[I]'I have had an ambition to pursue a knowledge of Western art, philosophy and scientific thinking since I was a teenager, and am also ambitious to improve my English. I hope to continue pursuing this knowledge and my ambition.'
Ideally you shouldn 't keep repeating 'ambition'. Three times is too often in such a short passage. "The knowledge" implies all of the knowledge. That would be a big ambition!
I prefer to capitalise 'Western' and 'the West', when they have the political meaning, to distinguish it from just anywhere that's west of somewhere else.
Student or Learner