Wikipedia:Reference desk/Archives/Mathematics/2018 July 25

= July 25 =

Physical Reference od data differences
sir for a particular series of data i have open ,low,high data on a daily basis can any one tell me what is significance of 1.max(High data)-min(low data) 2.max(low data)-min(high data) 3.{max(High data)-min(low data)}-{max(low data)-min(high data)} thanks in advance 112.133.223.2 (talk) —Preceding undated comment added 09:09, 25 July 2018 (UTC)

Does Analysis includes Calculus or the other way around?

 * Analysis says that Analysis is the branch of mathematics that includes Calculus.
 * Template:Areas_of_mathematics says that Calculus is the branch that includes Analysis.

Which is which? 193.253.244.40 (talk) 14:40, 25 July 2018 (UTC)


 * Yes, unfortunately it is confusing. The analysis article is correct--calculus is part of analysis. The template is really a navigational aid for reader that places emphasis on familiar topics as headers for related topics--it's not meant to show a strict hierarchy. -- 18:51, 25 July 2018 (UTC)


 * In the sense those terms are used in undergraduate math education, first you take a calculus course and then you take an analysis course (meaning real analysis, i.e. analysis of functions on real numbers). The calculus course gives you a basic understanding of derivatives and integrals and how to compute them, along with some applications and maybe a little bit about differential equations.  Most everyone takes a course like that if they are studying a science-related subject.  Real analysis then repeats the basic theorems of calculus, except this time with very careful mathematical rigor.  It's Epsilon-Delta proofs almost from start to finish.  This course is usually only taken by math majors (correct me if I'm wrong).  Complex analysis usually comes in a "math major" version and a "science and engineering" version.  The "science and engineering" version is like the calculus course except it uses complex numbers, so you study topics like contour integration, but again mostly from a computational perspective.  The math major version is more proof-oriented, like real analysis. "Analysis" as a topic in math is large and basically covers everything involving continuous functions and derivatives, including everything in calculus.  But an "introduction to analysis" class would cover just a subset of the stuff that a calculus class would, instead examining that subset in very fine detail. 173.228.123.166 (talk) 04:10, 27 July 2018 (UTC)
 * I would put it a bit differently. I don't think either analysis or calculus is exactly a subtopic of the other.  Rather, analysis is the branch of knowledge that provides a foundation for calculus, but users of calculus may not particularly care.
 * Analysis is a discipline of research mathematics, in which new progress continues to be made. Calculus is a fairly unchanging collection of techniques for solving real-world problems.
 * You can "do" calculus without having any real understanding of analysis; without, indeed, even understanding at a deep level what a real number even is. The interpretation of exactly what you're doing may be a little fuzzy, but depending on what you want the results for, you may well not care.  Which is perfectly fine.  But does indicate to me that you're not really doing analysis, which is why I'm not inclined to agree that analysis "includes" calculus. --Trovatore (talk) 00:41, 29 July 2018 (UTC)

Monomorphisms of perfect groups
Let C be the full subcategory of the category of groups whose objects consist of the perfect groups (i.e. groups that are equal to their commutator subgroups). Does there exist a monomorphism in C that is not injective? The usual proof for the category of groups does not work because the group Z of integers (which is free on a single generator) is not a perfect group. GeoffreyT2000 (talk) 18:16, 25 July 2018 (UTC)
 * Not fully up on the terminology, but I take it that f injective is meant to mean f(x1)=f(x2) ⇒ x1 = x2 and f a monomorphism is meant to mean f(g1(x))=f(g2(x)) for all x ⇒ g1 = g2. So, as I understand it, you want perfect groups X, Y, a homomorphism f: X→Y with ker(f)≠1, so that if U is perfect with g1, g2: U→X, then f(g1(x)) = f(g2(x)) for all x implies g1 = g2. --RDBury (talk) 08:18, 26 July 2018 (UTC)