dear prof. xxx:
i am a postgraduate student of （硕士毕业的专业、学校）, i went to your class and deeply touched by your wisdom and academic thoughts. i had the pleasure of reading your book （导师著作）, and can’t be more agree with your point of view and admire very much on your academic level. i would apply for your doctoral student of（考博的专业）.
my postgraduate tutor is professor xxx, and （硕士时期的研究方向） is my research direction. during my graduate study, i participated in many subjects, including （硕士时期做过的各项研究）. i have accumulated a lot of experiences about scientific research.
thank you very much for reading my letter , if given a chance to pursue advanced studies, i would highly appreciate. i'm looking forward to hearing from you.