dear admissions committee members:
in my teaching career, i have rarely come across a student of xxx’s caliber. she is truly an outstanding student with the most creative ideas among all the students i have taught. additionally, xxx has a deep understanding of mathematics and possesses the ability to handle math problems flexibly. for example, she can solve algebra problems with her strong understanding of geometry. likewise, she can calculate and analyze geometry problems with algebraic principles. all in all, xxx is a very gifted problem solver in math.
xxx is not only excellent at solving problems, but is also interested in discovering and exploring creative solutions. for example, as the question of the relationship between golden section and fibonacci numbers was presented to her in my math course, she immediately went to the library after class to refer to mathematical history online, and ultimately formed a clear and systematic understanding of golden section.
the deepest impression xxx has left on me is her teamwork spirit and the ability to solve practical issues by applying her deep and broad understanding of mathematical knowledge. for example, in research studies, xxx picked up a subject called “the study on the rationality of the transportation on the intersection of five roads” with another six classmates. according to the individual characteristics of each classmate, xxx developed prominent leadership skills to divide her partners into groups in order to leverage the distinct traits of every team member and assign them tasks accordingly. thereafter, she analyzed the data collected from the groups and made a conclusion. after much discussion, she designed several analog solutions and wrote a report on the subject, which she then submitted to the traffic department in this district in the form of a proposal. it received a very good public reaction.
in conclusion, xxx is a uniquely talented young lady with excellent analytical aptitude and outstanding interpersonal skills. i therefore highly recommend her for admission to your esteemed program.
i am writing this letter of recommendation for mr.x,my former student. i have known mr. x for more than 6 years 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 no. 1 on this 270 hours course in the talented student class which has 34 intelligent 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 at 5 a.m. 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 the 1st 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.