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=== Mathematical Notation === 
=== Mathematical Notation === 

−  PGML allows you to specify mathematics in two different formats: TeX and calculator notation. The TeX notation allows you to use the standard TeX and LaTeX commands to format your mathematics. The calculator notation uses MathObjects to parse and format the mathematics (so this is the notation that you use to create formulas in your PG problems, and that students use to enter their answers). Both formats come in 
+  PGML allows you to specify mathematics in two different formats: TeX and calculator notation. The TeX notation allows you to use the standard TeX and LaTeX commands to format your mathematics. The calculator notation uses MathObjects to parse and format the mathematics (so this is the notation that you use to create formulas in your PG problems, and that students use to enter their answers). Both formats come in two forms: inline and display style. The inline form uses spacing rules that try to minimize the impact on line spacing, while display style allows for easier readability at the cost of using more vertical space. 
−  To use TeXformatted mathematics, enclose it in <code>[`...`]</code> for 
+  To use TeXformatted mathematics, enclose it in <code>[`...`]</code> for inline math and <code>[``...``]</code> for displaystyle math. 
−  To use calculator notation, enclose it in <code>[: ... :]</code> for 
+  To use calculator notation, enclose it in <code>[: ... :]</code> for inline math and <code>[:: ... ::]</code> for displaystyle math. 
For example, 
For example, 

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What [:x:] makes [:(x+2)/3 = 1:]? 
What [:x:] makes [:(x+2)/3 = 1:]? 

−  +  both produce the same results (with inline math). 

−  And for example, 

+  Note that, unlike with TeX, displaymode math is not automatically centered on a separate line. If you want that, you must provide the formatting for that yourself: 

−  What [`x`] makes [``\frac{x+2}{3} = 1``]? 

+  [``\sum_{n=0}^{10} 2^n``] is flush left 

−  What [:x:] makes [::(x+2)/3 = 1::]? 

+  [``\sum_{n=0}^{10} 2^n``] is indented 

−  
−  Both produce the same results with inline math, but the second math is displaystyle inline, so the fraction numerator and denominator typically will appear larger. This can comes at the cost of awkward spacing between consecutive lines of text. 

−  
−  And for example, 

−  
−  Find [`x`] that solves the equation: [```\frac{x+2}{3} = 1```] 

−  Find [:x:] that solves the equation: [:::(x+2)/3 = 1:::] 

+  >> [``\sum_{n=0}^{10} 2^n ``] is centered << 

−  
−  Both produce the same results with inline math for the "x", and then displayed math on its own line for the equation. 

== Interaction with PG == 
== Interaction with PG == 