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Dear Sir/Madam,
I am currently pursuing a Bachelor's Degree in Computer Science and Engineering at The People's Education Society Institute of Technology (India). I am delighted at the prospect of spending my summer break soaking up the latest advancements in technology and German culture at TUM. The reason I am so deeply keen on studying in Germany is not only because I have been studying German under a private tutor for a few months now and want to study under a native speaker, but also because I did not have much time to interact with the local people of Germany and experience the education system during my short stay in June 2010.
My main interests are in the analysis and design of algorithms, digital design, linear algebra and on a completely different note, ‘Lernen, wie man Deutsch sprechen'.
I have chosen TUM's Summer University because I am convinced that it will broaden my thinking and expand my skill set by exposing me to the Automotive Industry, Business Management and best of all, German.
Besides taking courses at TUM, I also look forward to the opportunity to meet new people from various backgrounds. Listening to their multiple points of view will help me become a better Engineer.
Yours Faithfully,
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Your letter is very nice.
I would not capitalize the words "Automotive Industry, Business Management" and "Engineer."
I would set off the phrase "on a completely different note" with commas (both before and after).

Otherwise, I like the tone and the brevity. (I cannot comment on the German!)

Regards,
A-Emotion: stars
Comments  
I need some help with this letter. Can any of you tell me how I can make it better?
Thanks
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 AlpheccaStars's reply was promoted to an answer.
I made a few changes, keeping your suggestions in mind. Please let me know if it is better now. Thank you so much!

I have chosen TUM's Summer University because I am convinced that it will broaden my 
thinking and expand my skill set. I want to witness the best that the automotive industry has to offer, understand the fundamentals of project management, and most of all, learn how to communicate in German.

Besides taking courses at TUM, I also look forward to the opportunity to meet new people from various backgrounds. Listening to their multiple points of view will help me become a better engineer just as they will benefit by listening to mine.
I will be a very active and enthusiastic participant if I am selected. Thank you for your time and consideration.
Yours Faithfully,
It's fine, although I have a reaction to this sentence:
AnonymousListening to their multiple points of view will help me become a better engineer just as they will benefit by listening to mine.
I'm sure your multiple points of view will benefit others, but the statement might be taken by some readers as a bit arrogant or presumptuous.
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Thank you AlpheccaStars! I will edit that sentence!