The proper revision of the given sentence is: My classes for this semester are algebra, music, history, and writing
This refers to the editing of a text by the addition of a word(s) or phrase(s) and removal of obsolete ones.
Hence, we can see that when the original sentence is edited, the use of "is" is replaced with "are" as the speaker is referring to multiple items and hence they have to be in the plural form.
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