The recommendation letter to the esteemed program, how to improve quality of this letter?

the first letter

To Whom It May Concern,

I deem it a great pleasure to recommend Ye Gao, one of my favorite students to your esteemed program. As his class adviser, I have known Ye Gao since he entered our university. In the second semester of his sophomore year, I taught him the course of Financial Market. I also served as his graduation thesis advisor. Therefore, I'm well acquainted with this excellent student.

Ye Gao is an intelligent and diligent student. He could quickly comprehend what I taught. He always responded to me actively in class. From his original answers, I can tell that he has a profound knowledge foundation, which is inseparable from his extensive reading and in-depth thinking. What's more, he can flexibly use what he had learned into practice. After class, he often discussed with me his opinions about the current status of the china stock market that he paid special attention to. With the learned knowledge, he could make comprehensive analysis of its development trend and make correct prediction. Therefore, I think with such a clever mind, Ye Gao can accomplish his graduate study successfully.

I also want to highly praise his creative mind and strong independent learning ability. During his preparation for the graduation thesis, he made a brave attempt, tried to analyze the enterprises' M&A financing with the Logistics Regression Model. To the students of our school, it is a totally new method that they had never used before. And to master this method within a limited time was a heavy task. But Ye Gao thought it is the most propitiate method for his research. So he started to learn it by himself. In face of the difficulties, he didn't give up and kept on trying. Finally, he mastered the Logistics Regression Model in quite a short time and completed his thesis in high quality. Meanwhile, the analysis method that he used is so innovative that it became one highlight of his thesis.

Ye Gao's outstanding performance both in and after class proved to me that he is a talented student with strong learning ability and great potential. Therefore, I strongly recommended Ye Gao as a competitive candidate to your esteemed program. I have confident that this brilliant student will become a prominent student of your program. If you need more information about Ye Gao, please feel free to contact me.

Best regards,

the second letter

No more than one essay at a time, please!

Really thank you for your help.

Hi, I think the letter is actually quite well-written with very few grammatical errors. It does seem a little excessive in some areas - maybe that is the accepted status quo among these recommendation letters, I don't know. Anyway, here are some more specific suggestions:

I deem it a great pleasure to recommend Ye Gao, one of my favorite students[,] to your esteemed program.

... I taught him the course of Financial Market. {I would give the official course number - maybe "I taught hime Intro to Financial Markets 501"} I also served as his graduation thesis advisor.

... I can tell that he has a profound {"profound" just sounds a little excessive to me} knowledge foundation, which ...
What's more, he can flexibly use what he had learned into practice. {you "put into practice", not "use into practice"}

... current status of the [C]hina stock market that ...
With the learned knowledge, {"learned knowledge" sounds redundant} he could make comprehensive (...) and make correct prediction[s ].

... he made a brave attempt, {"brave attempt" usually implies that you failed at the attempt, although it was a good try} tried to analyze the ...

... So he started to learn it by himself. In [the] face of th[ese] difficulties, he didn't ...
... and completed his thesis in high quality.{"in high quality" sounds odd}

... I have confide[nce] that this brilliant student will ...