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If I were teaching a class, how do I say that the topics currently being discussed build upon the topics that were discussed in earlier classes?

I'm looking for colloquialisms but if you know about an archaic word or phrase that can be used in this situation, that is also welcome.

I found out about superstruct/superstructure but what I need is a word that applies to academia and not architecture.

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    Friday's class will elaborate further upon the matters dealt with in last term's seminar on prehistoric reptiles.
    – WS2
    Commented Dec 20, 2014 at 21:44
  • @WS2 Thanks. That lead me to "expand on" which works well for my purpose.
    – Vinayak
    Commented Dec 20, 2014 at 22:19
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    Are you introducing new material that extends earlier material (cryptography and number theory), or are you explaining the earlier material in greater detail (earlier versions and competing versions of Newton's calculus)?
    – jxh
    Commented Dec 22, 2014 at 19:00
  • @jxh In my case, it'd be the latter.
    – Vinayak
    Commented Dec 23, 2014 at 3:51

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In the context of explaining what has been taught in greater detail, consider expound:

2 : to explain by setting forth in careful and often elaborate detail <expound a law>
(Source: Merriam-Webster)

It could be used in your context in this way:

In this class, I shall expound the knowledge you have learned from your prerequisite courses.

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If you're looking for a colorful colloquialism, and the earlier topics which form the foundation of your later discussions are related to eminent historical personages (e.g. Newton's Laws, the Code of Hammurabi, etc), you could say you will be "standing on the shoulders of giants", a phrase which in the context of education is attributed to Isaac Newton:

If I have seen further it is by standing on the sholders [sic] of Giants.

The phrase is intended to convey that you'll be using the amazing work of earlier notable people as a basis or foundation for further exploration of similar themes or topics.

http://en.wikipedia.org/wiki/Standing_on_the_shoulders_of_giants

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  • Although I can't use it in this context, I find that phrase quite interesting. Thanks for sharing.
    – Vinayak
    Commented Dec 22, 2014 at 10:22
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If the dependency is solid/strict, then you can say that understanding the earlier topics is a prerequisite to learning about the later topics.

Sometimes this is formalized in terms of admission to courses: If you must have taken and passed course A before enrolling in course B then completion of A is a prerequisite to taking B.

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  • I know about prerequisite but that wouldn't work for my case.
    – Vinayak
    Commented Dec 21, 2014 at 5:50
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You could say that (the new instruction) "builds on a foundation established by" (the earlier traching)

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  • Thanks, but I've already found an answer in expand on as in "what we'll learn today will expand on the stuff we discussed last week."
    – Vinayak
    Commented Dec 21, 2014 at 5:58
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I'm probably entering the conversation a few years too late, but is "cumulative" the word/concept you're looking for?

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    Unfortunately, it's not but thanks for your answer. I decided to go with "expand" as in "topics we'll discuss today will expand on what we covered last week."
    – Vinayak
    Commented Aug 7, 2017 at 5:49
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Here is a possible sentence you could have said:

Today, as we progress sequentially through the course material, we will build on learning from our previous classes.

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