Keeping an updated tally of changing records - sql

Question

I have a list of students and their subjects:
id | student | subject
---|---------|--------
1 | adam | math
2 | bob | english
3 | charlie | math
4 | dan | english
5 | erik | math
And I create a tally from the above list aggregating how many students are there in each subject:
id | subject | students
---|---------|--------
1 | math | 3
2 | english | 2
The student list will keep on expanding and this aggregation will be done at regular intervals.
The reason I'm keeping the Tally in a separate table in the first place is because the original table is supposed to be massive (this is just a simplification of my original problem) and so querying the original table for a current tally on-the-fly is unfeasible to do quickly enough.
Anyways, so the aggregating is pretty straight forward as long as the students don't change their subject.
But now I want to add a feature to allow students to change their subject.
My previous approach was this: while updating the Tally, I keep a counter variable up to which row of students I've already accounted for. Next time I only consider records added after that row.
Also the reason why I keep a counter is because the Students table is massive, and I don't want to scan the whole table every time as it won't scale well.
It works fine if all students are unique and no one changes their subject.
But it breaks apart now because I can no longer account for rows that come before the counter and were updated.
My second approach was using a updated_at field (instead of counter) and keep track of newly modified rows that way.
But still I don't know how to actually update the Tally accurately.
Say, Erik changes his subject from "math" to "english" in the above scenario. When I run the script to update the Tally, while it does finds the newly updated row but it simply says {"erik": "english"}. How would I know what it changed from? I need to know this to correctly decrement "math" in the Tally table while incrementing "english".
Is there a way this can be solved?
To summarize my question again, I want to find a way to be able to update the Tally table accurately (a process that runs at regular interval) with the updated/modified rows in the Student table.
I'm using NodeJS and PostgreSQL if it matters.

Answer 1

Why don't you do it when student add subject, remove subject, or change subject.
When student add new subject: Just increase UPDATE tbl_tally SET student = student + 1 WHERE subject = :subject;
When student remove subject: Just decrease UPDATE tbl_tally SET student = student - 1 WHERE subject = :subject;
When student change subject: Just increase new subject by one and decrease old subject by one
UPDATE tbl_tally SET student = student - 1 WHERE subject = :old_subject;
UPDATE tbl_tally SET student = student + 1 WHERE subject = :new_subject;
I am not familiar with PostgreSQL, but in MySQL, you can even do it with trigger. I think PostgreSQL also has trigger.