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I study Mathematics and Statistics and one of the most common symbols we tend to write is μ which obviously is the lower case 'Mu'. It is one of the easiest symbols to learn when first encountered since it is so similar to u, both in writing and in the way it is pronounced. After all, 'Mu' and 'u' both have very similar pronunciations.

I have absolutely no experience in Linguistics, but I definitely know that the symbol W has its origins in Latin. Is there a similar connection in this case?

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    Answers given by others are fine, but I'd like to add the tidbit that while <µ> is not at all related to <u>, the modern Latin letters U, V, Y, W all derive from the Greek letter <Υ> (which became <V> in capital Latin script but was often written more rounded, like <u>, in cursive, eventually resulting in that becoming a distinct letter during the modern era, and which also produced <W> as a simple duplication mostly employed in Germanic languages; Latin <Y> was a simple re-borrowing from Greek by the Romans to transcribe actual Greek words). – LjL May 18 '17 at 20:09
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    It probably doesn't help that because of the visual similarity and the fact that "m" is taken for "milli--", "u" is used in place of "µ" as a shorthand for "micro--" when there's no easy access to Greek letters – Chris H May 19 '17 at 8:56
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    As an aside -- this letter can bite you if you take Latin-1-encoded text (which might include µ), convert it to Unicode, convert to uppercase, and then try to write that back as Latin-1 (containing Greek Capital Mu, "Μ", which looks like Latin Capital M "M" but isn't, and gives you a conversion error). This confused the heck out of me before I found the actual culprit. – DevSolar May 19 '17 at 9:18
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    @JDługosz: But if you do the uppercasing within Latin-1, it won't uppercase the µ (because in Latin-1 there's nothing to uppercase it to). I meant what I said. I encountered this in a software that takes virtually any input encoding, does internal processing in Unicode, and then converts back -- which, in this special case, failed, because no-one considered that in Unicode, µ can be uppercased, to something that is not available in Latin-1. – DevSolar May 19 '17 at 20:24
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No, there is no relationship. The lowercase form μ is just a calligraphic development of the uppercase form. Here's an illustration with colored dots to indicate the corresponding parts:

enter image description here

It's just a coincidence that this looks similar to the lowercase form "u" that developed from Latin "V". (Just as it's a coincidence that the middle of uppercase "M" looks like the letter "V".)

"Mu" is pronounced with an "u" sound simply because the second letter of the name "mu" is "u". This is a transliteration of the Ancient Greek name for the letter, "μῦ". I don't know the etymology of the Ancient Greek name; Wikipedia says it comes from Phoenician "mem". In Greek, it rhymes with the next letter, νῦ (from Phoenician "nun"); I would conjecture that this is part of the reason it was pronounced with the vowel υ instead of some other vowel closer to the one used in the Phoenician name, like ι.

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    I would also add that modern representation of μ by u which must have confused the OP is erroneous and non-etymological and was taken due to the visual resemblance. – olegst May 19 '17 at 10:35
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As you say, μ is the lower-case version of the Greek letter M. On the other hand, u is not Greek at all; it is Latin lower-case version of U or (in Classical Latin) V. There is no connection between the Greek M and the Latin V, either in shape, or pronunciation, or origin. They are two different letters.

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As @sumelic already explained, there is no historical relationship. The use of "u" instead of "µ" is an artifact of English-only character sets like ASCII. "u" is visually close enough to "µ" to be treated as a replacement. I know the usage specially from the short name of the MicroVAX II computer uVAX in the mid 1980's.

The use of "u" or even "U" instead of "µ" for the micro- prefix was sanctioned by some ISO standards dating back to early 1970's (See the article on Micro- on Wikipedia).

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No, in the same way ν is not related to v.

μ is based upon Μ, and M is more closely related than u is.

Let's compare it to a false cognate.

U comes from Greek Υ

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