Given a sentence in Tagalog language, translate the sentence to English language keeping the meaning of the original sentence intact.

[Q]: Tagalog sentence: Siya napili algebra bilang kanyang espesyalidad, superbisor sa kanyang pagiging DK Faddeev.
[A]: He chose algebra as his speciality, his supervisor being D K Faddeev.


[Q]: Tagalog sentence: a) Kung, Patunayan na may mga pagbabagong mula na para sa bawat permutasyon, May index iyon may karaniwang puntos.
[A]: a) If, prove that there are permutations from that for each permutation, there is an index that have common points.


[Q]: Tagalog sentence: Tsokolate PB2 ay halo-halong sa tubig upang lumikha ng isang tradisyonal na tsokolate at peanut butter pinaghalo.
[A]:
Chocolate PB2 is mixed with water to create a traditional chocolate and peanut butter mixture.