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  • Scared of Calculus - Required to pass Differential Calculus as part of my Computer science major

    - by ke3pup
    Hi guys I'm finishing my Computer science degree in university but my fear of maths (lack of background knowledge) made me to leave all my maths units til' the very end which is now. i either take them on and pass or have to give up. I've passed all my programming units easily but knowing my poor maths skills won't do i've been staying clear of the maths units. I have to pass Differential Calculus and Linear Algebra first. With a help of book named "Linear Algebra: A Modern Introduction" i'm finding myself on track and i think i can pass the Linear Algebra unit. But with differential calculus i can't find a book to help me. They're either too advanced or just too simple for what i have to learn. The things i'm required to know for this units are: Set notation, the real number line, Complex numbers in cartesian form. Complex plane, modulus. Complex numbers in polar form. De Moivre’s Theorem. Complex powers and nth roots. Definition of ei? and ez for z complex. Applications to trigonometry. Revision of domain and range of a function Working in R3. Curves and surfaces. Functions of 2 variables. Level curves.Partial derivatives and tangent planes. The derivative as a difference quotient. Geometric significance of the derivative. Discussion of limit. Higher order partial derivatives. Limits of f(x,y). Continuity. Maxima and minima of f(x,y). The chain rule. Implicit differentiation. Directional derivatives and the gradient. Limit laws, l’Hoˆpital’s rule, composition law. Definition of sinh and cosh and their inverses. Taylor polynomials. The remainder term. Taylor series. Is there a book to help me get on track with the above? Being a student i can't buy too many books hence why i'm looking for a book that covers topics I need to know. The University library has a fairly limited collection which i took as loan but didn't find useful as it was too complex.

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  • How can calculus and linear algebra be useful to a system programmer?

    - by Victor
    I found a website saying that calculus and linear algebra are necessary for System Programming. System Programming, as far as I know, is about osdev, drivers, utilities and so on. I just can't figure out how calculus and linear algebra can be helpful on that. I know that calculus has several applications in science, but in this particular field of programming I just can't imagine how calculus can be so important. The information was on this site: http://www.wikihow.com/Become-a-Programmer Edit: Some answers here are explaining about algorithm complexity and optimization. When I made this question I was trying to be more specific about the area of System's Programming. Algorithm complexity and optimization can be applied to any area of programming not just System's Programming. That may be why I wasn't able to came up with such thinking at the time of the question.

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  • Query on Booleans in Lambda Calculus

    - by darkie15
    Hi All, I have following query on lambda calculus which am not able to understand: Here is the lambda calculus representation for the AND operator: lambda(m).lambda(n).lambda (a).lambda (b). m(n a b) b Can anyone help me in understanding this representation? Regards, darkie

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  • Query on Booleans in Lambda Calculus

    - by darkie15
    Hi All, I have following query on lambda calculus which am not able to understand: Here is the lambda calculus representation for the AND operator: lambda(m).lambda(n).lambda (a).lambda (b). m(n a b) b Can anyone help me in understanding this representation? Regards, darkie

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  • If Scheme is untyped, how can it have numbers and lists?

    - by Dokkat
    Scheme is said to be just an extension of the Untyped Lambda Calculus (correct me if I am wrong). If that is the case, how can it have Lists and Numbers? Those, to me, look like 2 base types. So I'd say Racket is actually an extension of the Simply Typed Lambda Calculus. No? Question: Is Scheme's type system actually based or more similar to Simply Typed or Untyped Lambda Calculus? In what ways does it differ from Untyped and or Simply Typed Lambda Calculus? (The same question is valid for "untyped" languages such as Python and JavaScript - all of which look like they have base types to me.)

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  • Calculus? Need help solving for a time-dependent variable given some other variables.

    - by user451527
    Long story short, I'm making a platform game. I'm not old enough to have taken Calculus yet, so I know not of derivatives or integrals, but I know of them. The desired behavior is for my character to automagically jump when there is a block to either side of him that is above the one he's standing on; for instance, stairs. This way the player can just hold left / right to climb stairs, instead of having to spam the jump key too. The issue is with the way I've implemented jumping; I've decided to go mario-style, and allow the player to hold 'jump' longer to jump higher. To do so, I have a 'jump' variable which is added to the player's Y velocity. The jump variable increases to a set value when the 'jump' key is pressed, and decreases very quickly once the 'jump' key is released, but decreases less quickly so long as you hold the 'jump' key down, thus providing continuous acceleration up as long as you hold 'jump.' This also makes for a nice, flowing jump, rather than a visually jarring, abrupt acceleration. So, in order to account for variable stair height, I want to be able to calculate exactly what value the 'jump' variable should get in order to jump exactly to the height of the stair; preferably no more, no less, though slightly more is permissible. This way the character can jump up steep or shallow flights of stairs without it looking weird or being slow. There are essentially 5 variables in play: h -the height the character needs to jump to reach the stair top<br> j -the jump acceleration variable<br> v -the vertical velocity of the character<br> p -the vertical position of the character<br> d -initial vertical position of the player minus final position<br> Each timestep:<br> j -= 1.5; //the jump variable's deceleration<br> v -= j; //the jump value's influence on vertical speed<br> v *= 0.95; //friction on the vertical speed<br> v += 1; //gravity<br> p += v; //add the vertical speed to the vertical position<br> v-initial is known to be zero<br> v-final is known to be zero<br> p-initial is known<br> p-final is known<br> d is known to be p-initial minus p-final<br> j-final is known to be zero<br> j-initial is unknown<br> Given all of these facts, how can I make an equation that will solve for j? tl;dr How do I Calculus? Much thanks to anyone who's made it this far and decides to plow through this problem.

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  • Stochastic calculus library in python

    - by LeMiz
    Hello, I am looking for a python library that would allow me to compute stochastic calculus stuff, like the (conditional) expectation of a random process I would define the diffusion. I had a look a at simpy (simpy.sourceforge.net), but it does not seem to cover my needs. This is for quick prototyping and experimentation. In java, I used with some success the (now inactive) http://martingale.berlios.de/Martingale.html library. The problem is not difficult in itself, but there is a lot non trivial, boilerplate things to do (efficient memory use, variable reduction techniques, and so on). Ideally, I would be able to write something like this (just illustrative): def my_diffusion(t, dt, past_values, world, **kwargs): W1, W2 = world.correlated_brownians_pair(correlation=kwargs['rho']) X = past_values[-1] sigma_1 = kwargs['sigma1'] sigma_2 = kwargs['sigma2'] dX = kwargs['mu'] * X * dt + sigma_1 * W1 * X * math.sqrt(dt) + sigma_2 * W2 * X * X * math.sqrt(dt) return X + dX X = RandomProcess(diffusion=my_diffusion, x0 = 1.0) print X.expectancy(T=252, dt = 1./252., N_simul= 50000, world=World(random_generator='sobol'), sigma1 = 0.3, sigma2 = 0.01, rho=-0.1) Does someone knows of something else than reimplementing it in numpy for example ?

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  • Is there really such a thing as "being good at math"?

    - by thezhaba
    Aside from gifted individuals able to perform complex calculations in their head, I'm wondering if proficiency in mathematics, namely calculus and algebra, has really got to do with one's natural inclination towards sciences, if you can put it that way. A number of students in my calculus course pick up material in seemingly no time whereas I, personally, have to spend time thinking about and understanding most concepts. Even then, if a question that requires a bit more 'imagination' comes up I don't always recognize the concepts behind it, as is the case with calculus proofs, for instance. Nevertheless, I refuse to believe that I'm simply not made for it. I do very well in programming and software engineering courses where a lot of students struggle. At first I could not grasp what they found to be so difficult, but eventually I realized that having previous programming experience is a great asset -- once I've seen and made practical use of the programming concepts learning about them in depth in an academic setting became much easier as I have then already seen their use "in the wild". I suppose I'm hoping that something similar happens with mathematics -- perhaps once the practical idea behind a concept (which authors of textbooks sure do a great job of concealing..) is evident, understanding the seemingly dry and symbolic ideas and proofs would be more obvious? I'm really not sure. All I'm sure of is I'd like to get better at calculus, but I don't yet understand why some of us pick it up easily while others have to spend considerable amounts of time on it and still not have complete understanding if an unusual problem is given.

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  • Strategy for desugaring Haskell

    - by luqui
    I'm developing a virtual machine for purely functional programs, and I would like to be able to test and use the the wide variety of Haskell modules already available. The VM takes as input essentially terms in the untyped lambda calculus. I'm wondering what would be a good way to extract such a representation from modern Haskell modules (eg. with MPTC's, pattern guards, etc.). I did a little research and there doesn't seem to be a tool that does this already (I would be delighted to be mistaken), and that's okay. I'm looking for an approach. GHC Core seems too operationally focused, especially since one of the things the VM does is to change the evaluation order significantly. Are there any accessible intermediate representations that correspond more closely to the lambda calculus?

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  • Need help programming with Mclauren series and Taylor series!

    - by user352258
    Ok so here's what i have so far: #include <stdio.h> #include <math.h> //#define PI 3.14159 int factorial(int n){ if(n <= 1) return(1); else return(n * factorial(n-1)); } void McLaurin(float pi){ int factorial(int); float x = 42*pi/180; int i, val=0, sign; for(i=1, sign=-1; i<11; i+=2){ sign *= -1; // alternate sign of cos(0) which is 1 val += (sign*(pow(x, i)) / factorial(i)); } printf("\nMcLaurin of 42 = %d\n", val); } void Taylor(float pi){ int factorial(int); float x; int i; float val=0.00, sign; float a = pi/3; printf("Enter x in degrees:\n"); scanf("%f", &x); x=x*pi/180.0; printf("%f",x); for(i=0, sign=-1.0; i<2; i++){ if(i%2==1) sign *= -1.0; // alternate sign of cos(0) which is 1 printf("%f",sign); if(i%2==1) val += (sign*sin(a)*(pow(x-a, i)) / factorial(i)); else val += (sign*cos(a)*(pow(x-a, i)) / factorial(i)); printf("%d",factorial(i)); } printf("\nTaylor of sin(%g degrees) = %d\n", (x*180.0)/pi, val); } main(){ float pi=3.14159; void McLaurin(float); void Taylor(float); McLaurin(pi); Taylor(pi); } and here's the output: McLaurin of 42 = 0 Enter x in degrees: 42 0.733038-1.00000011.0000001 Taylor of sin(42 degrees) = -1073741824 I suspect the reason for these outrageous numbers goes with the fact that I mixed up my floats and ints? But i just cant figure it out...!! Maybe its a math thing, but its never been a strength of mine let alone program with calculus. Also the Mclaurin fails, how does it equal zero? WTF! Please help correct my noobish code. I am still a beginner...

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  • How to use objetcs as modules/functors in Scala?

    - by Jeff
    Hi. I want to use object instances as modules/functors, more or less as shown below: abstract class Lattice[E] extends Set[E] { val minimum: E val maximum: E def meet(x: E, y: E): E def join(x: E, y: E): E def neg(x: E): E } class Calculus[E](val lat: Lattice[E]) { abstract class Expr case class Var(name: String) extends Expr {...} case class Val(value: E) extends Expr {...} case class Neg(e1: Expr) extends Expr {...} case class Cnj(e1: Expr, e2: Expr) extends Expr {...} case class Dsj(e1: Expr, e2: Expr) extends Expr {...} } So that I can create a different calculus instance for each lattice (the operations I will perform need the information of which are the maximum and minimum values of the lattice). I want to be able to mix expressions of the same calculus but not be allowed to mix expressions of different ones. So far, so good. I can create my calculus instances, but problem is that I can not write functions in other classes that manipulate them. For example, I am trying to create a parser to read expressions from a file and return them; I also was trying to write an random expression generator to use in my tests with ScalaCheck. Turns out that every time a function generates an Expr object I can't use it outside the function. Even if I create the Calculus instance and pass it as an argument to the function that will in turn generate the Expr objects, the return of the function is not recognized as being of the same type of the objects created outside the function. Maybe my english is not clear enough, let me try a toy example of what I would like to do (not the real ScalaCheck generator, but close enough). def genRndExpr[E](c: Calculus[E], level: Int): Calculus[E]#Expr = { if (level > MAX_LEVEL) { val select = util.Random.nextInt(2) select match { case 0 => genRndVar(c) case 1 => genRndVal(c) } } else { val select = util.Random.nextInt(3) select match { case 0 => new c.Neg(genRndExpr(c, level+1)) case 1 => new c.Dsj(genRndExpr(c, level+1), genRndExpr(c, level+1)) case 2 => new c.Cnj(genRndExpr(c, level+1), genRndExpr(c, level+1)) } } } Now, if I try to compile the above code I get lots of error: type mismatch; found : plg.mvfml.Calculus[E]#Expr required: c.Expr case 0 = new c.Neg(genRndExpr(c, level+1)) And the same happens if I try to do something like: val boolCalc = new Calculus(Bool) val e1: boolCalc.Expr = genRndExpr(boolCalc) Please note that the generator itself is not of concern, but I will need to do similar things (i.e. create and manipulate calculus instance expressions) a lot on the rest of the system. Am I doing something wrong? Is it possible to do what I want to do? Help on this matter is highly needed and appreciated. Thanks a lot in advance.

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  • Using Taylor Polynomials Programmatically in Maple

    - by kzh
    I am trying to use a Taylor polynomial programmatically in Maple, but the following does not seem to work... T[6]:=taylor(sin(x),x=Pi/4,6);convert(T[6], polynom, x); f:=proc(x) convert(T[6], polynom, x); end proc; f(1); All of the following also do not work: f:=convert(T[6], polynom); f:=convert(T[6], polynom, x); f:=x->convert(T[6], polynom); f:=x->convert(T[6], polynom, x);. Is there a way of doing this without copying and pasting the output of convert into the definition of f?

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  • Understanding OpenGL Matrices

    - by Omega
    I'm starting to learn about 3D rendering and I've been making good progress. I've picked up a lot regarding matrices and the general operations that can be performed on them. One thing I'm still not quite following is OpenGL's use of matrices. I see this (and things like it) quite a lot: x y z n ------- 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 So my best understanding, is that it is a normalized (no magnitude) 4 dimensional, column-major matrix. Also that this matrix in particular is called the "identity matrix". Some questions: What is the "nth" dimension? How and when are these applied? My biggest confusion arises from how OpenGL makes use of this kind of data.

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  • Integration (math) in C++

    - by Chris Thompson
    Hi all, I'm looking for a library to find the integral of a given set of random data (rather than a function) in C++ (or C, but preferably C++). There is another question asking about integration in C but the answers discuss more how to integrate a function (I think...). I understand that this can be done simply by calculating the area under the line segment between each pair of points from start to finish, but I'd rather not reinvent the wheel if this has already been done. I apologize in advance if this is a duplicate; I searched pretty extensively to no avail. My math isn't as strong as I'd like it so it's entirely possible I'm using the wrong terminology. Thanks in advance for any help! Chris

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  • Uniforme distance between points

    - by Reonarudo
    Hello, How could I, having a path defined by several points that are not in a uniform distance from each other, redefine along the same path the same number of points but with a uniform distance. I'm trying to do this in Objective-C with NSArrays of CGPoints but so far I haven't had any luck with this. Thank you for any help. EDIT I was wondering if it would help to reduce the number of points, like when detecting if 3 points are collinear we could remove the middle one, but I'm not sure that would help.

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  • troubles with integration on matlab

    - by user648666
    I'd like some help please I really need to solve this problem. Well before anything thank you for your time... My problem: I have a matrix (826x826 double) and I want to integrate this matrix with respect to a vector of (826x1 double) I don't have the functions of any of this. Is there a command or an algorithm to take the integral of a matrix with respect to a vector? Please I really need help, I'm such a newbie at matlab. Sincerely. George

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  • How can I make Church numerals more human readable in lisp?

    - by Jason Baker
    I can define church numerals fairly easy using scheme: > (define f (lambda (x) x)) > (f f) ;0 #<procedure:f> > (f (f f)) ;1 #<procedure:f> However, this doesn't make it very easy to recognize that (f f) is 0 and (f (f f)) is 1. Is there a way that I can make these numerals more readable? What would be ideal is this: > (f f) 0 > (f (f f)) 1 The example is in scheme, but I'll take an answer in any lisp.

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  • Uniform distance between points

    - by Reonarudo
    Hello, How could I, having a path defined by several points that are not in a uniform distance from each other, redefine along the same path the same number of points but with a uniform distance. I'm trying to do this in Objective-C with NSArrays of CGPoints but so far I haven't had any luck with this. Thank you for any help. EDIT I was wondering if it would help to reduce the number of points, like when detecting if 3 points are collinear we could remove the middle one, but I'm not sure that would help.

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  • What's the formal name for this Syntax?

    - by rlb.usa
    Sometimes in Scheme, I have functions that take arguments like this add 3 4 What do you call this kind of "list" where it's elements are like a1 a2 a3 ? I don't think you can call it a list because lists are contained in parenthesis and elements are comma-seperated.

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