dear sir/madam:
　　i am writing this letter of recommendation for ,my former student. i have known mr. x for more than6years since his freshman year at "university of minnesota". at that time, he took the course-- "mathematical analysis," which i taught mainly for junior students majoring in mathematics. to my surprise, i found he was among the few students in his class who could keep up with the pace of my lectures. moreover, he often posed thought-provoking questions during the course. thus it was natural that i liked discussing with this young man and became familiar with him. the more i knew him, the more i found he was talented at mathematics. as you can see, he got excellent scores on the course. in fact, he ranked this270 hours course in the talented student class which has34intelligent others.
　　with his outstanding talent and solid mathematical background, he also did quite well in most other courses during his undergraduate study. by the way, you may wonder why his undergraduate scores look not so good compared to other chinese applicants. it is easy to explain, because he belonged to the talented student class, which were required to endure harder test papers and stricter grading than most other college students did at least at "university of minnesota".
　　he even served as prof. linda 's research assistant for one year. no one could deny his commitment to his job. as a matter of fact, prof. linda's electronic lab happened to be neighboring my office and i could always see him working in the lab, either repairing the instruments or helping prof. linda collect lab reports. maybe one more example will demonstrate his commitment more clearly. once he suggested compiling a fortran program to solve a complicated circuit problem in his class. in order to do that, he had to do a lot of computer work. however, because there were few computers available in our computer lab, he had to wake up at5. in winter (please note: "twin city" is a downtown near the north border of china, so it is pretty cold in winter and the heating system is not working very well.) to ensure the1st position of the long waiting line for his classmates and himself! at last he and his classmates finished the program successfully with his great efforts.
　　as to his personality, i would like to say mr. x is a warm-hearted, honest and upright student. he was always ready to help others. during my lectures, many students got confused at some points and i could always see mr. x help them explain during breaks. in the meanwhile, i must admit that mr. x was a bit impatient sometimes.