How to use commas around the word "both"?
Solution 1:
"This includes strengthening my knowledge in the fundamental subjects of this field, and gaining more experience in both robotics research as well as the implementation of developed theory on physical robotic systems."
No commas are needed. It sounds odd with "both" and "as well as" together. I recommend one or the other:
.. gaining more experience in robotics research as well as the implementation of ..
.. gaining more experience both in robotics research and the implementation of ..
It seems kind of strange to have a very general first statement followed by a very specific and technical second statement. If I was submitting this in a cover letter, I would join the two ideas together:
"This includes strengthening my knowledge and experience in both robotics research and implementation of developed theory on physical robotic systems."
Solution 2:
You need no commas around both.
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Both ... as well as is not a legitimate construction. As well as is not a conjunction like and: it is a complex preposition like in addition to (and with a similar meaning). It is not employed to include something within a construction but to append something (often something previously mentioned) to a construction which is complete without it, in the manner of an afterthought
RULE OF THUMB: Employ as well as only if you can enclose the construction it heads within parentheses.
Having mastered both German and French (as well as his native English), William felt well prepared to tackle the literature on the subject.
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There are far too many nouns and nominals for this sentence to read gracefully. Try to use more verbs and clarify your structure:
I hope on the one hand to strengthen my knowledge of fundamentals in this field, and on the other to gain practical experience both by conducting original research and by implementing established theory on physical systems.