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Are there any computer programs which can help you visualize mathematical concepts?

  1. Nov 13, 2009 #1
    Although I haven't been too much into math in the past, with the exception of statistics being a college minor, all of a sudden I have an interest in coming up with mathematical equations to describe/predict how certain things work.

    I want to take data sets and come up with equations to predict, outside the usual of what they teach in statistics classes. In statistics, they have multiple regression which takes multiple independent variables (X and more) to predict a dependent variable (Y) on multidimensional scatterplots. However, I want to see if I can tweak it to make it more precise, perhaps adding Calculus and others to an equation.

    Since I don't have a degree in Math, but rather minor in Statistics, I'm not as mathematical savy. So I was thinking if I could find a free computer program that helps you "visualize" how a wide variety mathematical equations/concepts work, then look at data sets/scatterplots, maybe I can brainstorm various formats for new equations, and then work out the details from there? Are there any free computer programs that one can download, which help you visualize 3D concepts in math, possibly allowing you to use your mouse to maneuver the image around? If not 3D visualizing, perhaps anything else that allows you to concept-ualize the many concepts within Trigonometry, Calculus, Polynomials, Geometry, and much much more, so that I can look at a scatterplot and get ideas? Anything that can give me insight?

    Any help would be greatly appreciated!
     
  2. jcsd
  3. Nov 13, 2009 #2

    whs

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    Re: Are there any computer programs which can help you visualize mathematical concept

    I am confused with what you really are looking for. You yourself even put 'visualize' in quotes.

    I don't think there is a program that lets you visualize how concepts work. I am not even sure what that means.

    Are you saying you need software to graph data? Or you want to learn about curve fitting?
     
  4. Nov 13, 2009 #3
    Re: Are there any computer programs which can help you visualize mathematical concept

    Sorry for any confusion, maybe this will help: I already have software to graph and also create graphics for data. I actually learned some about the free R Statistical Computing from a Statistics class, which has good statistical graphics, and am now trying to teach myself more about the program http://www.r-project.org/ However, it already assumes you know about the concept before you give it a command. My idea is to pull up data on a scatterplot from that program I already have, then look at a "visualize mathematical concepts" program (what I'm looking for) and brainstorm ideas for an equation. If that makes sense? (In the next post I'll include a picture of a possibility)

    Right now there are equations "in general" for scatterplots. What I'm looking for is I want to view a scatterplot I would already have in my hands and then come up with an equation unique to the specific data set (rather than only a "statistics" concept that works in general for any type of statistics scatterplot). For example I could come up with an equation that is specific to describing how human flirting works, more specific than ones used for scatterplots in general. Rather than just say I'm going to use the regular multiple regression equation of y^ = b0 + b1x1 + b2x2 ..., I could use that as a start and then add things like types of trigonometry/calculus/etc to make it fit the line more precisely for the specific data set. I could try some type of "nonlinear regression", tweak some details, and add other stuff in. Newton's Force = Mass X Acceleration is specific to a particular thing, rather than just being general like the concept of "multiplication", etc.

    I don't know if that helps at all, or if I'm just confusing in general?
     
  5. Nov 13, 2009 #4
    Re: Are there any computer programs which can help you visualize mathematical concept

    For example, I found at http://k3dsurf.sourceforge.net/ which has this:

    "Because Mathematics can be so fun!
    K3DSurf is a program to visualize and manipulate Mathematical models in three, four, five and six dimensions. K3DSurf supports Parametric equations and Isosurfaces."

    k3d1114mini.png
    k3d1161mini.png
    25049-2mini.png
    k3d1111mini.png

    I don't know if that would be a decent way to go about trying to visualize what may be good to make a line fit a scatter plot better, in addition to the concepts already in Statistics?
     
  6. Nov 13, 2009 #5

    whs

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    Re: Are there any computer programs which can help you visualize mathematical concept

    There are a million ways to make lines fit data. Cubic splines, linear regression etc. Statistics doesn't just concern itself with regression, but in my experience, you have many variables behind that data in a scatter plot. So you start looking at which variables are really shaping that data, maybe throwing out some here and there, minimizing errors and forming equations. (Thus making the line fit more precisely)

    I think I'm confused by you saying you have a scatter plot and add 'trig/calc/etc' to shape the line instead of looking at the raw data behind the plot.

    Why wouldn't you want to learn the concept behind the math?
     
  7. Nov 13, 2009 #6
    Re: Are there any computer programs which can help you visualize mathematical concept

    My original plan is to look at the raw data behind the plot. I just want to see if there are also other ways to add to describing/predicting the data points on a scatter plot, that may result in it being more precise/minimizing error variance. The saying "If it ain't broken, don't fix it", ignoring that may help me possibly come across different ways of doing things which still work. I'd still try to combine multiple regression techniques, and finding an optimal cutoff point for the explanatory variables for an adjusted R^2, ignoring some outliers so it doesn't throw the equation off, etc.

    Since Calculus is the study of change, it may be useful in describing/predicting on a scatter plot. Since Trignometry is the study of triangles and is often used to study the position of something relative to another thing, it may have some uses on the scatter plot.

    I want to understand the concept behind the math, I'm actually interested in a computer program that helps one visualize various concepts. So I'm thinking when I look at the original raw data on a scatter plot, thinking about these other mathematical visualizations may help me think of various ways of doing things.

    I just want something that will give a lot more insight than what an ANOVA table or equation like y^ = b0 + b1x1 + b2x2 + .... (by itself) will give me.

    I don't know if that makes sense, or if you're confused, or if you're not confused and think I've gone off on the wrong path?
     
    Last edited: Nov 13, 2009
  8. Nov 14, 2009 #7

    whs

    User Avatar

    Re: Are there any computer programs which can help you visualize mathematical concept

    It sounds like you want to find patterns in your scatter data that can be used to predict future points or interpolate, be it angles between dots or how the distance between the dots are changing, which is basically what statistics is.

    Calculus is involved in a lot of curve fitting techniques. Or I suppose you could print out a scatter plot and draw angles between dots and try to find a pattern, but you will be using the same statistics to analyze that pattern.

    I haven't used R but in SPSS (got it through school a long time ago, its really expensive without a school license) you can input all your data and you can tell it to spit out an ANOVA, lots of different curves etc.

    The problem is you are looking for a computer package to do things you can't define. You can say you did something specific like ANOVA'd the data and came up with some regression equations, but then you want to somehow add/combine trig or calculus to it. Too vague.

    Go pick up a book, or google around on curve fitting or more advanced statistical concepts, learn them and then use a computer package to graph a lot of them. Or for gigs, print out scatter and start messing around with it by hand.

    There are definitely many other ways to predicting or fitting the data than just using multiple regression. Hey maybe your data even mimics the behavior of of birds flying in packs, or something crazy like that.
     
  9. Nov 14, 2009 #8

    whs

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    Re: Are there any computer programs which can help you visualize mathematical concept

    To the best of my knowledge, like you said in the beginning, you must first learn and know the concepts before applying them to graphs or getting some visual representation of them through software.
     
  10. Nov 21, 2009 #9
    Re: Are there any computer programs which can help you visualize mathematical concept

    I've used SPSS in some non-statistics classes I took. All the statistics teachers (in the math department at the school rather than social sciences) said they prefered SAS because it's a computer programming language and thus allows you to have more control than point and click. Regardless, SPSS is still very useful and popular for good reason (especially if you don't want to learn the programming language code). I found a free alternative to SPSS, PSPP, however it doesn't have all the features as SPSS. The professor for one of the stats classes had us use R statistics because it has better control over graphing features than both of them. Then since it's a free program and very popular, I'm now trying to teach myself even more about R. I'm just really into looking for good mathematical visualization. R has graphing features, even 3D, for that. I'm just looking for something that's not mostly for statistics (R is programming language and can if you have patience to program your own commands into it, I'm just looking for something more, I just like to stick to the pre-set commands in R).
     
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