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How should an graduate student with Aspergers syndrome prepare for a teaching career?
I am an "abnormal" graduate student in the sense I had been diagnosed with Aspergers syndrome by a professional psychiatrist when I was in college. In college days I mostly study mathematics on my own and covered the subject by reading textbooks/lecture notes online, and I mostly learn by having private conversation with the professor instead of going to the lecture. However after entering graduate school I noticed for teaching undergraduate students, this approach does not really work. Last semester I tried to teach measure theory to my students in the probability class, and the result was in the end of the semester they still did not get what expectation really is.
This semester I have changed my approach and assuming that they knew nothing more than pre-calc. As a result my teaching performance has improved. But I still suffer from problems I assume normal instructors would not encounter. For an extreme example, I met a student asking me for quiz contents tomorrow and who makes the quiz, because the ones I gave tend to be more difficult. I responded that any event is likely including I die because of traffic accident or suicide because of depression, and in the above case there will be no quiz to prepare for.
(Added: When he pointed out this was quite bleak point of view, I suggested that) another quite unlikely event is I won Megamillion tickets and decided to quit grad school, so there will be no quiz too. (Added: Similar to this I also quoted possibility of me being late or there is a class cancellation due to snow storm. When he pointed out that no one can foresee these events, I suggested that is why having health insurance that enable me to see a therapist as well as covering physical diseases is important.) I suggested that he should prepare for anything that might happen with the quiz, and take consideration of the probabilities to maximize his performance of quiz with the time and energy constraint available.
(Added: When he suggested that bell curve is all he needed to pass this course), I also told him real life events often do not follow Bell curve and central limit theorem has limited value for random variable with no expectation exists. To make sure he is not confused, later at night I sent an email to the class repeating my points and suggested everything in the book we learned so far can be tested, and the bonus problem content can be coming from anywhere.
Later I received an email from the instructor of the course, claiming that the student was so unhappy that he suggested to remove me as an TA, because I made him "extremely uncomfortable" and "a bit scared". Further the student suggested I am "literally crazy". But I could not notice anything illogical in what I told him or craziness out of me. The instructor and I had a down to the earth conversation on this. I promised that this would never happen again. However, to be a responsible person I am confused what exactly went wrong. I suppose this is not an isolated event because the instructor told me he has received "many complaints" from students already. My questions are as follows:

What did the student went through? Why is he unhappy? I did not use any profane language or threatened him in any way. I think what I said are largely "abstract nonsense" everyone knows. In fact, I think I was being very polite for speaking with him on this boring topic for 15 minutes or not appear to be unhappy with him at all. I thought he would think like what I did during my student days, that before a test students wish the class might be cancelled and one can spend more time to review.
Has there been anyone else in this forum also having Aspergers syndrome? Can someone describe his/her experience and make some suggestions?
Is there anyway for me to avoid this kind of unwanted events in future? There is no prospect that I can "convert" to a normal person. And I do not want people to be unhappy with me for trivial events like this in future. I could have dismissed the case as the student being irrational, but I think there might be something deeper into it. So I think I should ask.
Even if there is no one mentioning this on my future teaching reference, would I be qualified for a teaching position in future once I got out of grad school? I ask because it is literally impossible for a graduate student in my university to get a serious research oriented post-doc unless he or she did something very remarkable. While I am not diffident about myself, I feel I should be serious with my future teaching career now, since I would have to teach as a post-doc as well and there will more teaching load.

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I think what I said are largely "abstract nonsense" everyone knows.

I'd bet that's part of the issue here.  When people ask a question, the general assumption is that the answer will try to maximize usefulness.  When this doesn't seem to be happening, it's viewed as a very strong signal.  For example, suppose I ask you "Are you having lunch with John tomorrow?" and you reply "I don't know.  Maybe he'll commit suicide tonight."  If there's no special risk of suicide, then this is a useless answer, since everyone knows suicide is a theoretical possibility that would disrupt the lunch plans.  So it's natural to interpret this answer as suggesting you honestly fear John will kill himself.  Giving a logically correct but near-vacuous answer is considered highly eccentric (if not done deliberately) or rude (if done deliberately).  Either way it will upset people, because it completely throws off their ability to judge what is really meant.  It can be OK as a joke under the right circumstances, but otherwise it's generally problematic.
So there's a real danger whenever you try to explain "abstract nonsense everyone knows".  It can be misinterpreted in many ways.  "He thinks I'm an idiot who needs to be patiently told things everyone knows", "He's making fun of me", "He's intentionally being rude", "He's gone crazy and can't stop talking about suicide and the bell curve even though they are irrelevant to my needs", "He's severely depressed and is trying to prepare me for the possibility that he might be gone by tomorrow [or is awkwardly asking for help]", etc.
Math culture can play a role here as well.  It's not uncommon for mathematicians to be a bit obsessive about logical correctness in everyday life.  For example, when someone asks me about my lunch plans, I have to fight to urge to reply "as far as I know" instead of "yes", since of course I don't really know for sure.  If I see a bag sitting my itself in my classroom as everyone is leaving and ask the class "Did somebody leave their bag behind?", I'm sure to get an answer of "yes" from multiple students.  Among mathematicians, this communication style is widely tolerated, and it can be viewed as amusing or a sign of in-group solidarity, but it can really provoke non-mathematicians.
So it's important to keep in mind that Asperger's and math culture can line up in ways that interfere with effective communication.  This is usually less important in advanced classes, but it can be a big deal in introductory classes, especially with students who are not majoring in mathematics.
Dealing with this can be nontrivial, but I'm confident you are on your way to sorting it out.  As I see it, the two biggest obstacles are realizing that there's an issue and recognizing that it's more than just "students can be irrational", and you've made it past both of these obstacles.

Even if there is no one mentioning this on my future teaching reference, would I be qualified for a teaching position in future once I got out of grad school?

Yes, Asperger's is far from rare in mathematics and it is in no way a disqualification for a teaching career.  Overcoming initial hurdles can lead to a very effective teaching letter, since this demonstrates a serious and professional commitment to teaching.
Many universities have a teaching center or the equivalent, where people can go for feedback or assistance with their teaching.  For example, someone could sit in on your class and offer advice, or video a session and go over it with you (seeing yourself teach from a student's perspective can be illuminating).  It might also be possible to be paired with a long-term mentor.  There can be advantages to working with someone outside the math department (who is not involved in evaluating you professionally) or within the department (who can offer better feedback on the clarity of your mathematical explanations).  Either way, it's worth looking into what resources might be available, since this can be a valuable way to improve and to demonstrate commitment.

+1 for invoking Mathematician's Answer

Cf. the cooperative principle.

+1 for the third paragraph. I always struggle when someone asks to a group I belong the question "Does someone want to do X?" How can I answer if I don't want to do X but I cannot ask all my group their opinion???

@Taladris: That reminds me of the old joke in which a bartender asks a group of mathematicians whether they would all like beer.  Each answers "I don't know", until the last mathematician says "yes".

(+1) In addition, I'd say "abstract nonsense" (and in particular random abstract nonsense) produces an impression of arbitrariness. Which is completely contrary to the students' need to be able to predict reliably what is to be expected in the exam (both with respect to the subjects covered and to the weight put to particular skills/knowledge that are tested). I'd be suspicious with respect to the fairness of grading of any examiner who exhibits signs of arbitrariness.

This is a very good (+1) answer, and seeing yourself teach from a student's perspective can be illuminating is golden advice (not only in this case)

First of all, kudos to the OP for sharing his problem. Without a doubt, this the first step towards addressing the problem. Unfortunately, most of the answers do not seem to get to the "meat" of the problem. And the main question is:

Was the OP rude to the student and was the student on the right to
  complain about this behavior?

The answer to both questions is a big YES. When someone asks a question about a test quiz and gets an answer like "I do not want to tell you because I might commit suicide because of depression" the student (in his human imperfection), has the right to feel "scared" and "awkward". But even then, the student still made the right choice: He notified the university "authorities" (the main instructor of the course) about the problem he faced. This is what we suggest all students to do (in this SE forum) when they are dealing with a dangerous  or threatening situation within the university campus. And although the danger was not real, the student felt that way, so he reported it. What would a teacher do, when one of his students told him when asked about a meeting, "I do not know if I can make the meeting tomorrow because I might be dead"? Exactly the same thing. Notify the university authorities. So first, I believe we must all agree that the student did the right call. Otherwise, the OP might not even have acknowledged the problem and how the student felt from this situation (which I am not sure if he totally gets is 100%). And BTW commenting on "I do not want people to be unhappy with me for trivial events like this in future", let me tell the OP that being "scared" by your university teacher is not a trivial event at all.
I am not a doctor and I cannot provide remote diagnoses. No one should do it especially online. But being a teacher is mostly about the students and not ourselves. We are still human, we are imperfect and we sometimes make irrational mistakes. But if something (disease, personal state, even grief) prevents us to do what is best for THEM, we should do whatever it takes (therapy, medication, personal leave) to protect them and be the best teachers we can be. Otherwise, we are not doing those young people justice.

I don't agree at all that this is the main question.  And even if it is, I don't agree that the OP was rude.  I recognise that the OP came across as rude, but rude is something intentional.  I have Asperger myself, and I strongly believe the OP that he or she meant no harm to the student.

@gerrit  According to Merriam-Webster."Rude: not having or showing concern or respect for the rights and feelings of other people". The OP's behaviour was textbook definition of it. And when people are rude they should apologize, regardless of their intention or pre-existing condition.

The OP shows a lack of empathy (which is a symptom of Asperger's, caused by lesser functioning mirror neurons), but not a lack of sympathy.  If I don't know that my behaviour causes grief in other person, then continuing that behaviour is not rude.  It is very well possible that I am concerned about your feelings, try not to hurt them, but unintentionally still do.  I don't agree that rude is the correct word in such a context.

@gerrit, there is still the "should have known" issue. Lack of intent through lack of information of which one_should_ have been aware is tricky.

+1 to Anonymous' answer.
In addition, you mention that you have Asperger syndrome. One of the key symptoms in Asperger - right in the first paragraph at Wikipedia - is "significant difficulties in social interaction and nonverbal communication". That is: your interaction with the student was likely "abnormal", to use the term that you used. And importantly, you probably have a hard time in understanding just what it is that caused the student distress.
What could have been "abnormal"? This is hard to say. Communication happens on many levels. Only a very small percentage (I have seen suggestions of 10%) are the actual information content. The rest is "everything else": choice of words, intonation, facial expression, body language, context, surroundings, relationships and so forth. It is very hard to explain what really goes on here. And of course your 10% information content could have been exactly on the mark, while the other 90% could have been just a bit outside what the student expected within the parameters of such a conversation. And that would be enough for him to conclude that you are "crazy". (Although of course telling this to your professor is rude.)
So, what can you do? One problem with Asperger is that you will need to consciously learn and practice communication norms that non-Aspergers soak up automatically, so they don't even need to think about them. I am not a therapist, so take my advice with a large grain of salt. But I would make sure that you stick with the actual information you need to convey (as Anonymous recommends). Given that you have problems in understanding how you come across, better to reduce the possibilities of being misunderstood. Don't do jokes, don't discuss six-sigma events like a meteorite hitting you.
In addition, I would strongly recommend that you look for help. Either talk to a therapist - student services at your university could probably help you there. Or at least look for a self-help group. Asperger's is not too rare, so you may find such a group close by. If you have a trusted (non-Asperger) friend, ask him to observe you in conversation and ask him to give you feedback. Maybe even take a video of you in an interaction so the two of you can go over it in detail.
If you work on your communication skills, I don't think you would be barred from teaching. One question is whether you actually enjoy it - many people with Asperger's don't enjoy interaction with other people.

The commonly repeated statistic is that 70% of communication is non-verbal. There's actually very little evidence to back this up. http://skeptics.stackexchange.com/q/15512/2974 and http://www.spring.org.uk/2007/05/busting-myth-93-of-communication-is.php.

-1 for advising to discourage communication. Practice, practice, practice.... Some of my best professors had Asperer's. Their lectures were logical, broken into small pieces, the expectations were clear, not to mention brilliant people. Focus on the strengths that come with Asperger's, and work on coming up with communication rules for yourself (social stories). But please don't stop trying.

@Orion: I'm not sure where I discourage communication. I recommend sticking with the actual information, not going into jokes and six-sigma events. Kind of like the logical lectures you like. And I explicitly recommed working on communication skills.

In the first place, I believe that the student was quite rude.
That said, your response regarding the quiz was presumably regarded as sarcastic and mean-spirited, even if it was not intended as such. I think that it is a fair question which deserves a reasonable answer, based on what you intend to do. That answer might be "Everything we've covered in class in the last three days, and in Sections X, Y, and Z is fair game for the quiz" if you don't want to be more specific.
Until you get more comfortable with teaching, I recommend making your courses extremely predictable. (This is especially true if you are a TA rather than an instructor.) You can get creative with your lectures, but I would recommend making all of your course policies very explicit (e.g. what material is covered on the quizzes), standard, and explaining them as clearly as possible. Your quizzes should focus on material emphasized in your lecture and/or the book, and not have any "trick questions".
In general, in ordinary conversation, I would usually recommend ignoring the possibility that highly unusual circumstances (i.e., your death) might occur. The question "What will you do?" may be interpreted as "What will you probably do?" or "What do you intend to do?"
Best of luck to you.

I disagree about the student being rude. Let's say you ask your teacher what the test covers, and the answer is "everything is possible; I may commit suicide because of my depression". Wouldn't you report it too? Sorry to be blunt but it's an extremely inappropriate and stupid answer

@AndreasBonini we can certainly discuss the appropriateness of the answer, but saying that someone is literally crazy is definitely rude.

@tim - I don't think that statement was intended for the OP to hear/see. The student privately contacted the instructor to express concerns with the TA's behavior, and the instructor went and blabbed it all to the TA. I think it was extremely unprofessional for the instructor to email the OP this information. I'd be very upset if I were a student in that section and I found out the professor basically just forwarded my comments to the TA and didn't even bother with a face-to-face meeting.

@AndreasBonini: I see your point, and acknowledge that my answer leaves room for disagreement. But "extremely inappropriate and stupid"? Please be more respectful.

@DaoWen: I think I should mention that the instructor did insisted for a face to face meeting. I essentially dismissed the case as the student was being irrational and misunderstood what I said. But this of course does not help me to see the underlying structure of the problem. So after some thinking I decide to ask at here.

@Anonymous I think that "it's an extremely inappropriate and stupid answer" refers not to your answer, but to the OP's reaction "everything is possible; I may commit suicide because of my depression".

@AndreasBonini: I agree "I may commit suicide because of my depression" is inappropriate, but since that's an Asperger symptom, please avoid classifying it as "stupid".

@Bombyxmori: While I agree that the student misunderstood what you (meant to) say, I'm not so sure that they were irrational (even if you do understand intuitively what is going on in their mind): Student prepares for exam. Tries to find out what to expect. Gets an answer that is far outside the expected, in a way that is either alarming (announces suicidal thoughts) or random nonsense (literally) => is alarmed that the exam may be totally outside the expected as well. To me this is analogue to e.g. s.o. crossing the street, car (originally at safe distance) unexpedly accelerates => alarm.

@cbeleites: Yes, I do not want to give the false impression that they can prepare for the quiz. I want to let them know real life is often random and one has to make reasonable guess at times. In this case the student would have to make an educated guess what might be on the quiz, and if he failed to do that he would have to study very hard in advance like I did, or more likely a combination of the two approaches. Neither solution is optimal but it would help out him much more this way than giving a few fixed topics and ask him to review these topics. My points on extreme cases was a hint.

@Bombyxmori: I'll write an answer and pick up this comment - I think it is important feedback for you that e.g. I did not get at all what you are explaining here from your answers you cite in the question.

@cbeleites: This is the underlying scenario that commonly happens everyday in grad school life. I felt everyone who ever worked as a TA for a reasonably difficult class would know already. So I did not bother to write it explicitly in my answer. But since you ask I should explain myself in a clear manner.

@Bombyxmori: a) I think being clear and explicit is our only chance here to sort out and explain communication problems. b) As for the "being rude" thread here: you may explain to students that due to your Aspergers you may appear rude but that you don't mean it. At the same time you should be aware that non-Asperger people use "I don't want to be rude, ..." as an introduction to being rude. So such statements can backfire. c) sorry, my first comment is missing  a not: "... even if you do not understand intuitively..."

@cbeleites: I did wrote a very, honest, clear questionnaire on how to improve my lecture from now on after this social fiasco, but my friends who read it concluded what I had was insulting and horrible. So I suppose I have to "double speak" sometimes to convey my message to make it polite. And this might be a point for confusion. In this case I do not know how to reject him in a polite manner, so I treat this as a math problem and give some hints. But the student clearly cannot follow.

@Bombyxmori: may be a cultural thing as well. I'd say "horrible" is not a helpful judgment: it doesn't give a direction how to improve. But insulting is bad news. Firstly insulting is unprofessional, and secondly insulting questions generate upset answers and complaints, but likely nothing useful for improving the lecture. "Double speak": you may need to adjust/calibrate the translation. My guess is that you need someone to help you with that who has very good understanding both of your condition and of normal communication. (I somehow imagine this is as if you were colorblind and required...

... to deal with red and green nuances - but I have no idea how good that analogy is)

Bombyx, I think just saying, as you wrote above: "Real life is often random, and you have to make reasonable guesses at times. You will have to make an educated guess what might be on the quiz or study very hard in advance. Neither solution is optimal but this will help you out more than just giving a few fixed topics" would have been an excellent and appropriate answer that would not have alarmed anyone.

I think the other answers have done a good job of explaining the why the student was offended by your response in this situation. So instead I will try to give you some general  "rules of thumb" that would help you avoid similar situations.
When someone asks you a question, before you answer, think about why they are asking and what the answer means to them. Often there's a deeper, more fundamental question underlying what the person actually asks, and that's the question that you need to answer. In this case, the student was nervous about the exam, and wanted to know how he could improve his chances of passing.
If you have to deliver bad news, acknowledge what it means to the other person, and stick to directly relevant facts. In this case, the bad news that you had to deliver was that you couldn't (or wouldn't, for pedagogical reasons) tell the student what was on the exam.
Here's an example of an answer that might have worked better in this situation: "I understand you're worried about the quiz. I can't tell you exactly what's going to be on it, but it will be material that we discussed in class. If you review your class notes, you should be well-prepared." The first sentence acknowledges how the student feels. The second sentence delivers the bad news. The third sentence answers the underlying question, sticking to the facts. You might add something helpful like "Make sure you understand the concept of 'expectation'."
This answer will not completely satisfy the student, who was probably hoping to be told exactly what the quiz would be so he wouldn't have to do as much studying. But at least it delivers the bad news in a way that doesn't make the student feel any worse than he already feels.

What did the student went through? Why is he unhappy?

I can only guess, but I would say that the student expected concrete and short answers, such as:

Question: "Who makes the quiz?" Answer: "I will be making the quiz" (unlikely events preventing you from making the quiz are implied).
Question: "what will be the content of the quiz?" Answer: "Everything we covered in the last X weeks" or "Chapters X, Y, and Z of the book" or "Topics A, B, and C".

Your answer to the first question was probably received as too general and off topic, and might have made the student uncomfortable because it was a bit personal (regarding depression and suicide).
As to your answer to the second question: everything in the book is not an answer students like to hear, but it certainly can be a valid answer (if everything in the book is actually relevant to the class). content can be coming from anywhere on the other hand will make most students unhappy, because they cannot prepare for it. I know it is just for bonus points, but still, it would probably be better to base those questions on the content of the book as well, as to not frustrate students.

Is there anyway for me to avoid this kind of unwanted events in future?

Try to give short answers that you think will help the students the most. You can - as you did in this case - follow that up with an email, in which you can go into a bit more detail.
And although there is nothing wrong with being a hard teacher, scaling down the difficulty of your tests will make students happier and more forgiving. You don't have to create incredibly easy tests just so students will like you, but if your tests are always more difficult than those of other teachers, this can make students resentful (even if their main objective is to learn, passing this class and getting good grades is important for them and their future).
As others mentioned, you might also want to look for outside help. This can be therapy if you want to and can afford it, but you could also discuss events such as this with friends/family/possibly colleagues, and send important email (and maybe tests) to them before sending them out to students for proofreading.

Even if there is no one mentioning this on my future teaching reference, would I be qualified for a teaching position in future once I got out of grad school?

I don't think you should let yourself be hold back by this. It seems that you would have to do some work (because you received "many complaints"), but if this is something you like to do, do it.

There have been a lot of useful answers already.  Although my own teaching experience is limited, my own Asperger's syndrome has frequently led to communication problems because of different understandings, so I will try to address your questions from an Asperger perspective.

Is there anyway for me to avoid this kind of unwanted events in future?

You can minimise, but not completely avoid.
All humans, in particular neurotypicals, are irrational.  The statement “I might be dead tomorrow” is rationally obvious.  Rationally, the statement might be expected to have zero impact (but see MSalters' comment).  However, it will have non-zero impact on almost everybody (including many Aspergers, who have been functioning in a majority neurotypical environment and have consciously or subconsciously adapted).  This illustrates that people are irrational — unless, as MSalters points out, listeners assume the statement must have non-zero information, and therefore assume there must be some non-literal (i.e. hidden) content.
You can minimise this kind of unwanted events by constructing a (mental) model of how information is perceived.  This is non-trivial.  It requires an understanding of Theory of mind.  For such an understanding, Asperger's Syndrome is a handicap.  Although Aspergers are likely over-represented in a mathematics department, Aspergers are still the minority.  So, we need to adapt.
Other answers have addressed how information is perceived in this specific example.  I'm almost sure you have experienced similar¹ miscommunications before — if you're not aware of any, then that's almost certainly because you did not receive the feedback you received now.  Therefore, my literal answer will be: No, there is no way to completely avoid this kind of unwanted events in the future.
However, you can minimise.  How would you go to construct such a mental model?  I would recommend seeking communication with fellow Aspergers.  There are many forums, chatrooms, and mailing-lists for Aspergers online, including some specifically focussed on Aspergers at universities.  Perhaps there is a autism meetup group at your campus or in your city.  As Asperger's, we need to adapt to a neurotypically-dominated world.  Based on my personal experience, at this stage in life, I think this is more productive than therapy.  Online or offline — sharing experiences with people with similar neurological wirings is no doubt helpful.

¹In this case, by similar, I mean: any misunderstanding that can be attributed due to an Asperger sender intending a literal content, but a receiver interpreting a non-literal content.

As a probabilist, the OP might like the following interpretation: "might" literally means "with nonzero probability", but most people use it to mean "with probability significantly greater than zero" or "significantly greater than baseline". "Will" literally means "with probability 1", but most people use it to mean only "with very high probability".

Being rational, the reason for communication is the conveyance of information. Hence, a rational listener would interpret “I might be dead tomorrow” as containing a non-zero amount of information. Thus, a rational communicator does not state the obvious, precisely because no information can be conveyed by it.

@MSalters That is a good point.  I did not think of that.  My answer is somewhat oversimplified.  I have edited to point out that, indeed, if a listener assumes the statement must have non-zero information, the logical conclusion in this case is that there must be non-literal information conveyed.

Now that I think of it, that "Theory of Mind" idea is somewhat flawed as well. I wouldn't like to play poker against someone with Asperger. It's way too easy for them to have a logically correct ToM. I think the real problem is that not a "model how information is perceived" but the handling of a multitude of models how information might be received. It's almost Schrodinger's cat: you can't look into someone's head to see how the information is received, and until they open their mouth you won't know ;)

@MSalters We're getting into semantics and off-topic here, but when I say a model I don't mean a simple deterministic model, but indeed the multitude of fuzzy models where one can never really be sure.  That's what I understand theory of mind to be anyway.  Also: even when people open their mouth you still don't know what they really mean (at least I often don't).  It is unlikely the undergrad referred to in the question would have openly spoken his or her mind directly to Bombyx Mori.

I somehow tend to see a large difference between "I might be dead tomorrow" and putting this into a likely context: "any event is likely including I die". I'd even say this is a literal difference.

You wrote:

I met a student asking me for quiz contents tomorrow and who makes the quiz, because the ones I gave tend to be more difficult. I responded that any event is likely including I die because of traffic accident or suicide because of depression, and in the above case there will be no quiz to prepare for. And another quite unlikely event is I won Megamillion tickets and decided to quit grad school, so there will be no quiz too. Similar to this I also quoted possibility of me being late or there is a class cancellation due to snow storm. When he pointed out that no one can foresee these events, I suggested that is why having health insurance that enable me to see a therapist as well as covering physical diseases is important.

This is a very odd response - if I had a teacher say something like that I would be alarmed as well.
First of all, suicide, depression, personal health, and therapists are all private topics that are personal, alarming, and intrusive to bring up out of nowhere. These are things you should be very careful about discussing with others, especially in a professional context. When you're talking to students, you have to have different boundaries than when you're talking to a friend - you have to be professional and not bring up personal and private things, especially concerning and alarming things like therapists and depression and suicide.
What were you thinking when you said that? Why did you bring that up? It's important to be aware of people's boundaries and how they might react when you say something, especially as a teacher.
Second, it's not in any way relevant to what he asked - he was asking for information on the test and none of what you said has anything to do with that.
I'm not sure if anyone's linked to this yet, but it would be good for you to read and study this and follow it when talking to people: http://en.wikipedia.org/wiki/Cooperative_principle

I suggested that he should prepare for anything that might happen with the quiz, and take consideration of the probabilities to maximize his performance of quiz with the time and energy constraint available.

This is oddly and very formally worded, but it's at least an answer to the question. Why not just give a simple and direct answer like "Everything we talked about in class could be on the test." I thought people with Asperger's were often very direct - doesn't that strike you as a clear and direct answer, whereas talking about winning the lottery or snowstorms is off-topic?

I also told him real life events often do not follow Bell curve and central limit theorem has limited value for random variable with no expectation exists.

Well yes, but again what does that have to do with anything?

To make sure he is not confused, later at night I sent an email to the class repeating my points and suggested everything in the book we learned so far can be tested, and the bonus problem content can be coming from anywhere.

Saying "everything in the book can be tested" is a fine answer, but I hope you didn't "repeat the points" about suicide - that's the kind of thing you could easily get fired for.

Later I received an email from the instructor of the course, claiming that the student was so unhappy that he suggested to remove me as an TA, because I made him "extremely uncomfortable" and "a bit scared".

Not surprising, seeing as you brought up suicide and seeing a therapist. That tends to make people uncomfortable and scared.

However, to be a responsible person I am confused what exactly went wrong.
  Is there anyway for me to avoid this kind of unwanted events in future? There is no prospect that I can "convert" to a normal person. And I do not want people to be unhappy with me for trivial events like this in future. I could have dismissed the case as the student being irrational, but I think there might be something deeper into it.

In a word - boundaries. Be aware of what boundaries people have, what they expect and don't expect, what they are comfortable with and uncomfortable with. This isn't trivial or irrational - it's a big deal. When people's boundaries are violated, the way you violated that student's boundaries, they feel very uncomfortable and it will cause you a lot of problems.
Suicide and mental health are an extreme example - that's the kind of thing people only talk about with people they're close to. Same goes for sex, religion, and politics. With people you don't know well, or people you have a professional relationship with (like students you teach) make sure you stay with "safe" topics of conversation.
I would suggest finding a therapist or social skills group or someone who can talk to you about this and help you get a better understanding of people's boundaries and expectations and how to relate to people in a professional setting.
By the way - this isn't just you. It's very difficult to figure out how to comfortably talk to people you don't know or people you have to be "professional" with, and this is true for everyone, Aspergers or not.

This is a very good answer. +1 for the link to the Cooperative Principle / Grice's Maxims.

Certainly many mathematicians are strange in one way or another. In some departments to the point that not being so makes you stand out. In one very prestigious department I worked in, it was quite common to make statements like " he was strange even by the demanding standards of this department."
So I wouldn't rule out a mathematics academic career. That said, I think it's unwise to become a lecturer/professor if you don't actually enjoy teaching.
I would echo what others have said regarding seek professional help. A large part of teaching is trying to understand the learner's point of view and this is roughly what Asperger's syndrome makes you bad at.
One coping strategy I would suggest is that every time something goes wrong, make a note of what happened and work out what the correct response should have been. Then remember this and use it the next time the situation arises.

Mark Joshi! I used to work through your book in distributions in the summer before grad school! I know you are a student of Melrose. How are you!

I am doing fine. I switched to financial maths in 99.

Thanks! My advisor is a student of Melrose. So I know about you.

I'm curious why you chose this as the "accepted" answer?  What about it strikes you as more informative than the other answers provided, from your perspective?

@Paul: It is very simple. I am reading Atiyah-Singer-Patodi paper on eta invariants at this moment. Mark Joshi used to work with world's leading expert in this field. So he is in a position better than anyone else in the forum to provide professional advice on this topic, because doing research with Richard Melrose is quite time consuming and demanding for any student. I am sure he knew what I am going through. To me his advice was clear, concise and most importantly very practical.

@Paul more likely, (and rather quite clearly) the OP selected this answer above Anonymous Mathematician's answer (which was unarguably the best answer provided) because he/she knows (of) the answerer in real life. But then again, you knew that when you asked, didn't you?

(posting anonymously, so can't make this a comment)
The first piece of advice I've been given is to accept that the majority of students are not really interested in learning, only in passing the exam. They are, in my experienced, obsessed with meaningless details like how many questions there are on the exam (who cares, when you don't know how long a question is?). Tell them exactly what they will be asked and when, so they can get marks with as little effort as possible (and repeat it every time they ask, even though you've already told them multiple times), and a good proportion of the students will be happier.
The second piece of advice I've been given is to not care about student feedback.
I don't think either of these fit well with being an Aspie.

You can only not care about student feedback if your employer doesn't.

@MarkJoshi, it is certainly true that some institutions will choose hype-up their attention to student evaluations, but I think more serious places realize that there are very serious limitations (statistically) to (especially lower-division, but not only) students' perceptions of their own welfare and how well a teacher serves it. Yes, of course, it is possible to "fail to communicate well", but that is (sometimes subtly) different from not having high student ratings.

I am very aware of all the arguments against student evaluation and I have made them at great length. However, that does not mean that I have won the argument against administrators. Some institutions love them.

Just to add to the ocean of answers:
When people ask something, there's the literal question and the actual problem. Usually they have surprisingly little to do with one another. This counts double when it comes to students.
I imagine the student was worried about not passing the test, and the uncertainty of what the test would contain was creating stress. They were looking to relieve this stress by obtaining more information. This is the kind of subtext that your condition blinds you to. I guess it's no use telling you to empathize with the student, since that's not really an option, although an analysis of the way people deal with uncertainty and stress might help you to understand some of the patterns.
I think a good thing to do is to be up front about it. Tell people about your condition and what they can expect from you. Your student was already stressed by the test and her own uncertainty, so an unexpected response form the TA exacerbated the issue, and made her lash out (albeit through your professor). If your students know about your condition, and know how it works, they can help the communication from their side. They can be more explicit in their questions, and when you respond in a strange way, they'll know where it comes from and how to deal with it.

This probably would be better as a comment, but I cannot comment yet so I have to write this as an answer:
I work with children with high function autism/ aspie. I think the "trolling" part was Aspie learned it is not good to just say "no I won't tell you" so OP do not have the intention to be rude, indeed a lot of Aspie would say a lot of weird things when they are learning how to deny a request in a more socially acceptable manner. And saying no is somehow difficult for 'typically developing' person, so yes it is really hard for Aspie to do that in a proper manner.
I think one safe approach would be just say no to the students, as in a teacher and student relationship, being direct would be okay, students may say you are strict (or even unkind), but at least they won't say you are weird. (But I won't suggest you to do so to your peers...)

Let me add some formulation suggestions, mainly in addition to mhwombat's answer and some feedback to the dialogue in the question.
I think an important assumption of "normal" communication is that the words are meant to transport an information content > 0.

Refrain of adding irrelevant sentences: do not talk of generally known but typically irrelevantly low risks (car accident, suicide).
People may interpret things into them that you never intended to say. In particular, the fact that the risk is important enough for you to state it will be interpreted as being substantially above the known general negligible risk. I emphasized negligible because negligible translates to  both negligible wrt. preparing for the exam and to neglecting to mention these risks in everyday spoken communication.
If you keep a conversation going, people will probably take this as a hint that a) you want to keep the conversation going and b) you want to communicate some content.  So, if you don't have a relevant statement to make, do not make a statement. No not make irrelevant statements (there are uses of this, also in exams, but maybe you should leave this to teachers who have a very keen perception of whether communication goes well, and who also know how to rescue failing communication).
The dialogue you cite leaves the impression with me that you actively kept up the conversation. Yet below you state that it was extremely boring to you. Such a contradiction between predicted (impression) and literally stated desire/emotion/communicaton aim will mainly tell people that they cannot successfully recognize/predict what you want. Logical conclusion: they don't know what you want and the expectation shifts towards difficulty as in possible failure in communication also in the future. Plus: expect it to be hard work to communicate successfully with you.
If you are not able to judge the students' emotions very well (with very well I actually mean a perception that is well above the average "normal" person's ability to judge emotions!), the time around exams is not a good time to try being funny or communicate by subtle hints.
In contrast to what other people suggested, I don't see for the described situation that being short, direct, honest and to the point with the answers about the exam ("I will prepare the quiz, and it can cover all the topics we had in the lecture so far.") would make the students unhappy or anxious or upset. In particular: this is not upsetting at all as I'd consider this the "default-value" for the answer and therefore totally expected.
But then I'm from a culture that has a reputation to be very direct.
Even if the student realizes that you probably don't mean what they would usually expect to be the meaning, they will (possibly emotionally/unconsciously) conclude that they cannot properly communicate with you - and that is highly alarming to students facing an exam: the failed communication leads them to fear that the communication in the exam may go wrong as well. This is completely rational: they conclude from a failure that failure may occur - though at the same time it is not comprehensible to you if you cannot detect the failure in communication. And in exam situations the acceptable risk of failed communication is very low.
You emailed

bonus problem content can be coming from anywhere

a "less alarming" formulation (assuming this covers the meaning you wanted to transport) could be

 To solve the bonus problem, you'll have to transfer techniques covered in the lecture to solve a new type of problem.

This will be less alarming than "can be everything" because it is a positive and more precise statement of what the bonus question is about.
In a comment above you told me:

I do not want to give the false impression that they can prepare for the quiz.

This was a highly unexpeced statement for me. In particular, the dialogue you described in the question did not suggest to me that this was a possible intention of yours. And I still find it slightly (situatively) contradictory to your statement "before a test [...] spend more time to review". I'm aware that I implicitly assumed that this statement would apply to the current test as well.
I met very few exams for which no preparation was possible or reasonable. Preparation for me means increasing the understanding of the subject and connecting it to other subjects rather than being able to repeat stuff from a list. So if you really and literally mean the students cannot prepare for the exam, state it. Logically, if the students objectively cannot prepare, they also need not prepare  - and because that is a very unusual situation, state this as well and in addition explain why they can and need not prepare for this exam - they'll be suspicious and not take your statement at face value otherwise:

You cannot and need not prepare for this exam. Don't worry, this exam is meant to be taken without further preparation, because [reason].

with [reason] e.g. being "you can solve all questions by logical thinking"

My points on extreme cases was a hint.

I wouldn't have gotten that hint. I may have gotten such a hint/nuance by someone whos communication I can judge very well. In the dialogue you quore, I'd have dismissed your sentences as weird/inadequate and possibly-to-probably irrelevant and my major conclusion would have been that I do not understand you reliably. Therefore, I would not even have looked for any hidden meaning: the chance of hitting the right hidden meaning [if there is any] would have been too low compared to the "noise" of obviously failed communication.
My guess is: just as you cannot judge the nuances of what the students say, they (and I) cannot judge the nuances of what you say.  Or maybe you overestimated the amount of "guessing" that goes on in "normal" communication.
But the result is anyways a communication problem that goes both directions. I think the solution here again is to go for very clear and direct subject related sentences without hints or other kinds of hidden meaning, keeping in mind the "> 0 information" criterium. Plus building up a reputation of having such a direct style of meaning literally what you say. If people can trust that they just need to take you literally, things may be much easier for both sides.

So, if it is not wise to restrict the world-view to bell-curve only, you could say:

 It is not wise to restrict yourself to bell-curves.

Although, personally, I'd have not said anything at all. (Which, by the way may be taken as a hint or not, but this does not matter particularly - you are safe either way)

(resorted statements)

I want to let them know real life is often random and one has to make reasonable guess at times.

While this is true in a narrow and literal sense, I have the suspicion that you may experience life (particularly where other people's reactions are concerned) as far more random than I do. E.g. most communication with other people (including their reactions) is highly logical and even predictable to me. I am not used to perceiving everyday life as random,  although I professionally do lots of statistics and I often take the role of the one who points out what cannot be concluded due to randomness/noise.
In the context of exam, I'd call randomness arbitraryness (of the examiner) and see it as totally inadequate. This would not be the "narrow randomness" of having different versions of the exam populated with random numbers to avoid cheating in the calculations, this is rather the randomness that means that the student has to be very knowledgeable in the subject in order to be able to guess what the examiner is driving at/wants to hear.
In other words, be clear about the separation of different layers of meaning in the exam and don't mix them. The topic of the exam being randomness does not imply that questions or grading should be arbitrary. On the contrary: questions still should yield a reliable and reproducible measure of the students' abilities wrt the topic of randomness.

In this case the student would have to make an educated guess what might be on the quiz, and if he failed to do that he would have to study very hard in advance like I did, or more likely a combination of the two approaches.

Well yes, but again on a "normal" level this is obvious - also for the student. The "> 0 information assumption" means that explicitly stating this emphasises this educated guessing, so you transport a meaning that this is far more relevant in the present situation than usually.

Neither solution is optimal but it would help out him much more this way than giving a few fixed topics and ask him to review these topics.

I don't agree, although I see your point. I may be thinking of a list of much broader topics than you think of, though. But IMHO the more general connections to other topics can only be made after one has mastered the narrower points and only the general level allows informed guessing. Otherwise the guess is not educated but wild.
And again, there should be no need to guess "what topic did the teacher have in mind here?". But asking good exam questions is an art that few people master.

Emotionally mature students are probably able to "buffer" some or even most
of the "weirdness" due to your Asperger's in normal lecture situations (in particular if they know about your condition). But they are probably unable to do so in stressful situations like before/during an exam. So exams (including some time before and when handing back the exams) are a time where you need to be extra careful.
As explained, failed communication will increase their stress/nervousness as in addition to the subject they realize they need to prepare for an additional psychological stress test.
Last but certainly not least I want to point out that the nervousness of students before an exam may include conditions like exam anxiety. The combination of student anxious because of the fact that they are facing an exam (which can be totally independent of their ability wrt. the topic of the exam) with your Aspergers is IMHO just heading for trouble.
Unfortunately, I cannot give any good advise on this: such a student would probably anyways try to not let you (or other examiners) know of their anxiety, particularly if that is triggered by a fear of examiners being unfair and arbitrary and taking advantage of their power [so it is tactically bad to show weakness]. If the communication with you does not work as with other people, this may trigger lots of suspicion and anxiety. And I guess this is a situation that you will basically be unable to recognize - most examiners may not be able to recognize it. For this, your only safe bet is to behave always as extremely reliable and fair and as predictable as possible.
Personally, I'd think it much preferrable to have direct, honest, to the point and expicitly logical communication than failed guesses how a fancy communication could be.

Hi! Your long response is appreciated, but I just want to point out that "review" before a test is reviewing all relevant knowledge related to the purpose of the test, not just going over lecture material the instructor covered in a limited amount of time. I thought this was the norm, as most real life tests I had was similar to this. I did not know this would be a confusing point for people.

@Bombyxmori: thx for the appreciation. a) this site is quite international, and there are definite cultural differences in how teaching/lectures "normally" work e.g. between the US and central Europe. b) In my university context, the "list of points" will list the relevant knowledge, e.g. "derivatives and linear algebra" (as in: test ist not about statistics) c) This whole question is about communication problems, so better be very explicit and literal. d) In addition, English is not my mother tongue, so I'm anyways not sure I get all nuances.  Confusion potential may be lower for others.

Hi! This is okay as I am not a native speaker as well. But I saw little point to give a boring test ask students to recite material they memorized from lecture notes and after the test they would totally forgotten. I thought a real test have to test their understanding of the material. And this kind of test one cannot just prepare by going through section 3.1, 3.2, 3.5 of the textbook. But I do not know how to show this to my students, that what one learned is what one understand after put away the textbook and formula sheets.

@Bombyxmori: There are recommendations around here of how much of an exam should be mainly repetition, how much should be applying stuff directly to new problems and how much should be transfer to new problem types. I'd say how to prepare a good exam is a totally different question. And judging from the exams I wrote and corrected, a generally difficult task...

My child was diagnosed mild Aspergers 2 years ago, and I found I have the same syndrome though I'm too late to be diagnosed. I'm in IT line which requires less communication more calculation. I prefer work/social/play with familiar people, nervous otherwise, good in maths, poor in language, communication. But people describe me nice, shy and smart. You'll be a good teacher in future, just need time to gain experience. Or do researching instead of teaching?

“I'm too late to be diagnosed” – I am no expert but I am not aware of any age limitation for diagnosis. (Not that I would suggest that you must have this tested – that’s something you have to decide.)

Good for you for trying to find out what went wrong!

What did the student went through? Why is he unhappy? I did not use
  any profane language or threatened him in any way. I think what I said
  are largely "abstract nonsense" everyone knows

Talking casually about death, dying, and suicide is a social taboo.  Some people may interpret this as frightening. As someone with Asperger's, you may have to memorize certain social norms.  Temple Grandin has noted (see her TED talk) that one thing that she thought was helpful is that when she was a child, social norms were taught to children ("children were taught manners").  Nowadays, most children are expected to pick up on social norms intuitively.  I found this book helpful (even if you aren't a girl): "A Smart Girl's Guide to Knowing What to Say" by Patti Kelley Criswell (Author)

Is there anyway for me to avoid this kind of unwanted events in
  future? There is no prospect that I can "convert" to a normal person.
  And I do not want people to be unhappy with me for trivial events like
  this in future.

One thing you might want to do is just tell the class that you have Asperger's.  You could start out a tutorial session with something like:
"Before I start talking about the material this week, I think I need to just let you know that I have Asperger's.  This means that I don't pick up on social cues very well.  So sometimes I might say things that are odd to you.  I am sorry.  I am trying to interact better with people, so if I do something odd, please feel free to tell me, and I will listen and take note.  If you want to learn more about Asperger's, you can watch this great TED talk at this URL.  Now let's get on with the material."
In my experience, students are much more willing to accommodate someone if they know what is going on, and if they know you want to improve.  It might make them happy that they can teach you something.


text:
Author states that he is owner of his photographs but they have been published in various journals
I'm editing a volume and I am responsible to obtain permissions for figures and photographs the authors wish to use in their respective chapters.
Now I have an author A who included several of his own photographs within his chapter which is great. My problem is that most of them have been previously published - in several different journals under several different authors (A is always among the authors). The author stated explicitly that these are his photographs but I'm not so sure. Do journals not normally claim figures along with the text and require even the authors to ask for permission to reuse "their" own content?
Does this apply only to figures or also to photographs? I checked the image caption in several of the publications and it never explicitly states "Photograph taken by A".
Do I need to obtain a permission from the copyright holder/owner of the journal? Should I just create a statement along the lines of 'Photo taken by A, previously published in A et al. 2010'? Should I make A sign a document stating that he always retained the copyright and can therefore license it for use in the present chapter? Should I contact our publisher instead of asking this on StackExchange? Probably, but you guys are much faster ;)
Context: The edited volume will be published in the U.S.A. by a STM-signatory.

How many pictures are included? The STM Association has a list showing whether you need to ask for permission (notify) the publisher before reusing a figure. http://www.stm-assoc.org/copyright-legal-affairs/permissions/permissions-guidelines/

The problem is that not all previous publications in which the images were published may be owned by STM-signatories.

In general, you have to options: 1) Ask the author to get the permissions from all previous publishers and/or make A sign a statement that he did or owns the copyright. 2) You ask the publishers for permissions. Usually, it's the job of the author.

The responsibility of certifying and negotiating copyright issues is typically the responsibility of specialized staff at a publishing organization, not that of the scientific editor of a work.
The responsibility of an editor here is just to make sure that the authors follow the process the publishing organization asks the editor to have them follow, which typically includes making copyright assertions or providing contact information to the people who will actually ask them to make copyright assertions.
Thus, if you have concerns, you can convey them to your contacts at the publisher to be sure that they are aware of these concerns and can sort them out. If you aren't the legal personnel responsible for sorting out the details, however, you shouldn't be trying to make any arrangements yourself: that is likely to create more problems than it solves.

When authors publish their work in scientific journals the copyright is almost always transferred to the publisher as a condition of publishing. Therefore the author no longer has copyright on their images. To republish the same images in a new work, written permission from the copyright holder (journal publishing house) is required. In practice all of the journal publishing houses I am aware of have simple webforms to fill out for obtaining such permission. Sometimes you can get this for free in as little as a week, in other cases there could be a delay of a few months and a fee imposed. Depends on the Publisher!

This is not true in all fields.  See, for example, arXiv's copyright statement or the ACM's licensing options

arXiv is not a publishing house or a scientific journal ... it is a manuscript depository with a commenting function. OP is asking about articles published in journals.

You are missing the point of that reference: arXiv is a dominant means of pre-publication in some areas of research. Accordingly, the copyright practices of journals in those fields have adapted in response, as indicated on the linked page: "Many journal agreements permit submission to arXiv using the non-exclusive license to distribute, which arXiv has used since 2004"

Yes many journals permit the word file to be deposited in arXiv or researchgate. However that does not mean the images in the journal can be republished in a 3rd party journal or book chapter publications without obtaining permission because those agreements are not in place.

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text:
Where to publish software-related work?
I am a researcher in computer science. I am used to publish papers on computer science problem resolution (machine learning, optimization, disabilities, pattern recognition...).
In recent work, we needed to create a specialized software incorporating many complex technologies. This software is used to conduct other researches on which we already publish.
We are wondering if we can publish on how the software helps to solve our problem and on how we designed it with multiples technologies. A careful debate on the possibilities, choices and architecture would be incorporated.
The problem is this is the first time we would publish such article and we don't know where to publish. We are seeking good scientific journals (if possible with an impact factor) accepting such papers. If you know one, can you tell me?

Not entirely clear what kind of software you are talking about. Since you mentioned machine learning: the journal of machine learning research accepts 4-page articles on open source machine learning software (impact factor ~3).

possible duplicate of Should I write a paper on open-source software I've built?

What field your software is targeting? In bioinformatics and cheminformatics, journals accept things like application notes. For CV or other image related software, they are mostly published in a conference.

If the software system is targeted for a research problem that is deep, recognized by the community, requires complex architecture and design, and from which a wide community can benefit from, then system conferences could be a good match.
I'll give you an example. Symbolic execution is a widely used and researched technique in software verification. People from Stanford developed Klee, a symbolic execution engine that aims to be highly practical and scalable. Making
such a system required taking care of quite some details. They published paper
on OSDI, and I believe they received best paper award. Klee paper.
Other than that, there might be conferences in your particular area that care
about building systems for the problems you mentioned, but I guess you already took a look into that. Hope this helps.

The Journal of Open Source Software is a good place to start. I believe it was created in 2018.
This article links a lot of journals that may be applicable.

I don't think there's enough information in this question to give a yes or no answer of whether this is publishable.  It might depend upon factors like: what problem it solves, whether the problem is novel, whether the problem is important, how novel the solution is, how useful this will be to others, how effectively you can evaluate your solution.
So, instead of giving a yes or no answer, let me instead suggest a process you could use to form an answer on your own.  I would suggest that you talk to your colleagues in your area and ask them the same question.  They will have the domain knowledge and will be in the best position to judge the contribution of your particular work.  Take a few minutes to sit down for coffee with them and get their advice.  Personally, I've always found this to be an incredibly valuable exercise.
I can't tell you where to publish it, as that is highly domain-specific: it'll depend very heavily on your field, the area of research, and the nature of your contribution (which you haven't told us).  In general, if you are thinking of publishing somewhere that you are not familiar with and where you are an outsider, it will be especially important for you to make sure that you learn the related work and the values and culture of that community.

The Association for Computing Machinery has at least two journals with the word "software" in the title:

Transactions on Mathematical Software
Transactions on Software Engineering and Methodology

I don't know much about the latter, but the former publishes mathematical software packages.

The Open Channel Foundation publishes software created by academics. They have published one of my software programs that I created for research.
http://www.openchannelfoundation.org/

They're looking to publish an article about the software in a scientific journal. This doesn't seem to answer that question.

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text:
If I think I have a publishable idea on a certain problem, how do I publish and proceed?
I'm new to research.  I'm working on a certain problem that has sort of been abandoned by all researchers (as far as publications go).  Anyway, I like it for its simplicity and easiness to grasp.  However, it's a new algorithm for a problem and a new way of possibly answering theoretical questions about the problem.
There is so little research out there on the certain problem, that it would literally take you a day or less to view it all and ascertain that indeed the idea hasn't been looked at yet.  I'm applying the well-studied field of integer programming / linear algebra to model each instance of the problem.
Anyhow, regardless of whether I answer a major open problem, I think the approach is valuable in itself, if for no other reason that it makes answering basic questions about the problem a lot more easy, sort of like how algebraic geometry answers questions about geometric objects using algebra.
How do I proceed?  Do I just spend a month perfecting the paper on my own and put it on arXiv?  Is that all?

There is so little research out there on the certain problem, that it would literally take you a day or less to view it all and ascertain that indeed the idea hasn't been looked at yet. --- Perhaps a statement like this can confidently be made in your field, but in mathematics even if it were the case that you could look over the research on something in a day, it could still take months or even years to shift through the literature (MR reviews, Zbl reviews, JFM reviews, things like this that few people seem to know about, etc.)

to find those handful of papers, books, unpublished but circulated notes, etc. and to be reasonably sure that you haven't missed something that has since been mostly forgotten (buried in someone's Ph.D. dissertation or something).

Thanks all for your guidance.  I am actually working with someone who's persuing a master's in math.  So, there's my "accademic connection."  Perhaps he could show the paper to his professors for endorsement.

You are on the cusp between math and CS, actually. The better way to "publish" your work is to write it up formally, with references/citations and everything and submit it to either a journal or a conference. Choose one that matches the content of your paper.
But also make sure it is a reputable journal and not one that just publishes anything for the money you pay them.
However, you also have to be prepared, with journals, for publication fees, even with reputable ones. Sometimes they may waive the fees, but you may need to find a way to pay them. And, for conferences, make sure you have some way of attending if your paper is accepted for presentation. In CS, conferences are usually preferred. In math, usually journals.

However, you also have to be prepared, with journals, for publication fees, even with reputable ones — Really? I have never paid a fee to publish a journal paper. (I work at the intersection of math and CS.)

@JeffE, yes, a number of high quality journals charge page fees for publications. Often grants pay them. Often universities pay them. Sometimes authors do. Sometimes they are waived. I'm pretty sure TransAMS does (or did, back when).

Strictly speaking, Transactions doesn't charge page fees for publication; they charge a per-article fee for open access, which I find rather silly given the existence of the arXiv.  (When I first started published 25 years ago, it was common for CS journals (SIAM J Computing, for example) to advertise voluntary page charges.  I took the word "voluntary" at face value and never paid them.  Nobody I knew ever paid them.  Our papers were published anyway.)

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text:
Conducting a training seminar without projector
What is the best way to conduct a training seminar inside a computer laboratory without a projector?
Is there an existing software program that could achieve the same results as conducting a training seminar with the aid of a projector?

Are you using existing material designed for a projector,or are do you need to design your own (and prefer software over a projector)?

there is an existing, but i could do with software over projector

Whiteboard markers?

Hehehe nice one @JeffE, sorry forgot to mention no, whiteboard.

Is there a window? Alternatively, can you spend $50 at Staples and buy your own whiteboard?

Put your seminar material online, and just have people view it at the same time as you talk. It can be any easily readable format, like PDF file or simply series of web pages. If you are not sure that people will follow, just put large bold numbers on each page, and announce what page you're at when you change page. (A bit like kids' audio book!)
Either that, or hard copies of the material.

I think were on the same page, but is there an online to allow me to change which slide they are looking at by changing my slides? is it possible?

Why would you want to? (I assume your students are adults.)

I'm not sure I get the situation:
Does "no projector" (and no whiteboard) mean

You do not want to use a projector (nor a whiteboard)?
=> IMHO you should then know what you want (and tell us why), without that we'll not know what to answer
Or: just there is no projector available
=> borrow projector somewhere
or is it no possibity to project to a suitable space
=> borrow projector and screen,
no possibility for placing a screen, neithr
=> or go for a different room?

CLI or GUI? If GUI, you can have everyone watch your screen w/ a remote desktop client. Other solutions for CLI too (screen program) but I guess you're using a GUI.

more or less the same idea, but i need something that does not require to be installed. Is there a web-based solution that could have the same results?

Never used it myself, but I think Big Blue Button does what you want.

Not installed on your or their computer? I think all OS have clients. You might need to install the server, but even that I don't think so. This is a user-level default software solution.


text:
Standing out in the era of big science
How do scientists who choose to work on big collaborative projects (e.g. LHC experiments, LIGO, etc.) differentiate themselves when time comes to apply for post doc/professor positions, considering their papers can have hundreds or more authors?

I might suggest changing the title of the question to something more akin to "How to stand out when working as a member of a large academic team?" to differentiate this question from a "how to do I stand out as the next Einstein?" question.  I very much like this question :)

Perhaps you could add value to yourself, the whole package, by getting involved in outreach.  Also, emphasize whatever special side talents you may have been contributing to the team effort, e.g. programming, team-leading, writing, editing, graphic design, web development, etc.

Primarily by succeeding in the informal respect economy that operates in these fields.
He or she needs to impress the people they collaborate with (especially those who work with them daily or weekly) by some set of

Playing an active part in a large number of useful side projects and analyses.
Spotting danger to the physical apparatus coming before things actually break.
Building, fixing and maintaining parts of the physical apparatus.
Contributing significant parts of the production software.
Dealing with difficult parts of the analysis (covariance analysis, systematic uncertainties, finding way to measure irreducible backgrounds, etc).
Doing a good job of promoting the project, giving talks and interacting with the press.

but most of all

Taking a leadership role in planning and organizing the experimental effort (from conception though feasibility analysis, design, construction, commissioning, calibration, operation through analysis and publication).

Starting at the level of a junior professor dealing with funding becomes a very important part of the mix, as does providing students and post-docs who are themselves good contributors.

The flip side is the way you evaluate candidates is heavily driven by who you know (it is easier to get a foot in the door if you have worked with someone at the hiring institution), by letters of recommendation and by word of mouth inquires (so gossip plays a part here).


text:
How to deal with a piece of text and materials that you do not consider essential?
How do you normally indicate a subsection, or a part of the text that it is not so important for the rest of text. Let me give an example:

[...] This method uses ABC as a coefficient.
Subsection: how to measure ABC
[some text and a plot, making up for roughly one column]

The subsection can be skipped, but is probably too short to appear as an appendix at the end.

the subsection "how to measure". measuring ABC is not so important but nice to have it in the text.

It depends a bit on your field of research.
In fields that have a somewhat strong relationship to mathematics, it is common that lemmas, theorems, examples, etc. are typeset in special environments. You can also typeset a note or a remark in such an environment, which allows the reader to easily skip over the part, and at the same time makes clear that reading this part of the paper is somewhat optional.
As an example, the publisher Springer provides a style file for the document typesetting system LaTeX for publications in their "Lecture Notes in Computer Science" series here. The documentation states in Section 8a that "note" and "remark" environments are available.
Here is how using a "note" in a paper looks like:

Note that there is no rule that prevents you from referencing to a figure in a note.

You don't need to tell the reader what they can skip; instead, you should tell the reader what is in each section and how the sections relate, and they will decide for themselves which sections to read.
The truth is that very few experienced researchers actually read a paper end to end like a novel.  Instead, a paper is typically subjected to a sort of literary triage, in which the reader first skims the paper and hits the high points (e.g., title, abstract, figures, theorems, conclusions) in order to determine whether the article is relevant enough and credible enough to invest more time in reading.  Even after that, readers will often skip around, deciding which bits are worth investing in reading thoroughly, and which to come back to later if needed.  See, for example, this nice manual on how to read a paper from a course at Rice University.
Some paper formats are effectively set up to enable such reading.  For example, many high-impact journals like Science and Nature have an ultra-short article format, in which the whole article functions as an extended abstract, and most of the details are typically relegated to the supporting information.
For long format documents, however, such as many other journals, or book chapters or theses, you instead want to be explicit about the structure of the document, saying clearly what the purpose of each section is in the introduction, and what the subsections are for at the beginning of a section.  For something that you are reviewing or reproducing for reader convenience, just say so, e.g.:

Section II.A reviews the measurement methodology that we have adapted from [cite].

and the reader will have enough information to know whether they want to read or skip.

I think you have the following options:

Use an appendix. If I understand you correctly regarding the amount of content that we are talking about, I would not consider it too short for an appendix and successfully published shorter appendices (two short paragraphs and one plot). As a reader, I would not feel “cheated” by any appendix that contains a figure.
I have never stumbled upon a journal guideline limiting the lengths of appendices and unless your journal has one, I would not assume that one exists. Should your journal have an internal rule about this, they will tell you soon enough and at worst you need an additional proof to rectify things.
Use a footnote or endnote. This is rather an answer to the general question as it does not seem to be applicable to your situation as you have a figure.
Move all the content into the figure caption and just refer to the figure. Of course, this only works if the content is appropriate for a figure caption.
I have seen one or two journals (but cannot name one right now) that allow authors to use floating text boxes. These are like figure or table floats but contain only text and are intended for background or supplementary information.