Is it not effective to learn math top-down?

Question: By top-down I mean finding a paper that interests you which is obviously way over your head, then at a snail's pace, looking up definitions and learning just what you need and occasionally proving basic results.  Eventually you'll get there but is this a bad idea?  Is learning each required math area by textbook the better way?
Comment: Trying to learn this way is a very good way to discourage oneself. I have been in this position before and it made me doubt myself and my abilities. I'm not a geometer by any means but the research my former advisor does has a lot of noncommutative geometry. Unfortunately, I was far from being able to read any of the standard texts and so I struggled with reading papers. I really started to doubt myself and I wanted to give up on several occasions. I don't recommend it - even for bright students. It's better to build up to it while still challenging oneself.
Comment: I tried to understand Wiles' paper (FLT) top-down and am still on the first sentence of math. :P
Comment: I could never be interested in the top without understanding what comes before it, but that's just me.
Comment: I respectfully counter @CameronWilliams point--I say it can be helpful, but it should have limits.  As an undergraduate CS student, it would probably be a bad idea for me to start with elliptic curves in number theory and work backwards from there.  But, **smaller steps** can be taken in a "top down" approach--for example, I could start by wanting to learn prime factorization, and proceed to elementary number theory (e.g. starting with modular arithmetic). That has a shorter "tree" of prerequisite topics, and won't leave me feeling discouraged. It's all about how much you take off in one bite.
Comment: I like to keep such papers around as a reminder of what I still need to learn: I'll occasionally pick them up, see if I understand anything else, check a few references, then go back to beefing up my "classical" skills.  Lather, rinse, and repeat.
Comment: As long as you don't ask us about stuff way over your head...
Comment: No, it's a very bady idea. You'll probably never learn the basics this way, which means you'll not become as good as you could have been.
Comment: Also see Conrad Wolfram's "Computer Based Math" scheme, which nicely combines an overall bottom-up approach with some top-down elements. Good introduction [here](http://www.computerbasedmath.org/resources/reforming-math-curriculum-with-computers.html).
Comment: If it's Wiles' proof you're after, some resources you might find useful are (in order) Simon Singh's [book](http://en.wikipedia.org/wiki/Special:BookSources/1841157910) (a pop-math overview), the undergraduate-level exposition linked to [here on mathoverflow](http://mathoverflow.net/questions/54612), and the number-theory-graduate-student level work linked to from [here](http://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem#Popular_accessibility)
Comment: I think it is very much dependent on the personality of the mathematician in question. I find it somewhat insane to work on mathematics from the bottom up, since what one is doing is unmotivated in such an approach. I find it a far more daunting and depressing prospect to learn all details of a large subject (say noncommutative geometry) from the ground up without any idea of what one wants to do with it. I also find it dangerous to do so, since you are staying so close to established thinking you have little chance of developing an original perspective or idea.
Comment: This said, if one is guided by beauty in one's experience of mathematics, I understand how problems with low overhead can be appealing. So this all seems tied to the individual's sense of mathematical beauty...which should drive one's mathematics!
Answer: I think this sort of question, and pursuant discussion/answers/comments, can be very useful for people who're new in the math biz. Namely, in my considered opinion, neither a "strict" bottom-up approach, nor "strict" top-down approach is optimal (except, in both cases, for a few extreme personality types). This is plausible on general principles, since, after all, the smart money says we should do a good bit of both, as in "hedging". And this is true, and for more than those general principles, in my opinion.
The way that "do both" is the only sensible route would seem to be that the extremes have lent themselves to highly stylized, almost caricatured, and editorially-pressured extremes. Research papers very often are written in the first place not to inform and help beginners, but to impress experts, etc. Sometimes journals' editorial pressures push in this direction. Peoples' understandable professional insecurities push in this direction. Experts' boredom with beginners' issues helps drift. And, at the other end, publish-for-profit situations push ... for profitability, which in real "textbook markets" means that "new" textbooks will mostly resemble old ones. We are fortunate that some people (Joe Silverman, as Matt E. noted) manage to move things forward within that strangely constrained milieu.
An important further point, in my experience, is exactly that of the question's "follow the branching graph of references backward to reach the ground..." 's hidden, unknown fallacy. That is, (having tried this in all good faith, very many times in my life) peculiar conclusions are reached when/if one does not give up, but pursues things to their actual ends. Namely, some significant fraction of the time, no one ever proved the thing that gradually was back-attributed to them... though it is true, and by now people have figured out how to prove such things. Another is that the "standard reference" is nearly incomprehensible, and only if one knows that subsequent explications were life-savers can a beginner find a readable thing.
And, of course, these graphs going backward branch so rapidly that literally reading everything referred-to is ... well, physically impossible for most of us... and even if one tries to approximate it, the effort is ... let's say... "not repaid in kind". At various moments I did estimates of how many pages I'd need to read to correctly honor all the background. When it hit "more than 10 pages a second, for the next 20 years", I knew both that I couldn't do it and that either it was crazy-impossible or ... not the real issue. :)
Yet, at the same time, exaggerated reliance on "popular" textbooks (excepting some like Silverman's... hard for the novice to know who to trust, yes, ...) really doesn't lead one forward/upward.
After all the above blather, my operational advice would approximately be that one should try to figure out _what_to_do_. Thus, any source which cannot be fairly interpreted as giving help is instantly secondary. More tricky are the sources that do well-describe the Mount Fuji at a great distance... To see Mt Fuji is a great thing. What should one do?
At this date, it seems to me that on-line notes on topics that otherwise seem to be "standard", but have become cliched, are far better than most "textbooks". But, yes, there is some volatility in this, because, as above, Joe S.'s books on elliptic curves are excellent, even while being entirely within all conventions and such.
Summary: run many threads...
Answer: I learn mathematics this way, to a certain extent.  I began my studies just a few years before Wiles's paper appeared, so I didn't have that to read when I started, but from Silverman's book on elliptic curves I learned about Mazur's theorem on rational torsion points on elliptic curves over $\mathbb Q$, and started trying to read Mazur's paper (the famous Eisenstein ideal paper, discussed here in more detail; let me just note here that it is the paper which initiated the research direction in number theory of which Wiles's paper is one of the highlights).
However, I didn't try to read this paper in isolation.  Using the bibliography as a guide, I tried to figure out what other material I had to learn to understand what he was doing, and went on to learn this material, from a mixture of text books (such as Serre's Course in arithemtic, for modular forms) and other papers (too many to list here!).  In the end, it wasn't until much later in my career that I developed anything approaching a complete understanding of what Mazur does in that paper.
If your goal is to become a research mathematician, then you need to develop a knowledge of mathematics, as well as intuition and a sense of the big picture.  You can't be dogmatic about how your learn this.  Sometimes papers help; sometimes textbooks help.  (E.g. if you want to learn elliptic curves, which is certainly necessary for understanding Wiles, it is silly not to use Silverman's book; it is simply a great text-book, which will teach you a lot much more efficiently than any other approach that I know of.)  Having a mentor, or just other, perhaps slightly more experienced, students around, to give advice on what is good to read and what to avoid, helps a lot.
If your goal is something else, then I don't really have any advice.  All my experience is based on learning mathematics with the ultimate goal of doing mathematics.
Answer: It really depends what kind of person you are. Most of the people I know hate this. I love it.
The most important thing to keep in mind, though, is that you'll almost surely end up somewhere entirely different. You'll start with a complicated topic, take a few steps back, and then try to move forward. But by the time you've made any significant progress, you'll probably have diverged and started studying something entirely different.
This isn't a bad thing. Self-study is governed by student interest much more than traditional teaching. As such, you'll inevitably go off on tangents and become re-directed. I think this is a feature, more than a bug. You'll naturally gravitate towards subjects you find interesting. (Just make sure that you actually make progress. It's quite easy to skim through basic results and lose interest before getting to the meat of a topic.)
Answer: In "Surely You're Joking Mr. Feynman", Richard Feynman describes being challenged by his sister to do just this, at an early point in his graduate studies when he was feeling overwhelmed by some of the papers. (And by the apparent ease with which his contemporaries appeared to absorb them.)
As I recall the anecdote, he describes staying up all night to work through one paper, which he finally grasps. He goes on to describe this as a seminal moment in his career, when he might have abandoned theoretical physics without his sister's goading.
Comment: This was actually later in Feynman's career, and it led to his discovery of the law of beta decay.  From p. 259 of Surely You're Joking: "'No,' she said, 'what you mean is *not* that you can't understand it, but that you didn't *invent* it.  You didn't figure it out your *own* way, from hearing the clue.  What you should do is imagine you're a student again, and take this paper upstairs, read every line of it, and check the equations.  Then you'll understand it very easily.'"  This was [around 1957](http://en.wikipedia.org/wiki/Weak_interaction#Violation_of_symmetry).
Comment: I like the word "goad".  Thanks for using it.
Answer: In general I think the best way to understand math is to do a lot of problem solving and specific computations in the area.  That way when you get around to reading a theorem about it you say "of course, that is obvious", instead of "huh?".  A simple example comes up when you try to teach students that the real numbers (or the integers) are commutative under multiplication.  They don't understand why you are bothering them with this since it's "obvious".  It's obvious only because they've worked a bunch of multiplication problems.
Personally, I have never understood a subject until I've worked a lot of problems.  I seem to need specifics, and then the generalities are easy to understand.
I wouldn't tell anyone not to do it top down, but it doesn't work well for most people.
Comment: Well, whether they are problems or examples, it is important to do it yourself, not read what is "worked".  There is nothing like trying to your own proof or computations to clarify what you do not understand.  And to the extent you can figure that out for yourself it will stick.  And the most fun is to come up with a better proof than the "worked" example.
Comment: I might revise "problems" to "examples". There is always a risk that "problems" are just random filler. We can maybe have higher expectations for "examples". Further, careful attention to important _worked_ examples, done by an expert, is much better than ugly-bad quasi-solutions to artificial problems done by semi-competents.
Answer: I would advise against doing this, as you will feel as if you know less, because everything will seem so new and overwhelming. Of course this depends on how much over your head you are.
Answer: In the specific case of understanding some research paper it makes perfect sense to follow a top-down approach. If you start bottom up it will take long time before you get ready to appreciate the paper you started with and probably you will lose interest in paper by that time. Also for people who are not in academic profession (like me), I believe this is the only approach possible.
Again if you follow the top-down approach seriously (like going through all the references in the paper and doing it recursively till you reach the level of knowledge you possess beforehand), it becomes more or less equivalent to the bottom up approach as you might find the related topics interesting enough to warrant their serious/independent study.
As an example from my experience I started to search the proof for Brent-Salamin AGM formula for $\pi$ and this opened up a whole plethora of interesting math for me including theta functions, elliptic function and finally leading to Ramanujan's modular equations. I got engrossed so much so in these topics that I created a whole blog out of it.
On the other hand I don't think I would have ever thought of learning elliptic functions independently (I had come across them long back in my undergraduate years and did not find them worth pursuing further). To sum it up while following the bottom-up approach you may probably miss the purpose and excitement.
Answer: If you want only superficial understanding of the content in a paper then the top-down method is useful, but if you aim at contributing something, then the tortuous, self-studying and time consuming method is the only better way. Learning new maths through textbooks is a highly challenging for anyone. There are only 5% textbook authors in maths who have the gifted ability to present a thing in such a manner that any genuine reader can learn directly through reading their books upto appreciating-level.
Comment: Which authors belong to this 5% ?
Answer: In my experience, this can be very difficult and also frustrating. If you aren't familiar with the basics, it can be completely non-obvious why a certain "big" result is actually important. Moreover, if you just look up what you need for the paper you are reading, you'll get a very restricted exposure to that area of mathematics. The ideas you've learned will only make sense in that one context and so your understanding will not be particularly robust. It is better to learn from the bottom up with lots of examples to build intuition. As you learn, try thinking of a given concept in as many different ways as possible so as to broaden your understanding.
Answer: I'll say from my own experience this has NOT been very effective.  Really, it seems that you won't really understand at all what's going on unless you have a very solid understanding of all the simpler math motivating the more advanced math you see.  One example of this is from when I was an undergrad.  There was a small group of us that always felt the need to take the most advanced classes possible.  The big problem with this is I think I spent a lot of time being immersed in "abstraction without motivation".  One example of this is I took a graduate course in functional analysis without fully adequate understanding of some basic stuff in undergraduate analysis (for example I didn't yet really understand why uniform convergence was so important).  I was able to solve the problems in the class and do ok, but I had to spend time later on in my career filling in the gaps.
Comment: Your interesting answer seems to me to support the very opposite of your stated position! Filling in the gaps.... Isn't this just what the OP proposes to do?


If you keep a bike inside for months in a row, do you have to check it?

Question: For example, if you keep it in a garage or in basement, I am thinking the tires might lose air and then the wheel will pressure down the tire. So do you need to check the bike once in awhile and inflate it?
Comment: If by "check the bike" you mean "check the tires", yes, of course - you have to do that after a few months whether or not it was in a basement. Are you asking about other sorts of bike maintenance?
Comment: Yeah, the tires should be checked every day for super-skinny tires (under 32mm), every three days for medium tires (32-38mm) and weekly for wider.  (And then adjust that frequency based your experience of how rapidly your particular tires lose air.)
Comment: @Jefromi, yes, about the tires mostly, but if I get info about the other parts, why not?, better. The given answer are more than enough for me.
Comment: I ask because it might have affected the depth of answers you got here, even if you found them sufficient, and also since there are related questions: [pre-storage maintenance](http://bicycles.stackexchange.com/questions/1429/winter-maintenance-before-putting-bike-in-winter-storage), [maintenance while in regular use](http://bicycles.stackexchange.com/questions/89/periodic-maintenance-task-for-bike-commuters), [how to store](http://bicycles.stackexchange.com/questions/60/how-to-store-a-bicycle-for-an-extended-period-of-time) (very minimal answers though)...
Answer: I'm gonna sorta disagree with Zen on this one.  If you're talking months vs years, and the bike was stored inside in a location where condensation would not have occurred (eg, not in a cold corner of a basement in a humid climate), and the bike was in good condition when stored, then all you need to do is air up the tires and wipe the dust off.
The tires and brake pads won't rot overnight, the lube won't leap off the chain.  Properly lubed bearings won't corrode.  Disk brake rotors (and caliper brake rims) may develop a slight coating of oxidation, but that will be worn off in the first ten miles.
If it's been stored for several years, however, you may want to squirt a little oil on the chain and give it an extra wipe, both to get the dust off and because oil does slowly evaporate.  And check the tires and brake pads for rot.
Once or twice a year a bike should get its cables lubed, and the chain should be cleaned and reoiled every 200 miles or so (or at least once a year).  This is unrelated to how long it's been stored, but a good time to do this is when you take the bike out of winter storage (though a better time is before you put it into winter storage).
Comment: There is nothing to disagree with. I said that rubber parts may degrade depending on the length of storage. I have seen, in my climate, bikes rust to non-repairable condition, but it depends on storage conditions. As for lubrication, read the bottle. Follow the directions. Most lubes will evaporate in normal storage conditions in 2-4 weeks. You should in fact check your bike before riding, every time you ride it, not just if you store it. But that doesn't mean it will automatically need major service to be ridable, it means check it. Perhaps you should read what was written before arguing.
Answer: Yes, if your bike is stored for more than a few weeks, you should check it thoroughly before riding it. The tires will lose pressure, and the chain will need lube for certain, and depending on the length of storage, rubber components like brake pads, tires, and hydraulic seals may degrade. In addition, surface rust, and sometimes deeper corrosion can develop which would require a more complete service.
Answer: Zenbike covered it, but I would also add (would comment but don't have enough rep yet!) that:
- Organic Disk Brake pads can become degraded over time, especially if the bike is stored in a oily fumey environment.
- In our garage / outhouse we have a problem with mice chewing through cables.. any cables they can find.. nom nom nom yummy rubber!
As with most things, regular short usage is better than no usage at all.


What techniques authors use to keep track of their cast?

Question: There is a problem as stories progress (especially in never-ending web novels) where the cast of characters keep growing. Some webnovels I follow are in the hundreds!
Is there a technique for authors to keep track of their cast of characters?
Comment: You might be interested in other questions about organizing notes, such as [Software to organise world building?](https://writing.stackexchange.com/q/9035/23159) or [Good ways to sort "rambly" notes?](https://writing.stackexchange.com/q/46892/23159)
Comment: Do you mean to keep track of them for themselves while they are writing, or to enable their readers to keep track of them?
Comment: I set up a private wiki, which allows for everything you might need, though it requires online access. While mine is hosted on a private server, services like wikidot host wikis for you. Not sure if there are any free wiki hosters that allow for private wikis.
Comment: Check out a question I wrote, which, I dare say, may be a duplicate to yours.  https://writing.stackexchange.com/questions/41850/creating-and-keeping-track-of-characters
Answer: The only technique there is really is keeping some sort of "character sheet" for each character.
If you can keep them all in your mind, that's great, but I guess you wouldn't have been asking the question if it were that easy for you. Otherwise, people use different platforms. I like OneNote, I've seen others use Scrivener, or physical folders with actual paper, some do just keep it all in their heads - whatever works for each writer.
You want to keep track of stuff related to each character: appearance, personal history, goals, views they express. The big stuff, like what kind of person they are - you're not going to forget that as a writer. But little details like eye colour or a food allergy - those are easy to mess up. They're not really important, so you write something in one scene, then forget about it and write something different next time the issue comes up. As an example, the character Thomas Raith in Jim Butcher's Dresden Files series is just under 6 feet in some books, a little over 6 feet in other books. When this was pointed out to the author, the next book mentioned how the character wears shoes with whatever heels are fashionable at the moment, so the first-person narrator isn't really sure about his real height.
The way you avoid this is you try to double-check such things on the character sheet you're keeping.
To clarify, you don't need to create all this stuff in advance. But as you're writing, make notes of what you're writing about the character, so you don't contradict yourself later. (And of course, if there's something you don't remember, such as whether you've already killed a particular minor character, you can Ctrl+f your file.)
Answer: Time for me to recommend one of my favorite webservices (free) again!  Archivos!
Why I favor this is it allows you to define and keep track of relationships between everyone, and also to events (who was at the battle of tweedledee?) and places (was the doctor on Mars at the start of the battle, or in the command ship?)
This is link showing some works using it: https://blog.archivos.digital/archivos-story-samples/
Basically, everything is a Story Element.
From https://blog.archivos.digital/archivos-faqs/

You can choose from the following list to define the Type of Story Element you're creating:
Person* – from protagonists to the smallest walk-on role
  Region* – worlds, continents, countries, counties, mountain ranges, forests, etc.
  Location* – towns, buildings, landmarks, ruins, etc.
  Organization – governments, guilds, religions, cabals, corporations, etc.
  Item – relics, artifacts, unique tools, cars, ships, etc.
  Event* – battles, treaties, plagues, births, deaths, graduations, etc.
  Culture– ethnicity, as well as speculative cultures (elves, dwarves, giants, aliens, etc.)
  Discipline – magic, kung-fu, cloak fighting, psionics, etc.
*These Story Elements have additional unique properties:
  Person allows the Storyteller to assign an optional gender (Male, Female, Other)
  Regions and Locations allow Storytellers to assign map graphics to the Element and configure it for display in the Living Map (qv)
  Events allow Storytellers to assign a date, date range, and/or time to the Event Element

So you can add relationships like work ones (hierarchy) or romantic, or who is in a group, etc.  Each character can have an image, and there's space for all sorts of notes, etc.
Answer: I would have a document like the one @Galastel suggests, which makes good sense for 'characterizing your characters', but I also keep a 'mindmap' with a visual representation of how all my characters are connected to one another.
I personally use 'Mindmeister.com' and have been quite satisfied with it. You can make your own rules for coloring and labeling, i.e.: Red line = family, blue line = friendship, green line = other...
You can export your mindmaps as pdfs to keep around or to send to potential readers, or the cast of a play if that is the case.
It is free to use, and they have a website + mobile apps. You create a log-in that works across these.
Answer: Maybe I'm missing something. The principle here seems pretty obvious: Keep notes. Make a list of all your characters and write down enough to remind yourself of the personality of each character.
Are you looking for something more specific?
Answer: Personally, I have a combination of the above ideas. Where I have a list of characters with their hierarchical attributes (affiliations, relationships, living/dead, romance, etc.) which is linked to their "File" which is written up in OneNote. I also have a mastermind map (also in OneNote) to allow me to visualize these characters.
Now, if I am being truly honest. I primarily write shorter stories (working on my first novel though) and I do this for each story. However, sometimes a character gets carried over or copied in essence to the other. This allows for faster writing and smoother character development, in terms of pushing along the story, as I can take what I need at a glance and keep working.


How much physical currency does the Fed transfer to banks per year?

Question: I just wonder since money has to enter the system somehow. Currently the Fed will supply whatever banks ask to meet their capital needs. But how much physical currency does the Fed, treasury, and mint transfer to banks per year? And which banks?
Answer: The amount of currency in circulation (bills and coins) is published by the Federal Reserve. (Available at the FRED web site.) The annual change in this time series is the amount created.
This is the amount outstanding, it does not tell us how much currency is being destroyed and replaced. Also, there is seasonal demand for currency, and some cash is shipped back and forth.
The creation of currency is not really a "transfer" (gift). The banks need to buy the currency by exchanging reserves (settlement balance at the Fed) for the notes.
Finally, the Federal Reserve does not single out how much it deals with any particular banks by name under normal circumstances. (During some of the special operations undertaken after the Financial Crisis, the Fed published some information about their counterparties.) The most you would get would be on the basis of the category of bank.
Answer: In the US and in the Eurozone, a lot of the money doesn't physically exist - this graph illustrates it quite nicely. In Europe, only 1,1B of the 10B Euro in circulation are cash (source) - all the remainder is electronic. When banks need money from the Fed, there is an electronic transaction from the Fed to the bank.
Cash is introduced in the economy through banks, through their request to the central bank for cash, provided upon need and perhaps against a fee.
Comment: So, why is it difficult to answer it? I don;t think you state that.
Comment: @luchonacho maybe the information is not publicly available. But one could estimate the lifetime of a banknote (6-24 months depending on denomination, 10€ notes need to be replaced sooner) and from the total amount conclude that the ECB prints maybe 300 billion euro per year.
Comment: @JoaoBotelho I think you meant  1.1 trillion by 1,1B, that should be altered, as it could be mistaken for billions (English short scale).
Answer: The specific amount is irrelevant because it is just a gift to banks.
The currency "purchases"  are offset by deducting their account, which is based on fractional reserves, which are limited by a reserve ratio based on how much currency the bank has. Which is a circular logic, and thus meaningless. Banks can withdraw whatever they feel like from the Fed.
Economics is of course about pretending that banks are bounded by some kind of law or whatever


Can you "extend" a drywall stud?

Question: I installed shelves in a closet with unevenly spaced studs. The shelves are mounted to the studs and they are level and secure. The shelve mounts can support a clothes hanging bar. The bar has holes where you can screw it into the wall. However, there is no stud where the rod hits the wall. When I try to screw the rod to the wall and the rod to the mount, the rod comes loose from the wall. There is a drywall stud very close to the place where the rod hits the wall. My thought is to screw a piece of wood into the drywall stud that will extend over the inch or so to where the rod hits the wall. Then screw the rod into the wood. Is this a good idea? Is there a better way?
Answer: The best way to handle this situation is to span two studs at the end of the closet with a smallish plank, screwing it into both studs. Then you can screw the rod end mount to that plank and rest assured that it's as sturdy as you can get it.
The "far" end of that plank will very probably screw to the stud at the far rear corner of the closet's end wall, which is kind of nice because that hides almost the entire plank.
An alternative, but one that's only suitable if you're definitely never going to hang a lot of clothing from that rod (clothing weight accumulates shockingly quickly), would be to use drywall anchors to attach the rod end mount to the drywall.

Can you "extend" a drywall stud?


problems with my touchpad on my netbook

Question: ive been having trouble with my touchpad its a synaptic pad. my problem is whenever i drag my finger across i a lot of times get this grey circle and i cant move anymore i have to take my finger off and start again its very annoying and the icon for the touchpad thats by the clock gets like a curved arrow in it and if i move my finger a little bit while this grey circle appears the arrow rotates in a circle its very weird! i have a Asus 1101HAB netbook and ive tried to update the driver when the asus updates appear and when i do it and restart the computer, then a couple days later maybe it pops up again saying i have an update and its for the touchpad and its the same version... not sure if its a bigger problem its only a week old that ive had this computer. If someone could help it would be much appreciated.
Answer: Ok it looks like my initial assumption was correct. After a bit of research on the Asus website, I found that your laptop should have multi-touch. This allows you to do two finger scrolling etc.
Im thinking by your discription of the taskbar icon that it thinks you are doing a rotate motion on the touchpad, hence the rotating arrow. This kind of action doesnt normally cancel until you remove your finger from the touchpad, as you mentioned.
If this is correct, then I would suggest turning the multi-touch settings off if you dont use them. If you do then you should be able to adjust the sensetivity of the touchpad, to make it less sensative as maybe you are accidentally touching it with other fingers and triggering the rotate function.
Could you perhaps turn off the multi-touch settings for a few days and see if this solves the problem?
Comment: There's a circular scrolling option as well, where all you have to do is look like you're doing circles a lot on the pad and that initiates a scrolling-type behavior too.
Answer: I have had the same issue, hence coming across your question. Could it be the scroll function that is sliding up and down the right hand side of the touchpad scrolls up and down and sliding along the bottom of the touchpad scrolls left and right. Very useful if you know it exists but confusing when it happens randomly.
Answer: Check the touchpad software that came with your laptop and make sure everything is configured correctly.
It sounds like your computer could be mixing up the movement of the mouse with keyboard strokes. Which I would usually say is a driver problem, however as you've updated your drivers this is the only other solution.
Answer: After much struggle with Synaptics configuration and its settings, I gave up on it and uninstalled that software. After this using the mouse pad and the little button stick has become very simple and efficient on my HP laptop.

problems with my touchpad on my netbook


Why does "I got 'busted' for smoking weed" mean 'caught'?

Question: How did the word 'busted' morph into a synonym for 'caught'?
Busted, down on Bourbon Street,
Set up, like a bowling pin.
Knocked down, it gets to wearin' thin
They just won't let you be....
Comment: My first guess would be an evolution from the term "bust" as in, "This is a bust!" That, in turn, may have come from the action of busting down a door in an attempt to catch a criminal. But these are just hunches.
Answer: I would have thought that it has its origins in the law enforcement term '[To carry out a drug] bust'. Although it is often used interchangeably with the term  raid, I would suggest that the physical act of gaining forced entry by "busting the door down" led to its becoming known as such.
Answer: Green's Slang Dictionary has bust meaning a break in or a raid dating from 1865, but the earliest reference to a police raid is from 1938. Later the word came to mean any arrest or criminal charge. This usage probably derives from burst meaning a burglary, which it dates from 1834.
I can recall Philip K. Dick using the word burst as a typically Dickian substitution for bust in one of his novels (sadly I forget which one), which would have required commendable self-discipline in the days before word processors.
Answer: Etymonline tends to back up MrHen's guess:

variant of burst, 1764, Amer.Eng. The verb sense of [...] "arrest" is from 1953 (earlier "to raid" from Prohibition).

Unfortunately this doesn't give us a lot of insight into how that meaning evolved, but "bu[r]sting in" to places where criminal activity is going on is as good a guess as any.
Comment: During Prohibition law enforcement would destroy (burst?) containers filled with alcohol during raids; perhaps there is a link there?
Answer: I think it originated in the 1930s in Chicago during the rise of the Italian mafia. Busted was used by cops when they arrested a mob member, referring to Italian basta — "enough, no more".
Comment: Thanks for your contribution. I note that the accepted answer also refers to the 1930s, so you may well be right. However, the normal protocol on this site is to provide some independent sources to substantiate an answer (rather than just "I think"). If you have ant such references, perhaps you would supplement your answer accordingly.


My child said to my wifes face that he loves his grandmother (wifes mom) more than her, can you offer some advice how to deal with this?

Question: My wife and I are feeling hurt, because my 5-year-old son said the other night that he loves his grandma (my wife's mom) more than my wife. He said this to her face. She has been in a very bad place ever since. Does this happen to you and how do you deal with your child loving your parents more than you? Have they ever told you they love them more? Will this change?
Comment: Thank you for posting. The situation seems like a very difficult conundrum. Can you please narrow down the topic you'd like people to respond to? As the question is now, it may be difficult to post a specific answer to your issue.
Comment: I feel like the title here is very different than the body - perhaps it should be updated more towards "Is this behavior appropriate for a grandmother?" or something.
Comment: yes your right, I think i was just in a panic and really needed some help so I wrote everything down at once, hoping to give a full story from my perspective. All parts of that story are related and relevant but I guess if I had to narrow it down, I was wondering what you think about the grandma's behaviour and what should she be doing as her role of a grandma? What could we do differently?
Comment: Related: [What to do when my 3.5-year-old says "I don't love you, I love mommy."?](https://parenting.stackexchange.com/questions/37655/what-to-do-when-my-3-5-year-old-says-i-don-t-love-you-i-love-mommy)
Answer: It seems you already talked to the grandma and it wasn't effective.
Now you need to take action. Because if you don't, it will never change. The grandma could get away everytime so far, so why would it change ?
After agreeing with your wife, have a talk with the grandma, stating you will reduce how often you visit her, because her behavior is affecting your family life.
And then do it : If the grandma ask you to come by, find a random excuse.
Don't cut her completely, your child still love her and wants to see her.

Don't focus too much on what your child say : as other answers mentioned, this will vary greatly from time to time.
But the behavior of the grandma is worrying : It is your child, so you get to decide the education. Comparing with other family is not an healthy behavior, it's an excuse for the grandma to do whatever she wants. At the end you should be the one who decides, no matter what is the decision.
The crying is also not healthy. I would go as far as calling it emotional abuse. Your child does not feel good seeing the grandma crying because he has to go. And he has to because of the parents. So the parents are bad.
The grandma should immediately cease this behavior : she's an adult and she should understand that the child cannot stay with her forever, and crying does not help anyone.

Also, don't mention you will see grandma less often to your child : it's not their fault, you don't want them to feel it's their fault.

Finally, as others mentioned it, you (or your wife) are not bad parents. Childs always have favorite. It will vary, the child will grow out of it soon.
I would be more worried about the behavior of the grandma. Be firm with her.
Comment: As an extra "always", the favorite is generally not the best caretaker but the one who most often lets the kids do whatever they want, which generally isn't healthy for kids anyway.
Comment: Unfortunately your answer has nothing to do with the current revised question.
Answer: Had my kids tell me they loved my wife more than me... just grin and bear it.
A few weeks later I was flavour of the month - had just fixed their bikes or something.
Don't panic - they change allegiance quickly and don't remember for long. It will sort itself out.
Edit:
Her bed? I would not let it go that far - keep to a standard routine... and get Dad to stand up as well...
We always had tea (supper) pause for a bit of light play, bath, teeth and bed around that age. Films are good but not school nights.
My daughter went through a stage of tears & tantrums to get her way... One of my sisters was looking after them as I was at work. Came home to find daughter was hiding in the bathroom trying to get her way... realised I was not going to fall for it and came out. My mum taught us well :)
Comment: @KayBei her bed? I would not let it go that far - keep to a standard routine... and get Dad to stand up as well... we always had tea (supper) pause for a bit of light play, bath, teeth and bed around that age. Films are good but not school nights. My daughter went through a stage of tears & tantrums to get her way... One of my sisters was looking after them as I was at work. Came home to find daughter was hiding in the bathroom trying to get her way... realised I was not going to fall for it and came out. My mum taught us well :)
Comment: Thanks solar mike. I need to hear these things. But I think many can agree that dealing with in-laws is hard enough sometimes. We are moving into their home in 2weeks, this covid situation has changed things for us. She's already talking with our son about sleeping in her bed and movies before bed....it's driving me insane.
Comment: thanks man, this is great support. ya one of us still sleeps in same bed as our son everynight or everyfew nights so he is used to that. When his grandma comes to visit, he always liked it when she slepped in his bed with him. He is already talking about doing this everynight. Your right tho, I will just have to keep a standard routine, and speak with her about this.
Comment: I would like to believe that he would change his allegiance, but my mother in law is adamant. I feel like she will do whatever it takes to keep him hooked to her. She litterally does everything for him. I notice he becomes more needy as a child and more dependent. My son has literally yelled at her, or has done/said something hurtful to her and she will not say a word, she just let's him walk all over her. It's a nightmare to watch your child become another person and most often not in a good way. He is a total different child with her. I don't know how i'm going to deal with it.
Comment: The OP has added some specific questions to more match this site's format as a Q&A. Now that the question is updated, can you reflect your thoughts in your answer please?
Answer: Don't panic man, this is the same everywhere. All children love their grandparents cause they give them what they like.
Comment: I agree here, there is something really special about my daughter and the attachment she has with her grandparents. They spoil her, let her do what she wants and she doesn't see them all the time so whenever she is there it feels extra special. I personally am okay with it because my grandparents passed away so I just want her to cherish every moment with them. To answer your question I would sit with grandma and just tell her that you love how much she loves your son, but it would be really helpful if she can also discipline sometimes (saying no) because it's effecting homelife
Comment: I feel like there should be a limit to this. Does it bother you? How do you cope with it?
Comment: If she really honest than let she love him man, where is the problem, and what you think about the worst scenario? The same happened to me couple of years ago but with my sister, and sometime my daughter use to tell me that she loved my sister more then me, but as @solar said, when I bought her new dress, she forget everything and I do the same. If I am in your position  leave it and don't bother yourself with this. Any way this is just my opinion and hope you will find a way to relax yourself
Comment: The OP has added some specific questions to more match this site's format as a Q&A. Now that the question is updated, can you reflect your thoughts in your answer please?
Comment: thank you for the advice. I will just do as you all said. Just let go a little and have a small talk with grandma. Thank you all.


What should students learn about security in an introductory programming course?

Question: Some folks have advocated that security should be integrated into computer science coursework, throughout the curriculum.  Suppose we are going to add one lecture on security, to a first course on programming.  (Keep in mind that it is a very basic introductory course, so advanced topics are not appropriate.)  What are the most important things that students should learn about security, in that context?
Comment: I think they should just add in safer programming tactics for someone who is just dabbling in it, to protect from simple things like buffer overflows. Then, if the student still shows an interest, the security can go more into depth. But that's just me =p
Answer: Security education should be contextual. There's not a lot to say about security when you're studying red-black trees or merge sort. But security should be a constant and pervasive factor as part of everything the student does.
Any security-related items should be required as a matter of course; bounds-checking and input sanitization, for example, should be absolutely required in all assignments. If the examiner can break the homework application by supplying invalid input, then points should be deducted. If array bounds aren't properly checked (assuming an unsafe language like C), then points off. It should't be sufficient to just have the thing pass the assigned test-case, it also has to be well-enough written that in a real-world scenario it wouldn't cause a disaster.
The students need to be used to always worrying about robustness and security the same way that chemistry students always should be worrying about lab safety. Security isn't something you study one semester and then move on.
If you're going to have a single lecture at the beginning about security, then it should primarily cover the security-related expectations that the students will be under. These expectations should be real-world expectations with respect to coding practices and should reflect the sort of vigilance that is always in the back of the mind for a good programmer.
This breaks down into several main areas, not all of which are appropriate for every language and every programming environment, here are a few that come to mind:

Language safety: An extremely big deal with C/C++, not so much with most everything else. Pointers, buffers, and that sort of thing fall into this category.
Input sanitization: Huge. Absolutely huge. I can't think of a single area in which this is not applicable.
Code clarity and documentation: Worth more than it sounds like. Many security vulnerabilities come from simple mistakes which stem from a misunderstanding of the code itself. The fewer mistakes you make, the better, even in the context of security.
Also, I'd throw in principles like "DRY" into this mix, since security vulnerabilities sometimes are the result of assumptions being out-of-sync within the code. The more places you specify a single value, the more likely you'll forget to change one of them, which can lead to security vulnerabilities. I remember a "no magic numbers" homework rule when I studied CS, where all numeric constants had to be assigned a name. It's a good policy to have for many reasons.
Privilege isolation: A bit more esoteric, but important in certain scenarios. The principle of least privilege is something that students need to at least be familiar with, for example; but it's difficult to make part of your day-to-day activity.
Security-specific items: Such as password storage, encryption, and stuff like that. This is more informational than directly applicable with respect to schoolwork, so I'm not sure where it fits in with respect to lesson scheduling.
It's important to learn about attacks like CSRF and token-stealing
attacks in the more abstract sense, but probably not in an
introductory course since it's a little advanced.
Answer: If this is only going to be one lecture and this is their first programming class, I think input validation is the most viable topic to go over. Some of your students will already be struggling to understand how x = x + 1 (x equals x + 1) when x = 1 just the line before ... that is until they realize that it is an assignment statement.
Topics such as encryption, ssl, and sql injection need to be integrated in courses that have related projects so that they can be practically applied.
Input validation, however, is something that they will carry with them for the rest of their engineering career.  It will help them mitigate the chances of their code being susceptible to buffer overflows, XSS, and (maybe)sql injection.
Answer: Im college student and I had that kind of course, first of they should teach how not to make mistakes in coding I mean, like protection against SQL Injection, or teach how to make own SSL connection and authorization, and a little about cryptology, I had like 7 sessions of that and all topics were explained pretty good... (I mean those topics weren`t just basics...)
Now in my opinion there should be a lesson about how to protect against sql injection, and some stuff about cryptology like program called PARI..., those should be basic
Answer: Regardless of the language used in education there are a number of principles that hold true, so I'm going to steal them from here Security Ninja

Input Validation - always check your inputs from untrusted sources
Output Validation - make sure your output is appropriate for the destination (e.g. escaping HTML characters...)
Error handling - dont give away too much information to the attacker
Authentication & authorisation - know how to do this right
Session Management
Secure Communications
Secure resources Management
Secure Storage

Learn and apply those principles and any software developed afterwards will be of a much better quality.
Answer: Matt Bishop has written some articles and has a preface in his book which discusses this
nob.cs.ucdavis.edu/book/book-aands/index.html


Using a Wii/PS3 guitar heroes guitar on a PS3/Wii console

Question: I'd like to know if there's any way to use a Wii guitar (drumset, etc.) on a PS3 - or a PS3 guitar on a Wii.
Do I need any adapters?
Answer: For the wireless controllers, there's no cross compatibility between consoles.  Each console uses a specific protocol to connect, and they don't talk to each other.
For USB wired controllers, it's likely possible with a 3rd party adapter, but each controller has console-specific buttons, so I don't know how that would work exactly.  For instance, my Xbox drum set has an "Xbox" button on the face of it.
Heck, the Wii Guitar Hero World Tour drums and guitar don't even work with Rock Band on the Wii - getting them to work with another console's games is right out.
As you pointed out (?) there's a Datel adapter available that adapts the Wii Guitar Hero Guitar (supposedly) to RockBand on the Wii and on the PS3, but people have had very mixed to negative results with it.
Comment: so what is [THIS](http://www.youtube.com/watch?v=sSrnGQwJq3Y) ... ? lol
Comment: Something I was unaware of :)  That's the trouble with trying to find out if something exists - if it does and it's common, great!
Comment: Indeed, there are both good and bad comments about it, that's why I asked here to know if anyone had any idea about any other device / adaptater or so ...
Answer: Although I don't know of a way to use PS# guitar on Wii and vice versa, I was able to use a a wired Guitar Hero guitar for the PS2, the one that came with the first Guitar Hero, on both the PS3 and Wii, though both require adapters.
I have used this adapter for the PS3 and this adapter for the Wii, though I'm pretty sure there are other compatible adapters.
Answer: ANY Rock Band or Guitar Hero instrument that uses a dongle rather then a factory controller is interchangeable. Guitar hero controllers are harder to interchange then Harmonix, but not impossible. To use them on consoles other then originally designated requires soldering. Harmonix instruments simply have a jumper near the microcontroller to determine which system the instrument is for.  This is true with ALL HARMONIX. Possibly those Red Octane controllers using a dongle as well. The simple fact is, if you search the web, everyone says no, not interchangeable, they don't speak the same language, bla bla. While this is true for non-dongle GUITAR HERO controllers, it is not for ROCK BAND, and those with a dongle. Here's why. The dongles were not made by Nintendo, Sony, or Microsoft. They were made by Harmonix and/or Red Octane. Therefore, they are not proprietary and unique to each system, and DO speak the same language across the board. The instruments that used the factory controller(wiimote, sixaxxis, xbox) to interface with the console generally are not really interchanged. Open a Harmonix controller, and look for a bubble of solder near the edge of the board labeled J1 - J1.5. Bridging one side is ps3, bridging the other is Wii. That simple! If you have any questions, send me an email. <code>[redacted]</code>.


Are we sure solar cycle is not related to the orbit of Jupiter?

Question: Are we still debating the relationship between Jupiter and solar cycle? If not, what is the common or mainstream opinion about this topic? Or in other words, have we disproved the solar cycle is related to the "year" of Jupiter?
Comment: Most of us are.
Comment: If it were connected, it would have to have a lot of slop in it.  The cycle is not anywhere near precisely pegged to Jupiter's orbit.  Another point is that the cycle is actually a 22-year cycle, with polarity flipping from one 11-year cycle to the next.
Comment: I have a few Sun-Barycentre distance graphs here: https://astronomy.stackexchange.com/a/44903/16685
Answer: I think for people who want to believe the Jupiter link to solar cycles it will be impossible to disprove.  They'll cling to it forever.
I think in a practical sense the "link" is little more than numerology.  The force Jupiter can exert on the Sun's atmosphere and internal structure is a minute fraction of the magnetic forces at work generated by the Sun itself.
A simple model helps.  Place two magnets a foot apart.  Now place a magnet a thousand feet away from both.  The effect of the distant magnet is one millionth that of the two close together.  That gives you a feel for the relationship between magnetic forces within the Sun's atmosphere and Jupiter's distant influence.  And gravity is an even weaker force.
As I understand it the current daring of models is the Double Dynamo, but certainly the dynamo type models ( all relating to electromagnetic fields generated by the Sun ) are the main contenders.
With people who propose the Jupiter link ( often extended to include Saturn ), there is a tendency to do a lot of algebra to find ways to relate various periods without actually justifying the supposed link on the basis of forces at work ( i.e. doing a simulation or a model based on real physics ).  This is why I call it numerology.
The dynamo models actually are based on real physics and make predictions, both past and future, which can be tested.  This also means the details of these theories can be refined in a proper scientific manner to tease out the truth.
Comment: Why would the solar cycle have to be driven by magnetic interaction from Jupiter? Couldn't the movement of the barycenter affect how the magnetic fields got twisted around?
Answer: The barycenter of the Solar System is the effect which should be considered physically. Although dominated by Jupiter other planets have substantial effect too, moving the Sun, with 99+% of all mass in the Solar System, around by entire Solar radii (700,000 km). Illustrated here
The diagram below I happened to stumble upon here. It shows the distance of the barycenter of the Solar System from the center of the Sun over time, with years on the circle. For some reason it spans from year 1773 to 1851. The peaks in the clover curve are regularly separated by about a sunspot cycle, or rather a bit longer. I suppose that the pattern of 2 big and 1 small sequential bulbs there reflects that Jupiter's and Saturn's orbital periods are about 3:1.
As StephenG says, that is just a numerological hint or coincidence, not an explanation. Another example is that the rotational period of the Sun is roughly similar to the orbital period of the Moon around Earth, with a similar error, but no one imagines any connection there.
It is however known that hot Jupiters, giant planets near stars, cause large starspots which rotate along with the planet's orbit. And the relatively tiny moons of Jupiter cause visible spots in the planetary aurora. Actually, the Sun causes an auroral "Jupiter spot"! So there are physics around which under certain conditions create sunspot-like effects.

Diagram: Barycenter distance from the Sun's center over time

Hubble image:The aurora on a pole of Jupiter in UV
Comment: It's butterflies all the way down!
Comment: So are you saying that the solar cycle is related to *all* the planets' orbits but since Jupiter is the largest, it dominates the cycle causing the mean to be closest to its orbital period than the other planets which merely perturb that cycle?
Answer: Jupiter's orbital period is 11.862 years.The amount of variation will be miniscule.
The solar cycle, while the average cycle time is 11 years, it can vary from 9 to 14 years. From the wikipedia article:

Since observations began cycles as short as 9 years and as long as 14 years have been observed, and in the double cycle of 1784–1799 one of the two component cycles had to be less than 8 years in length. Significant amplitude variations also occur.
Answer: Proportionate to the tidal forces that the moon exerts on the earth, the combined gravity from Jupiter (and other planets when in alignment) seem to be enough to perturb the sun's plasma.
https://www.iflscience.com/venus-earth-and-jupiters-tidal-forces-dictate-the-solar-cycle-suggests-new-study-52600

"Researchers from the Helmholtz-Zentrum Dresden-Rossendorf, a German Institute, have found evidence that the peculiarity of the regular solar cycle is to be found not within the Sun, but in its planets. Venus, Earth, and Jupiter have a tidal pull on our star that affects the hot plasma on its surface, much like the gravitational pull of the Moon affects tides on Earth. The team considered their regular alignment, every 11.07 years, to be the one keeping the tempo for the solar cycle. The model is published in the journal Solar Physics."
Answer: As another answer says, there is a tendency to do a lot of algebra involving planets' periods. Another approach however is examining the timing of actual solar events. In this case, solar flares and their time distribution is related to the relative motion of Jupiter and Saturn, providing predictions.


Why is there no [asp.net-core-mvc] tag?

Question: As I have noticed, there are only tags such as: asp.net, asp.net-mvc-3 and asp.net-mvc-4. However, there is no tag for asp.net-core-mvc. Why so? I believed it is a must-have to separate the question into a new category with different issues. I cannot create a new tag due to my reputation. Am I wrong?
Comment: I asked this in chat, got no real response. Good to ask this question!
Comment: Relevant question here (posted by the OP): http://codereview.stackexchange.com/questions/133616/reading-and-displaying-an-image-from-a-folder
Answer: .NET core is (very) new. I don't imagine it has many posts yet, nor can I see anyone using .NET Core MVC in production yet, which is probably why it is not posted here.
I think it'd be a good idea for a tag. We may also want to create ef-core, which is the newer version of entity framework and supersedes EF6, and potentially .net-core itself>?

Why is there no [asp.net-core-mvc] tag?


Dataset on university enrollment?

Question: I'm looking for a dataset with stats on tertiary education enrollment in the US, per state, at least a couple decades back. I've searched but cannot seem to find anything. Could someone help me out?
Comment: Have you tried contacting the College Board? They might not share it for free, but they have really good data. I don't work on education, but I have seen a few papers using College Board data.
Comment: will try -- thank you!
Answer: The National Center for Education Statistics , Digest of Education Statistics does have post-secondary education (university and community college) enrollment in the US per state from 1995 to 2017. There are some tables that has the data going back to 1970 but it skips some years so you may want to perform a  some sort of missing data imputation method (i.e. linear interpolation) to impute the middle years,  if you need all the years for your analysis.
However, their website does require some skillful navigation to say the least.
Hopefully,  my instructions will help.  Once you go to this website: https://nces.ed.gov/programs/digest/
On the left pane of your window go to the List of tables and figures section.  There is a  dropdown box below, select a year.
It goes to 1995.  Once you have selected a year go to chapter 3  Postsecondary Education, then select degree-granting institutions, then enrollment.   At this point you will need to find the table that has the state data.
From what I understand of the data that you are looking for, I saw it is in table 195 for most years (1995- 2006) , then its table 190 in 2007,  2008- its table 203  , 2009 - table 219 , going forward for most years the table number that has the state data your looking for seems to change but I am pretty sure its there in chapter 3.
For your research project a recommendation is to pay attention to how the NCES Digest of Education Statistics changes how define their state level enrollment data.   They also have more education data by state if you are curious to see what they have that could support your work.
If you run into trouble with these tables I would recommend to call their office.  The staff list is located here https://nces.ed.gov/ncestaff/stafflist.asp
I hope this helps.
Answer: Take a look at 120 years of higher education. Table 25 (in my edition) has state enrollments going back to 1869.

Dataset on university enrollment?


Sum up numbers from 1 to 100000 after removing zeroes

Question: Ok so i have numbers from 1 to 100000.I need to remove the zeroes from all numbers and sum up numbers from 1 to 100000.So if the number is 405 consider it as 45 , if number if 20039 consider it 239.
Is there any mathematical way to solve this, i mean any formula or anything.
Comment: Probably the best way is to do this with help from a computer. There seems to be no good way to do this without a computer.
Comment: i agree with dat. But that would require looping from 1 to 100000.I'm trying to find out if there is any other mathematical way to do this without looping
Answer: It's slightly more natural to consider the numbers from $1$ to $99999$, since they form complete sets of numbers with a certain number of digits; we can then add $1$ for $100000$ in the end.
There are $\displaystyle\binom5k$ ways to select $k$ of the $5$ digits to be non-zero, and they all lead to the same numbers when the zeros are removed. Every non-zero digit can take the values $1$ through $9$, whose sum is $9(9+1)/2=45$. The digits can be chosen independently, so the total for $k$ non-zero digits is $45$ for a given digit times $9^{k-1}$ options for the remaining digits times $\underbrace{1\ldots1}_k=(10^k-1)/9$ for the sum of the valencies of the digits, for a grand total of
$$
\begin{align}
\sum_{k=0}^5\binom5k45\cdot9^{k-1}\frac{10^k-1}9
&=
\frac59\left(\sum_{k=0}^5\binom5k90^k-\sum_{k=0}^5\binom5k9^k\right)
\\
&=
\frac59\left(91^5-10^5\right)
\\
&=3466789695\;.
\end{align}
$$
Add the $1$ for $100000$, and the result coincides with Mark's.
Comment: oh! Turns out there was a way to do this without a computer... Nice !
Answer: Given the Mathematica flag, you might consider posting this type of question on mathematica.stackexchange.com.  Nonetheless,
<code>deleteZeros[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
Total[deleteZeros /@ Range[100000]]

(* Out: 3466789696 *)
</code>
Answer: Look. You may ask how many numbers in 1-100000 end with 5 (the looks like xxxxx5 where $x \in \{0,...9\}$) let it be $a_{15}$ , then how many numbers looks like xxxx5x let it be $a_{25}$ and so on .
After that you should add all $a_{ij}$, were $i\in\{1,2,3,4,5\}$ and $j\in\{1,...9\}$.


Trying to make UISearchController function like language settings in iPhone in Swift

Question: I currently have implemented a UISearchController which is currently working fine.  Here are the attached screens that show how:

However, what I would like to do is implement it in a way that looks like how Apple implemented their language selection option in settings on the iPhone:

In Apple's implementation, the search bar does not hide the navigation bar when it is active.  Does anyone know how to achieve this functionality in Swift instead of the conventional way which I have implemented currently?  Just wondering.
Comment: Can you share your code so far?
Answer: There is a property called hidesNavigationBarDuringPresentation in the UISearchController class that by default is true that handle what do you want, so put it in false and you can achieve keep the navigation bar during the presentation as Apple do in the Language options:
searchbBarController.hidesNavigationBarDuringPresentation = false

I hope this help you
Comment: Thanks!  That did it.


How do I input Terminal commands when running a rails server?

Question: I just started using Rails a few days ago, and I'm having trouble with terminal commands. The textbook I am reading keeps telling me to run Terminal commands while having a Rails server running. This doesn't seem possible because the terminal just keeps outputting information about the server instead of prompting new commands, i.e. rake test. Is there a command I need to input to force the terminal to prompt my commands once I start the rails server?
Answer: From my rather limited experience of using Rails, I would first start the rails server and then create a new tab within the terminal to run your commands. To create the tab you might have to use something like Ctrl+Shift+T.
Answer: Istead of starting the rails server you can start the console with the command:
<code>rails console
</code>


What is the difference between "peasant" and "villager"?

Question: Can anyone explain to me the difference between peasant and villager? I can see that peasant refers to a social class, and villager refers to a physical location, but are these words interchangeable?
Answer: Peasant and villager are not completely synonymous. While a villager is just someone who lives in or comes from a village, peasant is more likely to be used in a pejorative way:

(especially in the past, or in poorer countries) a farmer who owns or rents a small piece of land
(informal, disapproving) a person who is rude, behaves badly, or has little education

A peasant might be described as of low social status, or uncouth, similar to a peon, serf, churl, boor, lout. Closer to villager are synonyms like yokel, bumpkin; but these still imply judgment or disapproval.
Villager alone lacks such a strong negative connotation. It could be used to describe someone from a village without obvious reference to their profession and without implying that they're ignorant or from the "back woods", though there are often assumptions that life in villages matches stereotypes such as being simpler, more authentic, or less modern: The villagers adjusted well after moving to the big city.
Interestingly, the etymology of both words reflects that they describe people from a physical location. Peasant is from Latin pagus "country or rural district"; villager is from Latin villa "country house, farm".
Comment: @Kiraz: it's the opposite, actually.
Comment: @kiraz, I'd say "peasant" is much more likely to be used pejoratively than "villager," or the pejorative meaning is stronger. If we say someone is a peasant, we're making a stronger statement about their lack of wealth and their low social status compared to if we say they're a villager. If we call them a villager, more context is needed to know if we mean to insult them (you might say, condescendingly, *aedia is a simple villager - she must never have seen what they're wearing now in Paris!*), just describe where they're from, or extol the virtues of "authentic" village life.
Comment: So, villager has a pejorative meaning compared to peasant, did I understand correctly?
Comment: @Alenanno, yes, I can see it now, thanks! it is just confusing.
Comment: @Kiraz no problem! :)
Comment: @aedia λ, thanks a lot for your help. There is no such difference in my native language, so I just wanted to learn which one could be more appropriate to use.
Answer: A villager is someone who lives in a village.
A peasant, instead, is "a poor farmer of low social status who owns or rents a small piece of land for cultivation (chiefly in historical use or with reference to subsistence farming in poorer countries)." [NOAD]
They're not really interchangeable, and not even synonyms, according to the Oxford American Writer's Thesaurus. Furthermore, you can't exactly use "villager" to refer to someone who lives in a city, simply because "village" and "city" are two different types of "people agglomeration". A village is generally even smaller than a town, which itself is smaller than a city.
Comment: @ Alenanno, how about people who migrated to the large cities from the rural parts of a country? How should we define these people in this context?
Comment: @kiraz: immigrant/emigrant depending on the point of view. That is the general term, I don't think there is a specific term...
Answer: I think OP may be conflating villager one who lives in a village, with villein (or villain) a feudal serf in medieval times.
In the UK (and US, I would hope), the word peasant can't really be applied to living people except as a "metaphoric" insult, though I believe there still are people living as peasants in many other countries. @Alenanno's definition of the word is as good as any.
In the UK today, villagers are likely to be significantly wealthier than the average of the population at large, if we accept the strict definition of the word. Poor people have long since migrated to urban areas in search of work (agriculture is largely mechanised these days). Rich people can afford the higher costs of maintaining an acceptable standard of living in a remote location.
However, those wealthy village-dwellers do employ domestic cleaners, gardeners, etc., and there are always other reasons why some people in a village are relatively poor. It's my impression that some of the wealthier people do sometimes refer to their poorer neighbours collectively as "the villagers", whilst thinking of themselves as somehow above such crude social stratification.
Answer: They are interchangeable in the context of a peasant who lives in a village, but not so for peasants residing outside a village, such as in a large city or on a farm, or for non-peasants residing in villages.
(Thanks @Martin Beckett for noticing I missed the last point)
Comment: They're not really interchangeable.  I used to live in a village and if you called me a peasant I would have taken great offence.
Comment: So I cannot use villager for a person who lives in a big city?
Comment: @kiraz, no. And you can't use it for a person that lives in a village but isn't a peasant
Comment: I do not think you can meaningfully speak of a "peasant" who lives in the city, unless you're doing it in the context of a society (China, perhaps) where the person did recently live as a peasant, and has not yet adjusted to his new status as a city-dweller. But this is really about social attitudes and prejudice, not language per se. And it's certainly meaningless in mainstream Anglophone communities such as US/UK/OZ, so I imagine you'd only need to speak like this in China/Russia/Afghanistan/etc., where you'd perforce be using the native language anyway.
Comment: @FumbleFingers, I did understand what you mean, thanks for your help.


Can the vice president of the United States be fired?

Question: Does the vice-president serve at the discretion of the president, such that he or she can be removed from office at the president's will?
Comment: Are you only interested in whether the president can unilaterally remove the vice president from office or are you wondering if there other options, such as through an act of congress?
Comment: Only implied with the word 'fired', but as elaborated in the body of the question, I was looking for the former.
Comment: It's not in the spirit of the question, but *technically* a president can "displace" the vice-president from that office, by the president resigning.
Comment: @DrSheldon: heh, clever you.
Answer: No. The President can not fire the Vice President.
Unlike the cabinet (e.g., Secretary of State, Attorney General, Secretary of Defense, etc.), and the White House Staff (e.g., Chief-of-Staff, Press Secretary, etc.) the office of the Vice President, his term and the requirements for his removal from office are all established explicitly in Article II of the Constitution.

Office, Term—United States Constitution, Article II, Section 1

The executive Power shall be vested in a President of the United States of America. He shall hold his Office during the Term of four Years, and, together with the Vice President, chosen for the same Term, be elected, as follows [emphasis added]

Removal—United States Constitution, Article II, Section 4

The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
Comment: Note that because the President and the Vice President are chosen for a term, the President has the option to choose a different Vice President for a re-election term. This happened with Andrew Jackson, who didn't get along with John C. Calhoun in his first term and chose Martin Van Buren as his running mate for his second term.
Comment: Is there an overlap? Is a cabinet member, for example, not also a civil officer who can be impeached?
Answer: Only Congress can forcibly remove a Vice President from office
The US Constitution only allows the Vice President to be forcibly removed from office via impeachment due to a high crime or misdemeanor (just like the President).

The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other High crimes and Misdemeanors. (Article 2, Section 4)

Impeachment is solely the responsibility of Congress, so the President cannot unilaterally impeach the Vice President, or any other elected official in the federal government.

The House of Representatives shall chuse [sic] their Speaker and other Officers; and shall have the sole Power of Impeachment. (Article 1, Section 2)
The Senate shall have the sole Power to try all Impeachments. (Article 1, Section 3)

In other words, the House of Representatives has the power to start impeachment proceedings and the Senate has the power to perform the impeachment trial. If the Senate rules to convict the elected official, they are removed from office.

Note that the Vice President is also the President of the Senate (Article 1, Section 3). The Vice President presides in this role for any impeachment case (e.g. for a senator), except for that of the President because the constitution says that the Chief Justice presides in that trial.
Technically, that means that a Vice President undergoing impeachment would preside over their own trial. This might have happened with Spiro Agnew, Nixon's first Vice President, who was charged with extortion, tax fraud, bribery, and conspiracy. But rather than undergoing impeachment, he resigned in August 1973 (this was about a year before Nixon himself was involved with the Watergate scandal).
Also, the Vice President always has the option to voluntarily resign. This has happened twice: Spiro Agnew as described above, and John C. Calhoun in 1832. Calhoun was Vice President under John Quincy Adams and later Andrew Jackson in his first term. Jackson and Calhoun disagreed sharply on a number of matters, but as shown above, Jackson wouldn't have had the option to fire him if he wanted to. Instead, Jackson chose Martin Van Buren as his running mate for his second term (and the two were successfully elected). Calhoun resigned a few months before his term as Vice President was up to become a Senator for South Carolina.
Comment: It's well established that members of congress are not subject to impeachment, so a senator would never be impeached.  Each house can expel its own members without needing to get the other house involved.
Comment: The article you link to concludes that a vice president could not in fact preside at his own trial (see https://www.alternatehistory.com/forum/threads/ahc-the-u-s-vice-president-casts-tie-breaker-vote-in-their-own-impeachment-trial.349143/): "The textual argument is accordingly hardly persuasive. This frailty is fatal to the Vice-President-Presides thesis, for the textual argument is its only support."
Answer: The president cannot fire the vice president; the vice president is elected by the electoral college, not appointed by the president.
The only mechanism for removing the vice president from office is impeachment by the House of Representatives followed by conviction by the Senate.
Comment: Interesting, ever since 1967, the VP's job seems more secure than the president's, what with the [25th Amendment](https://en.wikipedia.org/wiki/Twenty-fifth_Amendment_to_the_United_States_Constitution) being adopted in that year.


Why 了 is not used, and what is the meaning of 玩 in 上个星期天,我跟好朋友一起去林学院的农场玩?

Question: The sentence is:

上个星期天,我跟好朋友一起去林学院的农场玩。

I wonder why the writer doesn't add 了 after the verb to indicate that this action took place in the past.
Also, what's the use of 玩 in that sentence? And why is it placed in the end of that sentence?
Answer: I try my best to expalain it with my fair English.
First, here we have two verbs "去"and "玩". And there can be following cases for your sentense:

.....去.....玩。
In this case, both verbs are emphasized. That means, information described about these verbs are all important.
.....去了..... 玩。
In this case, with 了 after 去, the tone has slightly more emphasis on the verb related to 去.
.....去......玩了。
In this case, with 了 after 玩, the tone has slightly more emphasis on the verb related to 玩. (But this case is a bit not that natural in this sentense. Not that "fluent".)

By the way, here 了 means already.
Answer: 了 bears the meaning of what already in done in the past, but it is not a must to add in 了 in every sentence that is in past tense.
For this case, either adding 了 or not, both sentences will still have the same meaning, 了 becomes optional especially the front part of the sentence (上个星期天) already mentioned the time.
玩 has the meaning of play which doesn't make sense if translated to English. However the 玩 in this case means something like "Have fun" or "Enjoy" where the meaning is closed to "Play". So the meaning can be "My friend and I go and have fun in 林学院的农场."
Answer: 了 doesn't denote 'past', it indicates 'completion of the verb'
Example: 明天完成了工作後来见我 (come see me after you finished work tomorrow)
If you add '了' after the verb '去' and wrote "上个星期天,我跟好朋友一起去(了)林学院的农场玩" that would mean you did go there, and the action of '去' (go) was from start to end, completed
Look at the following example and you can see without adding '了' after the verb, you can express action that's not completed

"上个星期天,我跟好朋友一起去林学院的农场玩, 但半路遇上交通意外, 沒去得成"
"Last Sunday, I went to the farm of Lin College with my good friends, but we encountered a traffic accident halfway and the trip was ruined

In  this context, you cannot use 了 after 去, because the verb is not completed.
The original sentence didn't use 了 after 去 doesn't mean the verb is not completed. It could be either, just not stated clearly. Since the sentence end there, we can presume the verb is completed and they did went to the trip

'玩' here means 'to play' or ' to tour'
Comment: Of course you would say "after you finish work tomorrow" (present simple tense) in colloquial English.
Answer: Another way to see it is that 去玩 is 离合词(Separable Word). You can insert some words in between. 去玩 -> 去农场玩 -> 去林学院的农场玩.
去林学院的农场玩了 is also correct in my opinion.
去林学院的农场玩 VS 去林学院的农场玩了, the former doesn't indicate the tense and the latter indicates it happened in the past.
In your sentence, 上个星期天 already denotes when it happens, so there seems to be unnecessary to add 了 in 我跟好朋友一起去林学院的农场玩. But I can see a nuance between with and without 了.
上个星期天,我跟好朋友一起去林学院的农场玩了 sounds like the thing that the speaker is trying to tell is that he had gone to 林学院的农场 to play/have fun with my friends. Well, 上个星期天,我跟好朋友一起去林学院的农场玩 sounds like an incomplete narration, like in English: Last Sunday, while I was going to 林学院的农场 to play with my friend, ... ... Basically, I would expect to hear more context. But with 我跟好朋友一起去林学院的农场玩了, I wouldn't expect more to come (though the speaker might have more).
去了林学院的农场玩 is not correct or natural, because 去了林学院的农场 is a complete phrase. So, it's correct to say 上个星期天,我跟好朋友一起去了林学院的农场.
Answer: 了 is more like Had + Past Participle in English grammar. Which indicate the action is done for and over with!
But it's not really necessary in Chinese grammar, because you already specify that the action took place in 上個星期天 (Last Sunday).
The only difference between 了 and simple Had +pp. is that, in some cases, 了 contains some kind of emphasize feeling. Whether the feeling is good or bad, the usage of the word make the listener think that you're profound of the experience.
If you put 了 after 去, it means that you had been to that place and came back!
And somehow also put a emphasize on the place you go. It's very similar to the English just went.
So it's more common to use in the situation when you go somewhere very far!

A: 我昨天去了火星!
(A: I just went to Mars yesterday!)
B: 什麼!?
(B: WHAT!?)

As for why 玩 is placed at the very end of the sentence. That's because to some degree, Chinese grammar is more similar to German grammar. Which also place their verbs at the very end of the sentence.
So, if you have a little understanding of German, it will probably be easier for you to understand Chinese.
Good luck!!!
Answer: You use 了 to indicate that a situation is real. That is took place in this world or will take it in this world.
Is it possible that the context of the sentence:
"上个星期天,我跟好朋友一起去林学院的农场玩"
has something to do with describing a dream or a desire (something not real)?

Why 了 is not used, and what is the meaning of 玩 in 上个星期天，我跟好朋友一起去林学院的农场玩?


IIS websites hosting and OWA configuration

Question: hi i want to know how i can configure my IIS server to host more than 3 websites. And i have configured Outlook web access but if i want to access it using the FQDN it is giving me a 404 error but if i use an IP address it is working, when i check my DNS server it seems to be fine because it is able to resolve internal and external queries.
Answer: You can do this using host headers. Here is a visual guide: http://www.visualwin.com/host-header/.
Answer: You can configure sites in IIS to listen for traffic in two ways. Firstly you can configure it to listen on an IP address, or all IP address on a particular port, usually port 80. When you have a site that does that, not other site can also listen for all traffic on that IP(s) and port, the only thing it can listen for is a particular host header, which we will come onto in a minute. In IIS configuration it would look like this:

This site in IIS is bound to listen on all IP's on the machine, on port 80.
Another method, and one you need to use if you have other sites listening for all traffic, is host headers. We can supply a host header for a site so that this site listens on an IP or set of IP's, on a port, but only for a particular host header, such as www.domain.com. Any traffic directed to that IP and port on the server, that is a request for www.domain.com, is handled by that site, requests for say www.seconddomain.com are ignored by this site.
This way you can have multiple sites listening on the same IP, without conflicting, and only serving pages for their designated site and host headers.
This site below is set to listen on all IP's on port 80, but only for requests for www.domain.com and domain.com
Answer: Just by chance: Do you have forms authentication on in Exchange? I've run into errors when trying to access OWA without forms authentication. It's a common thing to overlook when setting up OWA.
I'm sure it's not likely the solution to your specific query, but I thought someone should mention it just in case.


What is the best exercise to increase the size of my chest muscles?

Question: I am going nearly 3 years for a gym. My BMI is ok. My height is 173cm and my chest in 36 inch. Can I further expand my chest ?Is there any good exercise ?
Comment: Umm shoulder expansion exercise? You mean shoulder exercise? Or do you want a chest exercise?
Comment: Chest exercise for gain size in the chest
Comment: I edited, and regarding the close votes I don't think 'what's the best hypertrophy exercise for my chest?' is primarily opinion based.
Answer: The reality is there are 3 or 4 ways to expand your chest visually in order:

Chest Muscles
Lat Muscles
Shrink Waist
Enlarge Shoulders

A good starting point will be Dumbbell Bench Press (generally gets better range of motion than barbell), Dips, Barbell Rows, and Flies and/or Pec Deck if you have one. For some depending on your mechanics Dumbbell Bench Press could be done on a slight incline for better activation. Another exercise you might want to consider though isn't as common anymore is Pullovers which can be done laying using a dumbbell, ez-curl bar, or cable pulley system set to a somewhat low position.
With any of these exercises chest width is going to be when you can feel it in the outer portion of your chest a bit and lats. Wide grip bench press for example. Deep full range of motion benching with barbell or dumbbells, incline bench with a nice deep bottom, flyes that you really let sink in the outer part, etc... If you do everything with a regular/narrow grip and stop at or above your chest then you're going to put a lot more emphasis on chest thickness and triceps then on width.
Combine this with eating excess calories of course. You can't gain size anywhere if you're not eating some level of excess.
Answer: Do a balanced program, meaning, train your back as much as your chest and shoulders. Do high volume chest exercises e.g. Dumbbell or Barbell Bench press, weight push ups and dips, you should at least be bench pressing 1.2xbw before changing it up for something. Train higher volume with medium intensity.
Answer: Be careful with too much bench pressing if you have a job where you arms are outstretched all day as you may end up with rounded shoulders.


Epub without a Table of Contents, is it possible?

Question: Ideally, I'd like to not have a ToC. But I understand that without one, an epub won't validate. Is there any way to create a ToC with no content, including no ToC header?
Comment: Just to be clear, you're talking about he `toc.ncx` (which is required) and not an html TOC that you can optionally include as a page (or pages) in your epub, right? If so, then I'm curious as to why you would want to remove it when reader need never see it if they choose not to.
Comment: I'm assuming that you REALLY want to know if it is required to list all TOC entries  because you want readers to "fly blind" when reading through the pages. See my answer below.
Comment: @beaker: because when you convert from Quark you get an empty page titled, "Table of Contents" which is superfluous.
Answer: I'm guessing that you are asking the question in the wrong way: you actually want to hide the HTML entries from the TOC so that the TOC doesn't spoil any surprises. I have good news. In epub3 you can create a navigation page and hide all the entries in that TOC.
Let me explain some basics. The terminology can be confusing because initially Kindle required a "logical TOC" (which was an HTML file linking to all the chapters) in addition to a TOC in toc.ncx  The real TOC (which is machine-readable) was in toc.ncx for epub2  but inside the NAV element of the required navigation document in epub3.
In epub3 it is no longer necessary to have a toc.ncx file (and for future versions it will be deprecated). Instead you include a HTML navigation document (which you mark by using the NAV  element in that file). For epub3, writers of the standards wised up; they realized that rather than requiring two different kinds of TOCs, why not just put everything in one navigation HTML document, with proper tagging and then forget about toc.ncx?
Fortunately, it is relatively easy to hide TOC entries inside the NAV element of the epub3 navigation document.
Here's how you do it in epub3.  "The presence of the hidden attribute on the root indicates that the entire list is excluded from rendering in the content flow." (Source)

Table of Contents

Preface

 Requiem on the Rappahannock

Version History

I'm not 100% sure you can hide all the entries (I haven't tested that), but I'm pretty sure you can hide almost all the entries (maybe you are required to have at least 1 visible TOC item).
If you want to hide one or more entries in epub2, edit this in package.opf.
 <spine toc="ncx">
        <itemref idref="cover" linear="no"/>
        <itemref idref="htmltoc" linear="yes"/>
        <itemref idref="alternate-toc" linear="no"/>
         ...

Linear="no" means to exclude it from the TOC entries for epub2 reading systems. Importantly, note that if you have an epub3 file, the reading system will probably obey the  and ignore whatever you put in the package.opf file.
I am talking about epub and epub3. If I remember correctly, converting from epub3 to mobi produces the same effect.
The ability to hide TOC entries is important for certain kinds of books (the first thing that comes to mind are Choose-your-own adventure ebooks and other hypertexts).
Comment: I'm converting from Quark; pretty sure that it's epub2. I am not even familiar with any epub3 creation tools other than iBooks Author. I'm getting a page titled, "Table of Contents" with no entries. This page needs to go. What I want to do is suppress that page; so I'm not sure how this is asking "in the wrong way."
Comment: you are speaking about a "logical TOC" then. You don't need to have a logical TOC for epub2 -- but Amazon strongly recommends that you have one.
Comment: I typically edit the HTML files directly rather than using a conversion tool. It sounds hard, but it's actually much easier to do if you know what you're doing. Sometimes when you convert from Word/Quark, etc, you need to know what is going on the underlying  HTML.
Comment: Often conversion tools like Calibre auto-generate this TOC page by looking at the heading for each chapter. But if the styles are inconsistently applied, then this autogeneration process will fail. I bet if you go to your source and style each chapter title as "heading" or h1 (or whatever Quark has), the conversion process will auto-generate the links in this logical TOC correctly.
Comment: Unfortunately, I don't know how to apply styles in Quark. I tried to futz with the underlying ePub html but am getting errors. I think those errors are beyond the scope of the original question, so I asked a new one here: https://ebooks.stackexchange.com/questions/7213/toc-errors-thrown


Would a slower and larger rotor blade be practical?

Question: Essentially a rotor is a rotating wing and the design of that wing generates lift. My question is this, why not increase the surface area of the rotor and slowdown the rotor speed. Rotor strength will also be increased. Slower rotor speeds will also reduce the turbulence created by the larger area of the rotor.
I believe that this will also increase efficiency as the reduced speed can result in smaller engines being used to do the same work.
Comment: If you reduce the rotor speed you limit the forward speed of the aircraft because the retreating blade will stall earlier. Aviation is about the art of compromise. A slower rotor might be more efficient, but that's of no value if the helicopter is then too slow to be useful.
Comment: It's just hard to make long and strong blades. And rotor speed has its own limit, too, which leaves the only option to be adding more blades. No one want to make a 20 blade rotor if they could get away with 2, yet you still see a lot of 5 blade helicopters.
Answer: Indeed a relatively large rotor has advantages:

Low induced velocities: less sand and bushes that are swept up by the rotor airstream.
Low autorotational rate of descent.
Low power required in the hover.

However, there are some disadvantages as well:

The size of the helicopter is less practical at landing, take-off, clearance of buildings etc.
The empty weight is higher, a very important factor in VTOL aircraft.
The hub drag is higher.

A smaller rotor will have a smaller and lighter hub and a lower overall parasitic drag: more efficient for cruising flight. There is a practical limit to blade radius of about 12 m due to static rotor droop when not spinning. From J. Gordon Leishman:

The static droop can increase quickly for larger rotor diameters and may cause problems when starting and stopping the rotor, especially in gusty wind conditions where the low centrifugal forces on the blades may lead to "blade sailing,"causing the rotor blades to flap and flex and perhaps impact the airframe.

The rotational speed of the rotor is determined by the tip speed, and is set such that at cruise speed the advancing blade tip stays below the drag divergence Mach number. Reducing the tip speed permits a higher flight speed to be achieved.
Image source
There is a design optimum for rotor disk size, determined by weight. The weight over disk area ratio is the disk loading and the analogy with wing loading of fixed wing aircraft is very strong: a large wing area creates more drag and construction weight. The relationship between disk loading and operating weight is partly governed by the square-cube law, and a clear trend can be observed when the two parameters are plotted against each other: there is an optimum governed by weight, and the optimum is not the largest rotor diameter.
Answer: Rogers says,

Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller.

Generally, all else being equal, if you can get a larger-diameter propeller or fan on your aircraft, you will have greater efficiency. We see turbofans getting bigger and bigger and bigger partially for this reason. It also underscores why the AeroVelo Atlas has such large rotors.
So why not just stick giant props on everything? There are many factors, including

The practicality of manufacture. Can you build blades long enough and stiff enough without negating your extra efficiency with weight?
The arrangement of the aircraft. Can you fit the prop under the wing, for example? Or for a helicopter, will the blades have enough ground clearance at their tips when the rotor isn't spinning?
The intended airspeed of the aircraft. As Airsick mentions in a comment, on a helicopter you might get very little forward speed before stalling part of the blade. On a fixed-wing airplane, you'll more quickly run into supersonic flow at the blade tips (which causes unacceptable drag and noise) as you try to spin the propellor faster.

Any aircraft design is the result of rigorous and extensive trade-offs and optimizations. The points you make are valid, but they are usually constrained by other factors.