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A 'simple' Physics postulation...

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TimFox:
My undergraduate education required several specific mathematics courses to qualify for a physics major.  The epsilon-delta method for defining and proving limits was an important part of that syllabus.
I do not think "it's fair to say" that there are not many physicists who have studied formal definitions of limits or epsilon-delta arguments, even if our expertise and study is limited compared with that of professional mathematicians.

dietert1:
Absolutely. In fact, as you explained before, often enough physicists invented new calculus to model reality and only after that mathematicians got interested. Sometimes mathematicians invent entities that no physicist will ever need. But you can't know in advance. Sometimes instances of those constructs were found in nature later on. One example i remember are certain types of mathematical groups useful to discover families of fundamental particles. Hope that's correct.

Regards, Dieter

TimFox:
This reminds me of my first year in graduate school, before I married, when I lived in a dorm with other graduate students in many different departments.
One mathematics student, who was otherwise a nice guy, did not like that the Mathematics department was in the Division of Physical Sciences (along with Physics, Chemistry, etc.), since he considered Mathematics to be one of the humanities (that happened to be sometimes useful to us scientists).  He was proud (and smug) that his two personal interests were of no use to science:  differential geometry and topology.  I had to disillusion him, since differential geometry is at the heart of Einstein's formulation of General Relativity, and topology was used in Feynman diagrams. 
I did not pursue particle physics, but group theory is very important to that discipline.
(When Werner Heisenberg said to me, and the other thousand guys in the auditorium, that he saw no reason why particle physics should be less complicated than quantum chemistry, I lost interest in that field.)

aneevuser:

--- Quote from: TimFox on July 13, 2021, 05:17:25 pm ---My undergraduate education required several specific mathematics courses to qualify for a physics major.  The epsilon-delta method for defining and proving limits was an important part of that syllabus.
I do not think "it's fair to say" that there are not many physicists who have studied formal definitions of limits or epsilon-delta arguments, even if our expertise and study is limited compared with that of professional mathematicians.

--- End quote ---
It'll vary from country to country, of course, and from university to university, and from precise course to course (and probably from decade to decade), but certainly in the UK, there are plenty of universities where a physicist won't formally study limits (and definitely won't study construction of the reals, or anything like that, which is certainly 19th C mathematics), and I suspect very few where the typical engineering student would formally study limits - they may have a brief intuitive overview of the idea of a limit, but most won't need anything more. Plenty will need to learn some "find the limit" techniques, of course.

In terms of numbers having studied such stuff, physicists are something of an intermediate case though, between mathematicians and engineers. If I had to summarise, I'd say I wouldn't be surprised if a physicist told me that they had studied epsilon-delta proofs, and I would be surprised if an engineer had.

TimFox:
Your last sentence is a more reasonable statement than your earlier statement "I think it's fair to say. You won't find many 'users of mathematics' (physicists, engineers, etc) who have studied formal definitions of limits, ...  But I don't think it matters too much, most of the time; you don't need to be able to make an epsilon-delta argument"
My personal experience is that we used epsilon-delta arguments in freshman calculus class, probably in the first academic quarter, to prove limits as part of understanding the nature of the differential calculus, etc.  (Perhaps times have changed since 1967.)  We did have one math-department course on "applied mathematics for scientists", but the other required courses were taken by science and math majors alike.  My undergraduate college did not have an engineering school, but some physics students went on to engineering school after graduation.  The epsilon-delta argument is not very difficult.

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