How to use Ximera

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This course is built in Ximera.

Mathematics cannot be learned passively: it must be actively constructed by the person learning it. With this in mind, this course is built around solving problems!

Here are some examples. Play around with it, get it wrong, try the hints out. Don’t be afraid to fail: getting an answer wrong never hurts you.

Some problems are multiple-choice:

Don’t pick me. Not me either. Pick me! Also an incorrect choice

Click on the choice that says ‘‘Pick me!’’

Some problems are select-all that are correct:

Don’t pick me. Pick me! Pick me too! I’m a correct choice too.

Click on the choices ‘‘Pick me!’’ ‘‘Pick me too!’’ and ‘‘I’m a correct choice too.’’

$3\times 2 = \answer {6}$

$3 \times 2$ is the number of objects in $3$ groups of $2$ objects

$3\times 2=6$

For this course, you should always have a paper and pencil near at hand to make notes, doodle pictures, or solve complicated equations. We strongly recommend that you really grapple with a problem before getting a hint, or moving on. The difference between what you learn by struggling with a problem on your own versus perusing someone else’s solution is astonishing.

With that said, even if you get an answer right you should always try the hints out afterwards. They might explain the concept from a new point of view, or challenge you to think in a different way than you solved the problem.

We support a few different answer types. Here are some example problems from the different answer types we support:

$\frac {x^2+y^2}{7} = \answer {\frac {x^2+y^2}{7}}$

Type $\verb |(x^2+y^2)/7|$

$\frac {\tan (x)}{2xa+b^2} = \answer {\frac {\tan (x)}{2xa+b^2} }$

Type $\verb |tan(x)/(2xa+b^2)|$

$\arcsin (x) = \answer {\arcsin (x)}$

Type $\verb |arcsin(x)|$

Note that typing $\verb |sin^(-1)(x)|$ does not work.

$|x| = \answer {|x|}$

You can type $\verb ! |x| !$ or $\verb ! abs(x)!$ , but $\verb ! abs(x) !$ may be preferable because it is easier to parse appropriately.

$\ln (x+1)= \answer {\ln (x+1)}$

You could type $\verb |ln(x+1)|$ or $\verb |log(x+1)|$

$\sin (\theta ) = \answer {\sin (\theta )}$

Type $\verb |sin(theta)|$

$\varphi = \answer {\varphi }$

Type $\verb |phi|$

$\rho = \answer {\rho }$

Type $\verb |rho|$

$\sqrt {x} = \answer {\sqrt {x}}$

Type $\verb |sqrt(x)|$

It would also work to type $\verb | x^(1/2)|$

$\sqrt [3]{y} = \answer {y^{\frac {1}{3}}}$

We do not have a ‘‘slick” way to enter this, so you should just type $\verb !y^(1/3)!$ , which is equivalent.

$DNE = \answer {DNE}$

Type $\verb |DNE|$ .

Capitalization matters, so $\verb !dne!$ will not work. This also means $x$ and $X$ are different.

$\infty = \answer {\infty }$

As you complete activities the green ‘‘completion bar’’ moves at the top of the page. This lets you know how close you are to being done with an activity.

You advance through pages either by completing them and clicking the ‘‘next activity’’ button, or by navigating on the little scroll bar at the top of the page.