I am trying to typeset equations using MathType in Microsoft Publisher. I think Publisher is an important requirement for me since I am creating an A0 poster.

Is it possible to typeset calligraphic letters in MathType? I have attached examples of equations I typeset in Latex below. The "V" and "O" are calligraphic, and not Greek letters.

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To answer the "I think Publisher is an important requirement for me since I am creating an A0 poster" part of your question, note that there are a number of LaTeX classes to create posters. See this post on TeX.SE for suggestions. You can also just set the paper height and paper width using the geometry package, and design your poster "by hand" in LaTeX.

If you are using other software to create your poster, you could still typeset the equations in LaTeX, maybe with LaTeXit, and include them in the poster as images.

Finally, this MathType fonts page lets you preview some MathType fonts, have a look at Euclid Math One for calligraphic letters.