Mathematics -

Decision Making Theory - (Game Theory)

 Basis/Introduction

This short blog essay will outline the personal opinion and issues that I have experienced with Decision Making Theory (additionally Game Theory can be a sub-section).

Context 

 Decision Making Theory is based on a number of principles (see MIT Open Courseware), including Euclidean Space, the symbol Φ (Phi) and Θ (Theta). These symbols are known as Mathematical symbols in addition to being known in the Greek alphabet.

Additional Points

So; what does this all mean?

Well let us break this down.

Euclidean Space (See Wiki in Citations): This is a 3D shape which knows no bounds also according to topology (see citations), Euclidean space is in my perspective a type of formation between how space is stretched. Euclidean Space also has it's own symbol which looks like a flashy R or letter with a power to a certain number or a logarithm (as I imagine this is known).

Topology: Topology shows us that, when something is stretched, this is stretched with no damage "no tearing or gluing" according to Wikipedia. This is an on-going process and continues forever under this process. You could think of this as the Universe as the "stretch".

Phi: This comes in a capital form and a small form, they differ in meaning the large form means the "golden-ratio conjugate (-0.618....) in Mathematics".

The small letter (lower case) means "the golden ratio " according to Wikipedia.

Theta: Lower case means the "plane angle". Upper case means in set theory "a certain ordinal number".

There are many mathematical symbols if you search for the list in Wikipedia, they will show - they are increasingly informative and aid you in your further understanding and knowledge of Mathematics principles and advanced Mathematics - a useful must know for beginners to Mathematics.

Conclusion

I hope this has been informative and that this has been helpful, these outline the few things game theory is set to do, in my imagination Game theory can be applied to Decision Making Theory (which is also raised in the MIT article). 

Therefore Mathematics also can relate to gaming in some element, in my opinion in conclusive Decision Making Theory - I am no expert but I believe so.

 Hope this helped as an absolute beginner's guide to Decision Making Theory.

MIT March 18th 2003, Massachusetts, USA, accessed 19th December 2011 <http://ocw.mit.edu/courses/mathematics/> 

'Euclidean Space', wiki article, 14th December 2011, accessed 19th December 2011 <http://en.wikipedia.org/wiki/Euclidean_space>

'List of mathematical symbols, wiki article, 10th December 2011, accessed 19th December 2011 <http://en.wikipedia.org/wiki/Mathematical_symbols>

'Theta', wiki article, 13th December 2011, accessed 19th December 2011 <http://en.wikipedia.org/wiki/Theta>

 'Phi', wiki article, 23rd November 2011 accessed 19th December 2011 <http://en.wikipedia.org/wiki/Phi>

'Topology', wiki article, 10th December 2011 <http://en.wikipedia.org/wiki/Topology>

13 - 12x = 3x - 6                          ..... My Basic Equation

Line 1: -12x = 3x - 19

Line 2: -15x = -19

Line 3: x = -14

I don't know if this is correct - although I am sampling Algebra to work out, I did basic Maths at school - nothing complicated, would appreciate some feeedback. 

-12 = x/2 + 4           ....Another Basic Equation

Line 1: -16 = x/2

Line 2: -16 .2 = x/2 . 2

Line 3:  -32  = x

Line 4: -12 = -32/2 + 4

Line 5: -12 = -16 + 4

Line 6: -12 = -12 (True)

Please correct me if I did this wrong - I would appreciate it.

Binomial Distribution - Heads or Tails

P(X=0)- Probability that Heads will be shown 0 times. Signifying X.

P(TTTTTTT)= (1/2)PowerOf7 = 1/128

P(X=1) = Probability that Heads will be shown 1nce.

P(THTTTTT) = 7/128 (7 . 1/128)

T-Test for Mean (Analyze Sample Data)

t = x - μ / σ √n = t (n - 1).

 Conservation of Momentum 

 Before Impact  ------->          <-----------

                       3ms^-1                 5ms^-1      

                     

                       4kg - A                     6kg - B     

----------------------------------------------------------------

After Impact:

                                          ------------>

                                             v ms^1

In Principle:

4 x 3 - 6 x 5 = 10v

giving:    10v = -18

           v - -1.8

Sigma

How is Sigma used in Mathematics?

Sigma is a letter that corresponds to our letter S (in some way), it is a Greek letter too, also used in Mathematics, there is an upper case (capital) Sigma and a lower case (small) Sigma, they are and .

= Often refers to a sum, if you have a list of numbers, say a1=9, a2=7, a3=1 and a4=7....

then...

means 'standard deviation'. This is a measure of spread or variation, in a collection of numbers. For example if the 30 students in your class write a test and everyone gets inbetween 70 and 80 then the standard deviation of the 30 scores would be quite small. If, however, the scores range from the 40's to 90, the SD (Standard Deviation) would be higher).

μ - Mu

http://wiki.answers.com/Q/What_does_mu_mean_in_statistics

Mu is generally the symbol for the mean of a probability distribution, it is sometimes used as the average of a data set, also called the mean of the data set, although you can also use the term "x bar".

σ_{M - Standard Error of the Mean}

_{This symbolises (the symbol} σ_{M) - standard error of the mean, the first symbol and the second symbol, together, to break it down the first symbol is small letter of Greek (sigma) and the second is the large letter 'Mu', all Greek letters if you know Greek alphabet or have studied Science or Maths you may know this already.}