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Archive for the ‘Applied mathematics’ Category

Equation terms

Standard deviation – The standard deviation is the measurement for how spread out your data is and is shown with a σ symbol

Null hypothesis – The idea that you are trying to prove wrong eg. That too much of your budget is going on coffee.

Alternative hypothesis – The idea that you are trying to prove right eg. The goverment is taking too much money from your budget. a cool random website I stumbled on along the way

More venn diagrams

Cartisan product – The two amounts of elements multiplied

Cardinality – How many elements in a set

Power set – All the combinations of a subset including 0

Trick for finding all the numbers in a venn diagram

If you know the combined eg. all three option put it in first

Venn diagram equations

∩ = And or Λ

υ = Or or V

– = not or ¬

Intersection – Where two circles connect and make another section

Union – All the numbers within the circles

Complement – The area outside of the circles but inside the box, specifically the numbers in this area

Disjoint – When the circles do not intersect

Power sets

If A = {1, {1}, {2}, 3}

The elements are each of the items within the outside brackets eg. 1, {1}, {2}, 3

The subset is the format of each item of a set eg. {1},{{1}}, {{2}}, {3}

Sets and relations


Any defined collection of items with something in common


A relationship is how items of a set relate to each other. Most often used to define a subset within a group

Language of sets

If the set has only a few members you can write all the elements between curly brackets eg. P = {Peter, John, Paul}

If there is a clear pattern you can use three eclipses (dots) eg. S = {2, 4, 6, 8…}

N = Natural numbers

W = Whole numbers

J = Intergers

Q = Rational numbers

R = Real numbers


Subsets are equal to their sets, so A=B and B=A

Odds and ratios

Number of out comes/Size of sample space (number of options)

eg. Rolling a dice

1/6 = Odds of getting any number

3/6 = Odds of getting either an odd or even number

Mutually exclusive – Independant events


If the dice is a complimentry of six…

The odds of getting 4 are 1/6 so the odds of not getting a 4 are 5/6

1/6 5/6 Both top numbers = the bottom number

Maths stats assignment

For the assignment I intend to use ravelry to find out how long people have been knitting and how long they have been members of ravelry also possibly their ages.

I could do this with or without a questionaire as the information is provided in profiles on the website, I will be asking for volunteers for it either way.

I have also thought about doing a knitting vs crochet questionaire but I’m not sure whether I will need to or not.

Truth tables and equations

Proposition – A declaration sentence that is either true or false

Compound proposition – A proposition which can be broken down into small propositions, eg.

If it is sunny outside then I walk to work; otherwise

I drive, and if it is raining then I carry my umbrella.

 This can be broken down into: Sunny outside, walk to work, drive to work, raining, carry umbrella.

Tautology – When a column in a truth table is completely true

Contradiction – When a column in a truth table is completely false

Contingency – When a column in a truth table is neither a tautology nor a contradition

These statements are both true

p Λ T = p (p and true = p)

p ν F = p (p or false = p)

Different meanings of some symbols

Λ = and = x

V = or = +

T = 1

F = 0

Predicate logic

Q = Relationship

Let Q(x,y) denote:

x = y + 3

In this equation the x is dependent, as in dependent on the the equation to exist, the y is independant, if any other part of the equation isn’t there it remains the same.

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