I thought the phrase needed an hyphen just like, say, class-centered methods. But Google proved me wrong.
Why is this? Maybe the hyphenated version and non-hypenated version are both valid?
Hyphens are tricky. You will find many expert English writers who don't always use hyphens correctly, or not all the time. However, when they make mistakes they will tend to omit hyphens which could or should be added, rather than including ones which should not be there. And in some circumstances, they are purely a matter of style.
Anyway ... when to use them?
You join words with a hyphen when they are acting as a 'compound modifier' to another word.
"Class-centred" are two words acting together as an adjective to describe "methods". The methods are class-centred. If you wrote "class centred methods", to be honest, most English speakers would not pick you up on it, and many would not notice anything was missing.
Course selection advice.
Unlike "methods", which are "class-centred", the "advice" is not being described by "course selection" in an adjectival way. They certainly modify how the advice is understood by the reader, but they are not acting as compound adjectives. 'Course' and 'selection' are both nouns, not adjectives.
Try this as a simpler example:
The blue-green train.
The blue steam train.
"Blue-green" is a compound adjective, linked by a hyphen. (Blue-green meaning something that is a mix of blue and green).
A "blue steam" train is a blue example of a train powered by steam. "Steam" is a noun which qualifies the type of railway locomotive we are talking about, but does not describe it like an adjective.
A way to 'test' for whether you need a hyphen may be to reword the sentence using the verb 'to be'
The methods are class-centred. [Works grammatically]
The advice is course selection. [Is nonsense - or means something very different from what you are trying to say.]
There is a good article here which goes into more detail, because there are lot of other uses and complexity. Most ambiguous of all is the use of hyphens with compound nouns (is it 'paperclip', 'paper-clip', 'paper clip'?) where rules are highly flexible. But that's not what you're asking here.