Wikipedia:Reference desk/Archives/Mathematics/2014 September 19

= September 19 =

is midrange = midpoint?
2 requests:
 * 1) Prove $$(max-min)/2 + min = (max+min)/2$$.
 * 2) Is Midrange = Midpoint?174.3.125.23 (talk) 11:23, 19 September 2014 (UTC)


 * 1)


 * 2) The midrange is a statistical concept while the midpoint is a geometric one. So, they wouldn't normally correspond.  However, if you represent data on a number line, and draw a line segment from the minimum value to the maximum to represent the range, then the midpoint of that line segment is indeed the midrange. StuRat (talk) 13:08, 19 September 2014 (UTC)


 * 1) LHS=
 * $$ \frac{max-min}{2} + min = \frac{max}{2} +(min-\frac{min}{2})

=\frac{max+min}{2}$$ AmRit GhiMire &#39;Ranjit&#39; (talk) 13:30, 19 September 2014 (UTC)
 * What is "LHS"?
 * Prove $$ \frac{max-min}{2} = \frac{max}{2} - \frac{min}{2}$$174.3.125.23 (talk) 10:44, 20 September 2014 (UTC) — Preceding unsigned comment added by 174.3.125.23 (talk) 10:43, 20 September 2014 (UTC)
 * LHS = Left Hand Side
 * See distributive law, more or less.
 * — Arthur Rubin (talk) 15:14, 20 September 2014 (UTC)

AntiDerivative
As we have


 * $$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.$$

Is there any simple way for calculating
 * $$ \int f(u)\ \mathrm{d}x$$

AmRit GhiMire &#39;Ranjit&#39; (talk) 12:08, 19 September 2014 (UTC)


 * You can try substitution but that only trades one integral for another. In general antiderivatives are inherently more difficult than derivatives. As another example, the product rule allows you to compute the derivative of a product in terms of the derivatives of the factors, but the closest thing for antiderivatives is integration by parts which, again, only trades one integral for another. --RDBury (talk) 16:28, 19 September 2014 (UTC)


 * I assume you mean f(u), where u=u(x). See Integration_by_substitution. Note that the way this is usually described is taking something of the form $$ \int f(x)\ \mathrm{d}x$$ and re-writing it as $$ \int g(u)\ \mathrm{d}u$$. SemanticMantis (talk) 17:07, 19 September 2014 (UTC)


 * Actually I need Antiderivative of : $$ \int f(u)\ \mathrm{d}x$$ in such a form that can be used without human intelligence. Actually I need it for developing algorithm or computer program for antiderivative. AmRit GhiMire &#39;Ranjit&#39; (talk) 00:31, 20 September 2014 (UTC)


 * If the derivative of u with respect to x can be written as a function of u,
 * $$ \int f(u)\ \mathrm{d}x = \int \frac {f(u)}{u'(x)}\  \mathrm{d}u$$
 * Is that what you are looking for? — Arthur Rubin  (talk) 15:12, 20 September 2014 (UTC)
 * Not exactly coz the variable in which function to be integrated and the variable w.r.t which derivative is not same.I mean $$ either \int g(u) {d}u      or \int g(x) {d}x$$ AmRit GhiMire &#39;Ranjit&#39; (talk) 13:47, 23 September 2014 (UTC)

"loops" in common-core math
A friend of mine asked: "What are 'loops' in common core math--to replace the times-tables? 8x7=56, 8x8=64, etc." I've never heard it before. What is it? Bubba73 You talkin' to me? 17:46, 19 September 2014 (UTC)


 * The mathematical 'loops' I know about are all covered at the disambig page loop. But I don't think any of those are likely candidates. So I don't know the answer, but let me clarify something: Common_Core_State_Standards_Initiative is a set of standards that basically try to outline what each child should be expected to know at the end of each grade. It says absolutely nothing about pedagogical technique, specific course design, textbook choice, etc. My point is, I don't think the CCSSI documents say anything at all about 'loops' in math education -- but that doesn't mean that some text book doesn't use that word as a means of teaching multiplication... Unfortunately, many weird and shoddy textbook companies have rushed to slap CCSI stickers on their newest books. This often leads to people conflating problems with the book with problems about common core. I could probably give you a better answer with a little more context, such as the name of the book and the grade level of the student. SemanticMantis (talk) 19:45, 19 September 2014 (UTC)


 * One type of loop in grade school math is the iterative scheme used in manually carrying out long division, see How to Do Long Division. The other kind of loop I have seen is cycling through flash cards to learn math facts--perhaps it is an alternative to staring at a multiplication table? --Mark viking (talk) 20:56, 19 September 2014 (UTC)


 * I suppose this method of manually multiplying 8×7 could be called "loops":


 * 1) Start with 0.


 * 2) Add 8 seven times.


 * Obviously one of the numbers has to be quite small for this method to be practical. StuRat (talk) 21:20, 19 September 2014 (UTC)


 * Flash card: loop and say 86.146.61.61 (talk) 22:12, 19 September 2014 (UTC)


 * Where did you see the term being used? I would guess like the others they are referring to looping as in programming so they are counting the number of times something is added to produce the product of a multiplication. Dmcq (talk) 22:13, 19 September 2014 (UTC)


 * My friend thinks StuRat is right. He got it: "Some woman at the antiques show telling about the Common Core math idiocy in FLA (and elsewhere)." Bubba73 You talkin' to me? 03:04, 20 September 2014 (UTC)

Peasant's algorithm. If A is even then $$A\times B = (A/2)\times (2\times B)$$ and we can compute $$2\times B = B + B$$. If A is odd then we have $$A\times B = B + ((A-1)/2))\times (2\times B)$$. But you can cut this short when you see a simple multiplication in the process. Example:

23*31 = 31 + 11*62 = 31 + 62 + 10*62 = 713

Count Iblis (talk) 19:19, 23 September 2014 (UTC)