khaled

well, first .. I asked for the order of mathematical topics\courses, not books, in order to reach a level to understand Quantum Theory ... besides, I don't know how I'm going to jump from specific types of calculus into Analysis on Manifolds, not even knowing Numerical\Functional analysis ... I need something general, if I can simplify it in a phrase "I want to learn everything in mathematics, what is the path" ...

So, in this case, you are not doing a Tree Search, you are doing a Local Optimization over a Function [math]f(P) = \; how \; optimal \; is \; program \; P[/math] I'd call it Local Random Genetic Optimization, but you might get stuck in loops, with no use of history .. the other solution around is to provide an incremental progressive algorithm, or else just stay with the random mutations .. and make some constraints to guide it, good luck

"time is considered a dimension, the time-flow is constant .. but what is different is how different objects realize time" -- my speculations So, I think that using a clock to organize our works, is based on using the time-flow of the clock machinery asynchronously ... in NLP (Neural Language Programming), there is a complex techniques to experience slow realization of time-flow for short amount of time, which, as theory says, can be utilized between time & time, to do some things, such as avoid a bullet, taking a critical escape path, accelerate an indirect punch

[math]Eph = \frac{hc}{\lambda}[/math] [math]\frac{Eph \lambda}{Eph} = \frac{hc \lambda}{Eph \lambda}[/math] [math]\lambda = \frac{hc}{Eph}[/math]

So, [math] \int_0^t (\gamma^{1/\kappa}-i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds = \int_0^t (\gamma^{1/\kappa}-(i\zeta{w}(1-t/s)_+^{H} \times i\zeta{w}(1-t/s)_+^{-1/2}))^{\kappa}ds [/math] [math] = \int_0^t (\frac{\sqrt[\kappa]{\gamma} - (i\zeta{w}(1-t/s)_+^{H}}{\sqrt{i\zeta{w}(1-t/s)_+})})^{\kappa} ds [/math]

Let's talk about limits and bounds, Program size = m Bytes, Max Program size = 200 Bytes Max Expansion size = Max(m) x Max Elements = 200 x 1000 = 200,000 Bytes ~ 195.3 KB If you keep all data, without removing past states, your space complexity becomes exponential and your search continue only for 100 steps only ... So, if you keep all data, for R runs, Total Size = [math]\sum_{i = 0}^{R}{d^i} = \sum_{i = 0}^{100}{{(195.3)}^{i}} = 1.1 E 220 TB[/math] -- which is a tremendous space if you keep only a branch of the tree, Total Size = [math]d \times R = 195.3 \times 100 = 19 MB[/math] -- reasonable Advice: try to minimize Expansion Size, Increase Max number of steps, -- Consider Progressive Merge and Semi-Random Mutation, that way your search covers a wide area of possibilities, and it allows random progression limited by general direction good luck

So, simply you are working on Genetic Programming, so what is the search you are using ? .. ex: Simulated Annealing and this search is to optimize a Program, where a Program is a set of Instructions, an Instruction is an unsigned 8-bit Integer Number of Instruction types = 2^8 = 256 Program [math]P = \{ I_1, I_2 .., I_m \}[/math] where [math]m = ?[/math] So, what is the value of m, is it static, dynamic, or a range of values ? -- is your search linear, exponential, local, or guided ? -- what is the size of your buffer, queue, list .. in terms of Max Number of Programs ? -- do you keep previously processed states (Programs) ? .. so that you don't go over the same one once again, & don't get stuck in loops -- how did you define SELECTION, MERGE, and MUTATION functions, in terms of algorithm ? good luck

The sheet contains information about celestial horoscopes, such as Aries, Taurus, Gemini, ..etc this sounds weird, so they knew how to calculate angles for the zodiac system Also, about how ancients calculated sin(90), and zero was invented by indian scientist .. I think if you think about it, Greek have their representation of numbers .. I = 1, V = 5, & X = 10 .. so, sin(90) in greek is simply sin(XXXXXXXXX) = I .. also, I think they have a symbol for zero (nothing), and based on how they represent the numbers, I think zero in greek is simply a gap .. 0 = __, 1 = I, 2 = II, 3 = III, ..etc

I'm computer science researcher, but I'm not really good at math, that I want to improve myself, I studied: Basic Calculus, Basic Geometry, Discrete Mathematics, Basic Linear Algebra, Basic Probability & Statistics I know how to get math courses, but in what order should I go .. I want to know the path where I can then understand Quantum, Super mathematics, ..etc best regards, khaled

I'm a computer scientist, so I'd say Logic, Discrete Mathematics, Analysis, Model Theory, Number Theory, Algorithms, with some interest in Geometry, and Quantum Theory ... To me, while I was still a bachelor student in computer science, which was five years, and since the second year, I have started to write researches in Logic, Algorithms, and Model Theory .. I was in the third year, I had no idea about scientific scholarships and researchers around the world meeting in conferences .. I wrote tens of papers, most were no good, but considered a start of realizing that I need to be good in the field to start writing researches .. and that I need to meet specialized people to help me in, In my senior year, I published a paper, with not much notations, about one of my attempts to do Randomness Generation ...

I've read that: some Lie Algebra can be with no outer derivation, and considered unsolvable .. I wish you don't ask me any details, I'm not good in math

well Alex Wilkie worked in Model theory and First-order logic, but I'm more interested in Artificial Intelligence and Algorithms, thus, I'd say Godel .. although Godel said "A formal system can not prove all true statements." based on his Incompleteness theory, I agree with him, but I'm still not good enough in mathematics that I currently have a bachelor degree, I need to learn more to be able to work on a research I started long time ago for a new type of logic, one that does not seem logical !

My list is different, because I'm in Computer Sciences and Logic ... My list contains: Thales, Aristotle, Euclid, Pythagoras, Al-Khawarizmi, Al-Kindi, Euler, Hamiliaton, Sigmund Freud, Einstein, Turing, Godel, Post ...

I'm not really good in mathematics .. but, differentiation and integration, sounds like cracking and collecting, to me it seem more like degrade and upgrade to a function f(x) ...

I am from middle east, studying mathematics was not good part of my high-school experience, although I worked out a mathematical model called the love formula, and published it as a small software in VB 6 .. anyway, I'd like to ask for an advice on a good place to get free online courses on mathematics, and algorithms ...

first, isn't [math]i = \sqrt{-1}[/math] ? and speaking about rounds, in rounding close numbers are considered the same [math]X1 = 0.1999999999... ~ 0.1999 = X2[/math] [math]X1 >~ X2[/math] [math]X1 * 10^c >> X2 * 10^c[/math] where: [math]c > 0[/math] I think playing with rounding depends on the application decimal degree of power

I'm not good at this, but my guess is that if you want to limit it at 7, max: X = 7 and Y = f(X) = f(7), where f(x) is the equation you use ... correct me if i'm wrong,

the three first parts were already solved, and as far as I know, there is a group nowadays trying to break the fourth part ...

Analysis, Logic, and Discrete Mathematics

if you want to deal with Keyboard Keys, you simply implement KeyListener, and for mouse, you can implement MouseListener ... public MyClass implements KeyListener { // ... public void keyPressed (KeyEvent e) { } // ... } KeyListener: http://download.oracle.com/javase/1.4.2/docs/api/java/awt/event/KeyListener.html

There is a technique .. which is forbidden, because it's technically a cheat ... The method is basically that division of bandwidth at any level in the networks is based on the ends, the system at time 0 use 100% of inherited bandwidth, then do equalization ... Well, you can ask your friend to limit his download/upload speeds to have the sum of 25% of your bandwidth ...

Learn everything in Computer Science is impossible .. take for instance Artificial Intelligence, although I do researching in A.I, There are things known as Multi-Optima Fuzzy-System .. which I don't know much of ...

The presented algorithm is the fastest .. because it's approximation-based statistical-approach algorithm,

In computer science ... An image is a 2-dimensional plane of pixels where every pixel have a domain of colors ... A Graphics is a graphical object-oriented framework, which can be 1-dim (vector), 2-dim (plane), 3-dim (object), 4-dim (animation) ...

I'd like to clarify some point, Python, Perl, Ruby are not Programming Language ... They are Script Languages, they are interpreted, just like BASH .. in Software Engineering, Script Languages have low consistency ... So, I suggest learning C, C++, or Java And if you are interested in System Programming, you can learn C (Unix/Linux), C++ (windows), or Objective-C (Mac)