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if I write a math. thesis using latex from Kile, then, while opening a new file in Kile, what is the option should I choose: article/book/report? Thank you!

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You should look at the ams classes, too. E.g. amsbook rather than plain book since this will automatically get you a bunch of maths set up. But it depends really on the format required by your institution. –  cfr Nov 30 '13 at 0:51
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book is the most appropriate from the 3, as it provides you with \chapters.

If I were you, I would also consider the memoir class, which provides lots of customization options and is very popular for writing thesis and books.

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