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I am writting an essay about a reseach topic on Computer Science and a doubt has arisen about the usage of the word 'following' as an adverb. For instance, consider the following sentence: "We following present the concepts related to software testing at Chapter 1 and Chapter 2.". It is correct to use "following" as an adverb in such situation? If not, what would be a better construction ('Following, we present the concepts...')?
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Hi, Magsilva, Welcome to English Forums. Thanks for joining us!

I've never heard the usage you propose. Your alternative sounds possible, but I've never heard that either.

I'd probably say, "We present these concepts related to software testing at Chapter 1 and Chapter 2, as follows:"

Best wishes, - A.

Edit.

I'm still puzzling a bit over your intended meaning for "testing at Chapter 1 and Chapter 2."

Is that where the testing is to be done? Are Chapters 1 & 2 a part of your essay?

Perhaps you should clarify this. I can only guess at your meaning, and this might affect the appropriateness of my original reply. - A.
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AvangiIs that where the testing is to be done? Are Chapters 1 & 2 a part of your essay?
Yes, chapters 1 and 2 are part of my essay. The paragraph with the sentence in question describes the organization of my dissertation (i.e., a brief description of the content of the each chapter).
If you intend to preview the concepts immediately following the sentence in question, I'd be inclined to say something like,
In Chapter 1 and Chapter 2 we will present the following concepts related to software testing: Blah blah etc. etc. (here they are).

Or alternatively, "The following concepts related to software testing will be presented in Chapter 1 and Chapter 2 (or Chapters 1 and 2):"

Somehow, I still feel uncomfortable with the function of the sentence.

Best of luck, - A.

(Sorry about the edits. I'm still waking up!)

I guess you caught my point about the preposition "at."

We are presenting such and so at chapter one. The "at" seems unnatural to me. We'd usually say "in."
AvangiI guess you caught my point about the preposition "at."
Yes, I got it. I will review my text and fix that. Thank you Avangi!
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Hi again. I probably shouldn't have changed your tense to future in these suggested versions:

In Chapter 1 and Chapter 2 we will present the following concepts related to software testing: Blah blah etc. etc. (here they are).

Or alternatively, "The following concepts related to software testing will be are presented in Chapter 1 and Chapter 2 (or Chapters 1 and 2):"