asctech / mooculus

Mooculus

Live version

A live demo is available at mooculus.osu.edu. You may also be interested in enrolling in the associated Coursera course.

The materials for our calculus two course are available at https://github.com/kisonecat/sequences-and-series.

Installation For OSX and Linux*

Preliminaries

First you must install gcc. You can get it for free here.

Next, install MySQL server; I recommend choosing the dmg.

RVM And Bundler

Now you need to install rvm. This can be done by copy and pasting the following command into your terminal:

\curl -L https://get.rvm.io | bash -s stable --ruby

Hopefully, the installation was successful. If it wasn't, I recommend the "google the error message" strategy. You must now put the line

source ~/.rvm/scripts/rvm

at the end of the (hidden) file ~/.bashrc. Open a new terminal and check that you are using a new version of ruby by running

ruby --version

You should see 1.9.3 in the output somewhere. If you see 1.8.7 or similar, something went wrong and I will again punt to the troubleshooting strategy outlined above.

Now we will install bundler. This can be done by running

gem install bundler

Geting Rails Up And Running

Go into the mooculus repo and run

bundle install

After doing this, we need some preliminary steps:

cp config/database.yml.template config/database.yml

bundle exec rake db:migrate

bundle exec rake exercise:all

Then, check that everything works with

bundle exec rails server

and navigate to localhost:3000 in your browser!

Upkeep

If you add more exercises, for them to be loaded, you must run

bundle exec rake exercise:all

* Linux users should be able to follow these instructions after insuring that ruby, ruby-dev, libxml2-dev, libxslt-dev and libmysqlclient-dev are installed

mooculus's Issues

Differentiator should be able to treat function symbols as well

For example if y is a function of x, the derivative of xy with respect to x should be xdy/dx +y.

In the long term, handling partial derivatives would be good too.

Function parser should handle (a)(b) = a*b

Skill Practice

We could either have a list of exercises or an exploration that allows skill practice.

Forums

If our forum could pull from the chapter/section structure to automatically generate sections, that would be good too -- (mostly I'm thinking for future courses)

Adjustable level of detail for derivative story

For example, it would be nice to disable explanations for polynomial parts of expressions, or whatever. Maybe suppress explanation of sum rule.

It seems like the rules people have most trouble with are product, quotient and chain rule, so it would be nice to have a story where only these are explained.

Exercises: Entry test

Perhaps we should have an "entry test" this would allow a new user to start with exercises that are at an appropriate level for them.

Alternatively we could simply weight the exercises in a more sophisticated way.

Textbook: Chapter 9

In the mean value thm section we might want to address the idea of multiple constants and the (anti) derivative of 1/x

Textbook: Infinite limits before infinite limits

Currently the textbook asks about infinite limits before infinite limits are introduced.

The answer to these questions is DNE

Should we not do this?

Get the test server working!

Textbook: Freehand draw

Maybe it would be cool if we had a option for "hand-drawn" pictures...

http://tex.stackexchange.com/questions/39296/simulating-hand-drawn-lines

Remove extra parenthesis in parsedExpression answer type live display

Textbook: Marginnote and environment

Currently the tufte-style class does not permit marginnotes within environments. This is limiting. I found this solution at tex-stack exchange, but have yet to implement it.

http://tex.stackexchange.com/questions/63012/using-marginnote-inside-a-math-environment-in-tufte-book

Make "Checks and Xs" for multiple answer types

Currently, if we mark a student wrong on a problem with multiple answer inputs, they do not know which of the answers is wrong. Putting green checks or red Xs next to the input boxes after clicking "check answer" would fix this,

Make this repo public!

Jim and I really do not see any issue with making the repo public, and there are many advantages. What do we need to do to make this happen?

Derivatator: x^pi

At the moment - pi is not considered a constant...

Textbook: Word problems

We need more fanciful problems like the space faring civ and actors and icecubes.

Start using hypercalc for better numerical precision?

http://www.ylmass.edu.hk/~mathsclub/HyperCalc/HyperCalc.html

Explorations: Newton's method and Euler's Method

A newton's method exploration would be really cool - showing the tangent lines etc, and how they can sometimes be "trapped"

Also -- probably an exploration for euler's method would be good.

Textbook: thoughts for next-time

• Are the problems in the correct order? E.g. 1.3 needs to be
  re-ordered, in particular, 6 is too hard too early. MARKED
• break limits into two chapter (just uncomment the chapter in
  infinity and cont)
• Add "tolerance" word problems to limits section (2.2 I think) see
  section 2.5 of Finney Thomas Demana Waits.
• Do we really want to do the chain rule before derivatives of trig?
• Add curve sketching in "Basics of Derivatives" this can be done
  through tables etc.
• Place derivative of e^x in the next chapter (Derivative of e^x,
  Product Rule and Quotient Rule)

Textbook: Chapter 0

So there should probably be a chapter 0.

Functions

• Dfn of a function

Plotting a function

• Fxn vs formula

Inverse function

• Just the basics, we'll get into the details in later chapters
• Compare the situation of \sqrt[3]{x^3} = (\sqrt[3]{x})^3 and \sqrt{x^2} != (\sqrt{x})^2

Textbook/Videos: Ideas for Cool contexts

http://mathoverflow.net/questions/83097/are-there-any-related-rates-calculus-problems-that-dont-feel-contrived

http://themathblogger.wordpress.com/2009/10/05/business-calculus-word-problem/

the faucet problem would be really neat.

Textbook: Limits at Infinity

Add one with x-> -infty and a sqrt...

(this needs to be an example)

Subhints are broken

It would appear that subhints no longer work...

Exercises: Formula entry seems "angry"

The formula entry seems "angry" when it cannot parse an equation:

Error: the expression is invalid.

In red seems to be yelling or something, perhaps a nice "blue"

"I'm not sure what you mean yet"

or something similar?

Textbook: Rewrite examples

In Example 2.1.4 (Basics of Derivatives, d/dx |x|) I handle the problem in cases.
It would probably be better handled just by saying |x| = \sqrt{x^2}

In Example 5.1.3, I make goofy choices for f(x) and g(x) (which appealed to me at the time)

Perhaps Example 5.1.3 should be something like d/dx |x^3+4|

Have a "test mode" option on the app

Khan academy already has a test mode for viewing problem types and variable assignments. We should really have a way to use this while developing...

Automatic Differentiation

We need to be able to take a syntax tree and return an array containing the step by step process of differentiating the expression.

Textbook: Add fixed point problems to IVT

See video

Allow multiple live updates when using multiple parsedExpression answer types.

Every parsedExpression input box should have a live update beneath it.

Textbook: Concept of Derivative

Probably need to emphasize

f(a+h) = f(a) + f'(a)h + ep(h)h

in basics of derivatives.

Optimization problem

I know of a train catching problem that is cool

Function parser should handle emdash for -, and ** for ^

Exercises: Continue or not?

Add a "No, I'd rather work more of these problems" choice.

Exercises: Hints for derivatives involving log

should say \log not "log"

Design: Future Ideas

I know this is least of our worries right now but we might want to check out:

http://designmodo.github.com/Flat-UI/

Textbook: Inverse Trig

In the notes, I use various pythagorean identities. A more insightful solution is to draw a triangle.
We have the Tikz skills - let's use them.

Textbook: Wording of exercises in 8.2

Some care should be taken to re-write the problems copied from the other open source text.

"A box with square base is to hold a volume 200."

bothers me. (I'll fix it later)

Textbook: Mooculus.sty Procedures etc

Currently each procedure or main definition is "hard-coded" as a separate environment.

This is clunky.

Textbook: Fundamental Thm of Calculus

The proof needs more picts.

also perhaps instead of using \ep, we should use the extreme value theorem to pick out u,v etc.

Also the connection to Euler's method could be explained better.

Textbook: Integration -- more props of integrals needed

I need to add a Property of Integrals stating that
[
\int_a^b f(x) \d x + \int_b^c f(x) \d x = \int_a^c f(x) \d x
]

Maybe also:

If f(x) < M for on [a,b] then

\int_a^b f(x) \d x < M\cdot (b-a)

function parser should use complex numbers for arithmetic

As the singularities of a holomorphic function are of measure 0, we have a very low probability of having domain issues if we use a lot of complex numbers to test for function equality. For example,

e^(log(x)) would work properly because you usually avoid the branch cut.

Refresh on Mooculus is moving through the finite exercise bag

We should probably increase the size of the bag, or generate a new bag once all the exercises in the bag have been displayed.

Multiple choice makes the correct answer bold

The first time I load a multiple choice exercise, all answers are bold. After answering correctly and moving on, only the correct answer is bold, giving the answer away. Refreshing solves the problem for one question.

I have no idea where this is happening in the code.

Textbook: List of thms

If we could pull out the thms listed in the front into a separate document, that might be nice.

Also - if we could include important dfns/procedures without numbers, that might be nice too

We should have a "Flashcard" exercise type

Sometimes you just want to have practice recalling basic facts. Flashcards are great for that, so we should have a flash card exercise type.

Entering Formulas

The Differentiate input works differently than the input on the exercises.

I'm sure this is well known, but just in case, I've made an issue.

Textbook: Order of Exercises

Are the problems in the correct order? E.g. 1.3 needs to be re-ordered, in particular, 6 is too hard too early.

Differentiator should treat negative exponents with power rule, not with logs.

Textbook: Inverse Trig

This section probably needs more exercises...

In particular, maybe we should add the "triangle" exercises that we do at the beginning of 1151.

Also this section could use some more pictures...

Textbook: Derivatives for integration

We need to be sure to include examples of functions that differentiate to common fxns.

E.g.

d/dx \frac{x^4}{4}

d/dx ln(tan(x) + sec(x))