we establish some results from linear algebra

[YAMATO2201]

Please look at the following sentence of mine.

In this section, we establish some results from linear algebra, starting from the universal definition of tensor products of vector spaces over the real number field ℝ.

Should I retain the second comma?

 

[YAMATO2201]

Yes, but you don't need the first one after "section".

Thanks, Robert. :-D

1) In this chapter we discuss singular homology groups.

2) In this chapter, we discuss singular homology groups.

Do you think #1 is stylistically better than #2?

 

[Raymott]

It may be stylistically better in most cases, but it's not the only way to go. To me, the comma is optional.

 

[YAMATO2201]

It may be stylistically better in most cases, but it's not the only way to go. To me, the comma is optional.

3) Obviously Mary has changed her mind.

4) Obviously, Mary has changed her mind.

I prefer #4 to #3. What about you?

 

[jutfrank]

This time the comma is necessary since Obviously is a comment adverb.

 

[YAMATO2201]

Obviously I’ll have to think about your offer carefully.
https://www.macmillandictionary.com/dictionary/british/obviously?q=Obviously+

Obviously we'll have to finish this part of the course before we can begin the next one.
http://www.wordreference.com/definition/obviously

Are these sentences incorrect?

 

[YAMATO2201]

Obviously is a comment adverb.

Theoretically, the value of the funds could triple in the next few months.
http://www.learnersdictionary.com/definition/theoretically

Is Theoretically a comment adverb?

 

[jutfrank]

Obviously I’ll have to think about your offer carefully.
https://www.macmillandictionary.com/dictionary/british/obviously?q=Obviously+

Obviously we'll have to finish this part of the course before we can begin the next one.
http://www.wordreference.com/definition/obviously

Are these sentences incorrect?

Yes. Like I said, Obviously is a comment adverb so they need commas.

 

[jutfrank]

Theoretically, the value of the funds could triple in the next few months.
http://www.learnersdictionary.com/definition/theoretically

Is Theoretically a comment adverb?

Think of a comment adverb as providing the speaker's attitude towards what he's saying. There could be sentences where theoretically is not doing this, but in this sentence it probably is.

What's important is that it relates to the entire clause that follows, so when it begins a sentence it needs a comma after it to show this.

 

[jutfrank]

"The value of the funds could theoretically triple in the next few months."

Would you put a comma after 'theoretically' here?

The adverb is not being used at the beginning of a sentence.

 

[YAMATO2201]

Theoretically, the value of the funds could triple in the next few months.
http://www.learnersdictionary.com/definition/theoretically

Is Theoretically a comment adverb?

"The value of the funds could theoretically triple in the next few months."

Is 'theoretically' a comment adverb?

Without more context, I would assume the Theoretically in the dictionary example is being used to give the speaker's comment or opinion on the rest of the sentence.

I suppose your version is not necessarily the speaker's comment or opinion. It might be a quotation from somewhere.

Would you put a comma after 'theoretically' here?

No, I wouldn't.

 

[YAMATO2201]

Think of a comment adverb as providing the speaker's attitude towards what he's saying. There could be sentences where theoretically is not doing this, but in this sentence it probably is.

What's important is that it relates to the entire clause that follows, so when it begins a sentence it needs a comma after it to show this.

I just came up with the following example sentences.

5) Clearly, he explained it. (Clearly is a comment adverb.)

6) He explained it clearly. (clearly is not a comment adverb.)

 

[jutfrank]

I just came up with the following example sentences.

5) Clearly, he explained it. (Clearly is a comment adverb.)

6) He explained it clearly. (clearly is not a comment adverb.)

Yes, you're right that clearly in each sentence has a different use.

In 6), you could class this use as an adverb of manner. It says how he explained it.