Meaningful mathematics

Two types of mathematical content

Lurch allows users to type math in two ways:

  • meaningful math, which the user wants Lurch to read and grade, giving feedback about its correctness; and
  • expository math, which the user wrote to give some intuition for a human reader of their work, but which Lurch should ignore.

In the previous tutorial page, we entered only expository math, not meaningful math. If we asked Lurch to check our work, it would give us no feedback at all, because it knows to ignore content we've explicitly called "expository."

Why two types of math?

Students will almost always want to use meaningful math only, so that Lurch will read and grade all of their work. But instructors may want to enter a mix of meaningful and expository math.

For example, if an instructor is defining a new set of axioms, and they want to intersperse examples that explain the axioms, they don't want Lurch to misinterpret the examples as axioms, or as student work to be graded. (The instructor might even give examples of what you can't do with the axioms!) So they would use meaningful math for the axioms, but expository math for the examples.

Exercise: Meaningful math

  1. In the Lurch application below, click the Insert menu and choose "Expression."
  2. In the dialog that pops up, type a simple expression, like \(x<0\).
  3. Click OK to place your math into the document.

To edit your new content, you have the same options as you did for expository math; you can click it or place your cursor on it and hit enter.

Important: Recognizing meaningful content

You have surely noticed that the expression you just added is surrounded in a blue-ish border. This border distinguishes meaningful content from non-meaningful content, and makes it clear which portions of your document Lurch is paying attention to. We'll talk more about this decoration (and how to hide it when you don't want to see it) in later parts of this tutorial.

For power users

Just as expository math expressions can be entered using an equation editor or LaTeX notation, meaningful mathematics can also be entered in more than one way. (Again, users happy with the equation editor can skip this section.)

Exercise: Change the input mode

  1. In the Lurch application above, click the Edit menu and choose the Preferences item (at the very bottom, which may require you to scroll).
  2. Find the setting for "Type of expression editor to use" and change it to "Intermediate."
  3. Click OK to save your settings.

Much like intermediate mode for editing expository math content allows you to use the equation editor or LaTeX notation, the intermediate mode for editing meaningful math expressions allows you to use the equation editor or a custom Lurch notation for meaningful expressions.

Warning: This is not LaTeX

LaTeX was designed for presentation, not meaning. The notation used for meaningful expressions in Lurch is not LaTeX, but a derivative of AsciiMath specific to the Lurch project. We hope to make this notation customizable in a future version of Lurch, but in this early phase of the project it is not. You can read more about the Lurch notation here. Or you can choose to use the equation editor instead.

Like with expository math, meaningful math has three editor modes, and you can choose the one you like best:

  • Beginner mode is the default mode and uses just an equation editor widget.
  • Intermediate mode incorporates both the equation editor for those who wish to use it and a text box that uses Lurch notation.
  • Advanced mode is for those who have mastered Lurch notation, and shows a very minimalist dialog that aims to let you stay in the flow of your work.

Is lurch grading my math now?

No, but that's the very next thing! Learn how to have Lurch grade your document.