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Show HN: Interactive Calculus via LaTeX

ximera.osu.edu

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Re: Show HN: Interactive Calculus via LaTeX

#11

Post by jovas »

skh wrote: post #3
jovas wrote: post #2

Tools: https://github.com/ximeraproject Source: https://github.com/mooculus Linear algebra: https://ximera.osu.edu/laode/linearAlgebra

I really like the interactive exercises. I teach math at a community college and would like to create interactive exercise sheets for some of my classes. I’m not familiar with Github and poked around a bit but I could not figure out how the answer checking was done. In one problem I did the answer was 6 and I was pleasantly surprised the answer 5+1 was counted as correct. Do you know how this is done?

If you goto:

https://ximera.osu.edu/introduction

you can see how to make your own materials.

There is a set of example environments here:

https://ximera.osu.edu/examples/exampleActivityCollection

Re: Show HN: Interactive Calculus via LaTeX

#12

Post by skh »

kisonecat wrote: post #5
skh wrote: post #3

Earlier quoted context omitted.

I really like the interactive exercises. I teach math at a community college and would like to create interactive exercise sheets for some of my classes. I’m not familiar with Github and poked around a bit but I could not figure out how the answer checking was done. In one problem I did the answer was 6 and I was pleasantly surprised the answer 5+1 was counted as correct. Do you know how this is done?

I'm one of the developers of Ximera. Expression equality is handled by https://github.com/kisonecat/math-expressions using a few heuristics, which is necessary because Richardson's theorem says this problem is undecidable. The main trick is to regard the expressions as complex-valued functions, find a point where the value is (nearly) equal, and then check for numerical equality in a neighborhood. (Doing this over th…

Thanks for the response and info. I looked at the README and it seems like you all use Javascript for this. I was thinking maybe Maple or Mathematica was used. I'm impressed with the calculus notes/exercises I saw. It looks professionally done. The fonts/colors are nice.

I'm going to try to make some stuff myself. I would mostly do it for developmental math, college algebra, and trig. I haven't dug too deep into how to make my own stuff using Ximera but I'm hoping I won't have to write Javascript myself to handle checking expressions.

Re: Show HN: Interactive Calculus via LaTeX

#13

Post by skh »

jovas wrote: post #11
skh wrote: post #3

Earlier quoted context omitted.

I really like the interactive exercises. I teach math at a community college and would like to create interactive exercise sheets for some of my classes. I’m not familiar with Github and poked around a bit but I could not figure out how the answer checking was done. In one problem I did the answer was 6 and I was pleasantly surprised the answer 5+1 was counted as correct. Do you know how this is done?

If you goto: https://ximera.osu.edu/introduction you can see how to make your own materials. There is a set of example environments here: https://ximera.osu.edu/examples/exampleActivityCollection

Thank you for the links and reply. The materials for calculus are very good. They look professional. You guys did a great job.

Re: Show HN: Interactive Calculus via LaTeX

#14

Post by rmbeard »

jovas wrote: post #10
pvaldes wrote: post #9

Can't see how is this better than using sweave

Can sweave be integrated with a learning management system? Ximera allows authors to write online interactive texts, that can serve as the HW system for a class. The student's work can be directly sent to the grade book via LTI. Moreover, you can simultaneously produce a PDF that looks like a traditional text. http://www.lulu.com/shop/the-ohio-state-university-math-depa... Which nobody needs to buy, since the PDF gen…

There are some R packages that allow for development of e-learning materials, these are Rmarkdown based so similar to knitr rather than sweave, but basically the same idea. The downside is the lack of symbolic support in R. Ximera does look interesting however. A second question I would have is how this would compare with Jupyter interactive notebooks which have LaTeX support and automated grading as well as symbolic algebra capabilities? Nevertheless additional tools are always welcome.

Re: Show HN: Interactive Calculus via LaTeX

#15

Post by kisonecat »

rmbeard wrote: post #14
jovas wrote: post #10

Earlier quoted context omitted.

Can sweave be integrated with a learning management system? Ximera allows authors to write online interactive texts, that can serve as the HW system for a class. The student's work can be directly sent to the grade book via LTI. Moreover, you can simultaneously produce a PDF that looks like a traditional text. http://www.lulu.com/shop/the-ohio-state-university-math-depa... Which nobody needs to buy, since the PDF gen…

There are some R packages that allow for development of e-learning materials, these are Rmarkdown based so similar to knitr rather than sweave, but basically the same idea. The downside is the lack of symbolic support in R. Ximera does look interesting however. A second question I would have is how this would compare with Jupyter interactive notebooks which have LaTeX support and automated grading as well as symbolic…

I don't think Jupyter offers a facility like $\frac{\answer{2}}{4} = 1/2$ for putting answer blanks in the middle of mathematical expressions. For sagemath, code like \sage{derivative(f,x)} also works, even inside an \answer.

An activity in Ximera has state, and this state is synchronized (via Fraser's differential synchronization) with all open clients, so the instructor can watch a student while they work in Ximera, and even edit the page alongside them.

Re: Show HN: Interactive Calculus via LaTeX

#16

Post by kisonecat »

skh wrote: post #12
kisonecat wrote: post #5

Earlier quoted context omitted.

I'm one of the developers of Ximera. Expression equality is handled by https://github.com/kisonecat/math-expressions using a few heuristics, which is necessary because Richardson's theorem says this problem is undecidable. The main trick is to regard the expressions as complex-valued functions, find a point where the value is (nearly) equal, and then check for numerical equality in a neighborhood. (Doing this over th…

Thanks for the response and info. I looked at the README and it seems like you all use Javascript for this. I was thinking maybe Maple or Mathematica was used. I'm impressed with the calculus notes/exercises I saw. It looks professionally done. The fonts/colors are nice. I'm going to try to make some stuff myself. I would mostly do it for developmental math, college algebra, and trig. I haven't dug too deep into how…

Maple and Mathematica are not open, and it's important that not only the resources be open-source, but also the underlying technology stack, because we're trying to not only teach students mathematics but the most engaged students need to "look under the hood" and learn how the technology works.

So we do support SageMath for more complicated answer validation. This depends on the public SageMath cell servers, which provides cloud-hosted SageMath and enables things like \sage{derivative(x*x,x)}. It's also more performant to rely on JavaScript.

For developmental math, answer validation is somewhat harder than for calculus, because often you want to distinguish between say (x+1)^2 and x^2 + 2x + 1.

We run workshops on how to use Ximera. The next one is at UFlorida in October. If you're interested, there is some travel support available. Contact us at ximera@math.osu.edu

Re: Show HN: Interactive Calculus via LaTeX

#17

Post by rmbeard »

kisonecat wrote: post #15
rmbeard wrote: post #14

Earlier quoted context omitted.

There are some R packages that allow for development of e-learning materials, these are Rmarkdown based so similar to knitr rather than sweave, but basically the same idea. The downside is the lack of symbolic support in R. Ximera does look interesting however. A second question I would have is how this would compare with Jupyter interactive notebooks which have LaTeX support and automated grading as well as symbolic…

I don't think Jupyter offers a facility like $\frac{\answer{2}}{4} = 1/2$ for putting answer blanks in the middle of mathematical expressions. For sagemath, code like \sage{derivative(f,x)} also works, even inside an \answer. An activity in Ximera has state, and this state is synchronized (via Fraser's differential synchronization) with all open clients, so the instructor can watch a student while they work in Ximera…

If I understand your comment, correctly, then grading facility in Jupyter allows something like that I believe. My question related more to any symbolic/computer algebra capabilities Ximera may have, or does it just allow for interactive documents without computational tools?
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