Capitalisation of "Section" and "Chapter" in a Ph.D. Thesis

I am submitting a Ph.D. thesis fairly soon and my supervisor has flagged my use of capitalisation in "Section" and "Chapter" as possibly incorrect. I have googled about a bit and I see mixed opinions.

So my question is, when writing a computer science Ph.D. thesis, what is the correct way to capitalise "Section", "Chapter", "Appendix", "Figure", "Table", ... ?

For example, what is the correct capitalisation for the following:

• "In Chapter 3, it was shown that..."


• "In the previous Section, a method was presented to..."


• "The graph in Figure 3 shows..."

Answer

"In Chapter 3, it was shown that..."

This seems correct. "Chapter 3" is the name of the third chapter. Names are capitalised.

"In the previous Section, a method was presented to..."

This seems wrong. "Section" is not referring to the previous section by name, therefore no capital.

"The graph in Figure 3 shows..."

Correct. Same as the first example.

So the rule (I use) is, if it is a proper name, then use a capital. This means, if it is of the form "Section $n$", where $n$ is a number, then it needs a capital.