Hi, I have a problem with the homework: "Vowel harmony in noun sentences". 
In the example 1 at the second sentence (noun sentences) there is written: Ben öğrenciyim. But I understood that for the vowel rules if the suffix start in -i and the word finish with vowel (-i group), I drop one of the vowels. So, why is not: öğrencim? Thank you!

Öğrencim=my learner

Öğrenciyim=i am learner

You can see explanations here:

http://www.turkishlanguage.co.uk/tobepos.htm

http://www.turkishlanguage.co.uk/possadj.htm

http://www.turkishclass.com/turkish_lesson_125

As explained by Turkish 2412, there is a difference between noun sentences and possessed nouns for adding suffixes.

öğrenci = student (noun)

(Ben) öğrenciyim = I am a student (noun statement)

(Ben) öğrenciydim = I was a student (noun statement, past tense)

(Benim) öğrencim = My student (noun)

(If you were a teacher talking about a student of yours, you would use this form)

Kedi = cat (noun)

(Benim) kedim = my cat (possessed noun)

(Onun) kedisi = his/her cat (possessed noun)

(Ben) kediyim = I am a cat (noun statement)

(Maybe if you were in the play "Cats", you might be able to say this)

Hope this doesn´t confuse you. 

The suffixes are different.

-m is possessive, -im is personal suffix. This difference is clearly seen at the vowel-ended words.

öğrenci+m----------------------------->öğrencim (my student)

öğrenci+im----------------------------->öğrenciyim (i´m student)

doktor+m------------------------------>doktorum (my doctor)

doktor+im------------------------------>doktorum / ben doktorum (i´m doctor)

I thought you get confused about the combinative letter "y".

http://www.turkishclass.com/turkish_lesson_254 (n, s, ş and y)

and about the suffixes:

http://www.turkishclass.com/turkish_lesson_258 (personal suffixes)

http://www.turkishclass.com/turkish_lesson_259 (possessive suffixes)