tag:blogger.com,1999:blog-3722233.post8053688063665145317..comments2024-03-18T23:13:09.570-05:00Comments on Computational Complexity: What to call the top and bottom part of (n choose k)Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3722233.post-69205372230521217822014-07-25T04:16:41.353-05:002014-07-25T04:16:41.353-05:00Thanks for this post. Seems like there’s always so...Thanks for this post. Seems like there’s always something new I learn even after being in the field for 25 years.e.l.http://www.cocoon-bobbin-oil.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-52711911163671884742014-07-15T03:17:55.996-05:002014-07-15T03:17:55.996-05:00Well, the poll may be closed, but I would suggest:...Well, the poll may be closed, but I would suggest: the top index, the bottom index. This requires forgetting the old C^k_n ... ^^Anonymoushttps://www.blogger.com/profile/07053643846148626100noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-92135356182647150302014-07-14T17:01:15.457-05:002014-07-14T17:01:15.457-05:00You raise an interesting distinction. My intent wa...You raise an interesting distinction. My intent was what to use for the top and bottom part in our papers that we write. I've never had to refer to the top or bottom part in a classroom. However, once something is common in papers it might end up getting spread into the classroom. And I certainly agree that this would be a terrible terminology for students.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85018527769077647542014-07-14T13:32:19.751-05:002014-07-14T13:32:19.751-05:00Math notation for many is already too complex. Man...Math notation for many is already too complex. Many of the suggested names fail to take into any account the actual pedagogy for future understanding of the mathematics involved.<br /><br />For such a simple and fundamental notation which has broad use in "lower level" mathematics and is therefore accessible to a much broader range of people, calling them numerator and denominator seems highly disingenuous! Though on some level, the written notation for \binom {a}{b} might seem to logically "suggest" calling them numerator and denominator, I would warn against it - particularly as this logic is more likely to come from neophytes and is far more likely to confound them when defining the notation with respect to the actual definition which really does have a traditionally defined numerator and a denominator. <br /><br />The alternate category of notations in the vein of C(n,k) screams out to call both n and k INDICES! The notation really stands for an actual numerator and denominator, namely: \frac{n!}{k!(n-k)!}. Thus there is already a numerator here: n! and a denominator k!(n-k)!. Calling n a numerator and k the denominator is likely to throw off FAR too many students starting out in what is an important area of mathematics. If forced to make a choice (pun intended) other than indices, the concept of calling them something like "outcomes" and "possibilities" makes far more logical sense in terms of what is actually taking place. Otherwise, perhaps a nomenclature like: "top partition"/"bottom partition" would make more logical sense for the processes that these notations are used within?<br /><br />Mathematics if far too logical a field for us to be so careless with our nomenclature. Most of its point is to be increasingly more specific in our thought while still allowing broad enough generalizations to categorize like things as like. Calling n and k numerator and denominator runs counter to both of these goals.Chris Aldrichhttps://www.blogger.com/profile/13031382155173157140noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-4367484829352660562014-07-14T12:43:32.600-05:002014-07-14T12:43:32.600-05:00FIxed, Thanks.
FIxed, Thanks.<br /><br />GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-62079216680704768802014-07-14T10:59:53.552-05:002014-07-14T10:59:53.552-05:00The typos in this post (in item 5 and the winner) ...The typos in this post (in item 5 and the winner) are more confusing than usual.Anonymousnoreply@blogger.com