khaled

Thanks for your replies, and one of the problems is "N = NP" Problem, which is related to Algorithms & Computer Science ... So, That's the closest thing to me as a Computer Science student ... you said "but not impossible that a relatively inexperienced mathematician could tackle them." Well I tackled some things on 4 of the problems ...

I am average at simple Calculus, simple Probability & Statistics, simple Geometry & Linear Algebra ... and I'm very good at Mathematical Logic, Discrete Tomography & Graph Theory, Algorithm I have two questions --"i know they sound silly", Q1: Am I good enough to try solving one of the Seven Millennium Prize Problems ? Q2: If I propose a Paper using a simple proof using the simple principles in mathematics, do I have to know everything about the complex systems built over the simple principles of mathematics ?

That is a Serious Flaw in your engine's Logic -- P ≠ P not to mention that -- P ≠ a ± b -- is a wrong statement P ≠ a ± b -- decomposed is P = a + b P = a - b which is conditionally true as following ... solution: b = 0 , -infinity < a < +infinity Let me help you with the basics: in a Simple equation with 2 unknowns, P = a + b P is called a Left-hand, which is considered as an Output a and b are unknowns ... So, if you want to make a system to check for all values in a range, you need to feed these values in range to the unknowns not the Left-hand ... and see the output of the left hand ... one more thing, the equation: P = a ± b is not one equation it's two composed equations ... P = a ± b --> ( (P1 = a + b) AND (P2 = a - b) AND (P1 = P2) ) good luck

you can consider Election Methods applied on a Group that gives back an Integer Set which outputs an Elected member, the Integer Set S = { S1, S2, S3, .., Sn } where Si = [1,n] represent election choices for n members of a Group ... and then a Frequency Test can be one way for Election, where Elected Member has Max Frequency in S, given example: group of 10 members made an election, S = { 3, 10, 6, 2, 2, 3, 7, 3, 1, 5 }, Elected = 3 Election is one important example in daily-life from Mathematics of Statistics ...

If the initial quantity is X and the new quantity is Y, then the ratio of difference between X and Y = ( Y / X ) * 100 % and the ratio of the advancement of Y over X = (Y - X)/X * 100 % so if X = 100, and Y = 150, Y:X = Y/X * 100 = 150/100 * 100 % = 1.5 * 100 = 150%, means Y is 150% of X (Y-X):X = (Y-X)/X * 100 = 50/100 * 100 % = 0.5 * 100 = 50%, means The Raise was 50% of the original Quantity

Ok, im specialized in Mathematical Logic and Computer Science .. but, I'll try to help ... Let me say what I understand from your thread: You have a program that periodically measure number of particles, And insert it into A series ... So, given period D, and Testing time T, we have series S where ... [latex]S = \{ \Phi_1, \Phi_2, \Phi_3, \dots \}[/latex] the program's algorithm should be like this: --------------------------------------------------------- SET: TYPE { INTEGER, INTEGER }, S = { EMPTY_SET } PROMPT: " ENTER TEST TIME, IN STEPS: " INPUT: T = KEYBOARD.INPUT ( ) INTEGER: t = 0 INTEGER: PHI = 0 +WHILE ( t < T ) +-- PHI = FUNCTION.GET_NUMBER_OF_PARTICLES ( ) +-- S.ADD ( { PHI, t } ) +-- t = t + 1 +WHILE_END PLOT.SET_VALUES ( S ) PLOT.X_AXIS ( 1 ) PLOT.Y_AXIS ( 2 ) PLOT.DO_PLOT ( ) PROGRAM.HALT ----------------------------------------------------------------- explanation of the algorithm: SET: TYPE { INTEGER, INTEGER }, S = { EMPTY_SET } here we define a set, where every element of the set is composed of two integers PHI = FUNCTION.GET_NUMBER_OF_PARTICLES ( ) you have to define the function that will return number of particles S.ADD ( { PHI, t } ) here we add { Number_Of_Particles, Time_Tag } as a new element to the Set S PLOT.SET_VALUES ( S ) give the set of Values to be plotted on a 2D plane PLOT.X_AXIS ( 1 ) tell the plotter that the first component of every element in the set is the X axis PLOT.Y_AXIS ( 2 ) tell the plotter that the second component of every element in the set is the Y axis PLOT.DO_PLOT ( ) ask the plotter to plots the values on the screen note: This algorithm is abstract, specifications are made at the coding level ... good luck,

What if his theorems were based on incompleteness ..?

I think (based on your initial post), equation: (mg - ma)/g = m(g/g) - m(a/g) = m - m(a/g) given: mg-ma = g-a, m = 1 OR 0 for m=0: m - m(a/g) = 0 for m=1: m - m(a/g) = 1 - (a/g)

possible, considering textual contexts and books as a space graph of alphabets .. and since letters come as words, we can consider words in a context as a vector spaces, where relative contexts are interpolated ...

Any ideas on good books on Mathematical Logic ?

Linear Systems are interesting when it comes to its applications ... however, is it true that not all formulas are transformable to linear system ..?

the 1st Dimension, is an infinite line, or a Circle, just like what mister ajb said ... Your statements are wrong if we take them together .. let me explain: 1. because in 2Dimenional, a plane can have a width & a height ... and if you go into 3Dimensional, a space can have width, height, and depth ! 2. in 1Dimensional, a Line can have a length, the line itself have width of Zero, given that the line when represented in 2Dimensional Plane is from negative infinity to positive infinity on the X-axis, but on a single value on the Y-axis (Assuming K) the width would be |K-K| = Zero true, in reality, there exist no other than 4Dimensional objects, consider time as the fourth, even the surface is still 3Dimensional, but mathematically it's taken as 2Dimensioanl as a consideration of an abstract plane ... My assertion to "in reality, there exist no other than 4Dimensional objects, consider time as the fourth" as following: 1. since Atoms is the primary component of everything, and since Atoms have a constant set of irregular movements -- then we can say that every object in reality is in constant movement at all times, and thus every object is 4D 2. since the stability of things is related to having an atom not separated from its contents -- then we cannot have a surface consisted of what is less than atoms, and since the atom -- have a spherical shape, it has width, height, and depth ... 3. moreover, even if we made a plate of electrons or so .. those parts also have width, -- height, and depth .. so the smallest possible stable thing to that would be an Atomic Plate ...

So, what books would be suggested for Mathematical Logic ..? anyone ...

1D is a line, 2D is a plane, 3D is an object ... and the 4th Dimension can be one of many things: - Time - Color - Direction - ... If you are interested in physics you can consider every point (x,y,z) as an Atom and the 4th dimension can consist many things related to Atoms in physics, The structure can be applied in computer program to study physics of Particles ... Also you can consider every point (x,y,z) as an Electron, and with giving the required constraints for quantum mechanics, you can work on quantum mechanics in visual ... Best of luck,

are there general courses in Mathematics related to Mathematical Logic .. so that I can look up courses that I can cross-attend in my university, also, we share the same building with mathematics\science college, so I can easily cross-attend ...

I think the fourth dimension is time, representation of a 3D object in the 4D space would be either by using an Animation, or by showing multiple copies of the object in 3D space where every copy has a Time tag,

I'm a bachelor-degree student, we studied Pre-Calculus, Calculus, Linear Algebra, Probability and Statistics, and Discrete Mathematics, I can't ask the mathematics department to get a course, and Yes, I'm asking for hints on a self-study on Mathematical Logic ...

I am a computer science student, interested in theoretical computer sciences ... I have improved myself in Algorithms, and had a basic course in Discrete Mathematics, My main interest lies in Mathematical Logic, and my question is What do I need to get in order to improve myself in Mathematical Logic ..?

i heared it's possible, given an expression, we can embed pi fraction 22/7, i know if you write (22/7)(double) in C it will return 3.14.. approximation but if you embed the fraction in a dynamic expression in a function, it will give more flexibility ... like this, first version:: given X: return (22/7) * (1/X) * 100,000,000 X=3 .. = 3.14159 / 3 = 1.04719666 * 100,000,000 .. = 104,719,666 2nd version:: given X: return 22/(7 * X) * 100,000,000 X=3 .. = 22 / 7*3 = 22/21 = 1.04761904 * 100,000,000 .. = 104,761,904 difference = 42,238 if this was a Money Transfer, 42,238$ is gone because of a miscalculation!

@hobz im not expecting less iterations, i am asking for a way to create a system for vectors, the space is in [math]\mathbb{R}^2[/math], can be then represented as a Matrix ... i want to learn more about how can vectors help me maintaining the matrix for example to do transformations, and renderring objects in the 2D display ...

I have learned LaTeX because in my college i have to write reports and papers in LaTeX, test: [math]|x| = \{ \begin{matrix} \color{red}{-X}&\color{red}{if X<0}\\ \color{blue}{X}&\color{blue}{if X>0}\\ \end{matrix}[/math]

i just imagined a truck with the following written on its side, Flying Hard-disk company ! ,lol

1. the screen consist of PIXELS 2. consider screen as a matrix of m x n where each element is a PIXEL 3. in RGB color system, each PIXEL have a value consist of three components ... Red+Green+Blue where each component have a value from 0 to 255 MATRIX screen of size m x n: | P1,1 P1,2 .... P1,n | | P2,1 P2,2 .... P2,n | | . ... . | | . ... . | | Pm,1 Pm,2 .... Pm,n | where, m x n = the screen resolution and 0 <= Px,y < 256 | algorithm (given x, y, c): | | 1. give the element Px,1 the value c | | 2. for every element from Px,2 to Px,y: Px,i = Px,i-1 +0.5 | | 3. terminate this method can create a linear gradient ... now with any help from linear algebra mathematicians, we can improve general methods, to iterate through this matrix, with more unique mapping ... .. waiting for replies, ideas, ...

what is the relation between the magnet we know [ N | W ] and the inner core of the earth, is it some kind of a special massive magnet, or it works with different mechanism ..?

i don't know but, files types have extension .xxx and its content start with a unique code [ CODE ... ]