two real numbers
What is factoring?
multiplication of summands with a common factor
e.g.
2(3+4) = 23 + 2*4
What happens if the denominator is zero?
not defined
What do you call a real number “a” multiplied “n” times?
nth power of a
a- base
n- exponent
What is a^0? e.g. 10^0?
1
What is a^1 e.g. 23^1
a e.g. 23
What numbers can only be used for logarithms?
Real and positive numbers
What numbers can be used for natural logarithms
Natural numbers
What symbol is used as a summation sign
Sigma sign
What is are the numbers below the summation sign
lower summation limit or summation or running index
all natural numbers
What do you call above the summation sign
upper summation limit
it should be greater than or equal 2
What kinds of numbers are on the side of the summation sign
Real numbers
What symbol is used to denote multiplication
PI
What are parameters?
symbols that stand for freely selectable e.g.: a, b or c
What are constants?
have a single fixed numerical value
e.g.: pi or e
What are variables?
unspecified numbers but can be defined through application, they can change
e.g. x, y or z
What is a domain?
range of numbers that indicate the values of a variable
symbol: D
What is a term or expression?
numbers, parameters, constants, variables linked together by mathematical operations
x+y (a+b)^2
What is an equation?
if left side is equal to right- true statement or satisfied equation
Otherwise, false
What is a linear equation?
equation with 1 variable with 2 parameters
e.g. ax+b
a cannot equal 0
What is a nonlinear equation and give examples
equations that cannot be transformed to linear equations
e.g.: quadratic equations and cubic equations
What are inequalities
the relations of parameters are stated
e.g. smaller, larger, equal to
What does this symbol <=> mean ?
transformation has not change the value of equation, because operation was performed on both sides
What is this symbol II called?
penultimate line
What is a quadratic equation
ax^2+bx+c
b, c or both can be zero
A solution in the quadratic formula can only exist if:
b^2-4ac is greater than or equal 0
What is the rule of transitivity?
If a <b & b<c
Then a<c
What is a set?
A group of elements
symbol: S
e.g. set of natural numbers:
N={1,2,3,4….}
What does … mean in a set?
elements are not complete
What is the symbol that an element is part of a set ?
∈
What is the symbol for subsets?
⊂
What is a subset?
if a certain set also belongs to another set
e.g. Natural numbers is a subset of integers: N ⊂ Z
What is a union?
displays all elements that belong to a set
e.g.: A ∪ B = {1,2,3,4,5}
If A={1,2,3) and B={4,5}
What is an intersection and what is its symbol?
shows all elements belonging to 2 sets
e.g.
If A ={1,2,3} & B={3,4,5}
then A ∩ B = {3} (a intersect b)
What is a difference?
shows elements that belong to a set but not another.
e.g.
If A={1,2,3,} & B={3,4,5}
A \ B= {1,2}
What does percentage mean?
out of 100
What does percentage sign mean
that a number is divided by 100
What is the percentage formula
W=G*p%
