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.
尊敬的領導：
您好!
首先感謝您在百忙之中瀏覽我的推薦信。今向貴單位推薦我系畢業生xx同學。
該生是我校數學專業的畢業生, 希望貴單位能接納她成為其中的一員。
她非常聰明，她的抽象推理能力高於她的同齡人。我還記得每次上課提問的時候都是她首先舉手回答問題。除了這個，她渴望學習，平時會有許多創新的想法，其中一些反映了她的獨創性和獨立思想。她勤學好問，喜歡思考。在課程結束時，她取得了98的高分，超過了班上其他同學。她認真學習專業知識，並多次獲得獎學金。
在學校和班級的各種活動中積累了一定的經驗，使自己具有良好的身體和心理素質，且有很好的溝通和適應能力。
自入校以來，經同學選舉，她擔任了班級團支部組織委員，具有一定組織領導能力。任職以來，她積極配合校、系分團委的各項工作，因時制宜地開展各種校內外活動，拓寬了大家的視野，豐富了大學的學習生活，多次被評為校優秀幹部，受到全校師生的好評。通過參加學校和班級的各種活動她積累了一定的經驗，使自己具有良好的身體和心理素質，且有很好的溝通和適應能力。
總之，該生是一位符合現代化要求的全面發展的大學生。現在該生渴求能到貴單位去工作，使所學的理論知識與實踐有機地結合，能夠使自己的人生有一個質的飛躍。望貴單位予以重點考慮，她一定會不負您的重託!
感謝您在百忙之中讀完這封推薦信，誠祝事業蒸蒸日上!
推薦人：xxx
3月27日
尊敬的xxx:
xx外國語學校的數學教學水平很高，在高一高二兩年就完成了整個高中所要求的所有數學課程，並在此基礎上有所拓展。雖然課程難度較高，但xxx的課業表現十分突出，在年級排名前5.
在數學學習上，xxx有極大的熱情，在課堂上，她總是聚精會神的聽講，做筆記時，在每道題後面，都會習慣性空出10餘行。課下，她在與同學討論自我回顧時，在空白處再記錄下自己的認識。她經常會把筆記進行整理分類，遇到問題是會到辦公室來向我請教。這樣的筆記大大提升了學習效果，我還在班級里向同學們推薦xxx的學習方法，號召大家向她學習。在完成課後作業時，我會布置一些挑戰性的難題，xxx經常能夠想出多種不同方法解決問題。
為了拓寬學習視野和思路，xxx每天還會進行課外學習，期間她完成了許多具有一定難度和較大靈活性的習題。她還會與我交流有關問題的學習心得，有時候還會提出對課程教學該進的建議。我發現這位學生對數學有較深刻和獨到的理解，這是班上大部分學生所欠缺的。
xxx對於數學的熱情，再加上她的學習能力，使她在數學課程中保持了一貫的優秀，還多次在學校學科競賽取得好成績。
推薦人：xxxdear sir/madam:
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.
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