text:
While teaching how should I give justice equally to both female and male students?
I am 27 years old unmarried male teacher. I have been a teacher (lecturer) for the last 6 months in an Engineering institution. My students are 4 to 5 years younger than me.
The problem is that while teaching I have soft corner towards female students. I don't understand whether it is due to opposite gender attraction or due  to female students asking more doubts than male students. I help  female students more than male students.  I know that it is against moral ethics of teacher's profession. But I couldn't change my attitude. Now, I think that male students might have noticed this and they may make complaints against me to the principal.
So what changes can I make?
While teaching how should I give justice equally to both female and male students equally? Or should I quit teaching?

What kind of environment are you teaching in? "principal" implies primary or secondary school, but your students are 22-23 years old. Please [edit] your post to clarify.

P.S. for what it's worth, studies suggest that teachers in general tend to treat male and female students differently (example), but usually not to the point where it's so noticeable that the students are complaining to the principal.

@ff524 Different should mean appropriate. As one probably should treat a self-conscious, still unexperienced student differently from a confident, highly skilled one. Everyone to maximise their individual potential.

@ff524 I am teacher in an Engineering institution  where there are many departments. Each department has its head of department. And all these heads of department come under principal. Also, I am thinking that "students may have noticed this and they may complain against me to the principal."

@ff524 in the US, maybe. My (Scottish) university has a principal, but neither my primary nor my secondary school did.

@ff524 "principal" implies primary or secondary school -- not true in general.

Male students complaining that you are giving too much attention to the female students: that is not as bad as female students complaining that you are giving them too much attention!  But in any case: now that you know about it, you must change.

Have the students complained, or are you afraid they might? Both situations are quite different.

@Davidmh no student has complained yet but I am afraid that they might do

Might be time to go back to some elementary school ideas.  Like uh... put the student names on popsicle sticks and draw them randomly.  Ok maybe that's not good for university.  Still, there are ways to even things out by taking the decisions out of your hands a bit more.

Some suggestions? Is there a counseling center on-campus that you can go to?
If you can speak in confidence with trained personnel about these types of issues, that could be a great first step.
I would avoid bringing this up to your engineering department as a first step, though.
Good luck!

Normally, the problem is the other way round.
For instance, one phenomenon is that I often found with male students is that they override/overrule/overtalk female ones. If that happens more than sporadically, I interrupt them and tell them to let the other student speak out (of course this cuts both ways). I mention this as a concrete example for a trigger/action based approach that works well to reduce imbalance. With this, I get good participation from the whole group.
You talk about "soft spots". Beware, this signals danger. Your student's gender should be strictly taboo for how you deal with them. It is absolutely essential that all your students feel equally respected. Is it that you give more time to females? Then actively allocate more time to males. Is it that you encourage females more? Balance this by introducing some competitive element (such as voting on responses, competitive problem solving); male students tend to like that (of course, I am generalising, it needs playing by ear). Intersperse your presentations with adventurous anecdotes of topic-relevant scientists.
Generally: make a point of addressing more of the neglected students.
BTW, this does not only hold for gender, but also for preference by activity or ability. Activate less able, or less active students. If you do that well, you earned your badge as teacher.
Under no circumstance treat your teaching as a dating opportunity. It is not. Getting a jealous girlfriend might be an idea to help getting things under control - if you cannot do it yourself, it may be the way to delegate that job to her (and I am not yet entirely sure whether I am joking here).

If you really can't change your actions, find a different profession.
You're aware of the issue - you admit you spend more time helping the females than the males.  Find a way to equalize that problem.  Be sure that you make your time available to all genders - use office hours, or clarify to all students how to get help from you.  Look for the patterns where you realize that you cut off help from the men and continued to help the women - there's like an unconscious bias that you may be able to over come with a pattern.
Changing a pattern like this may not be easy - but it's what's rightfully expected.
Also ponder - why - why do you give women more time?  Are you hoping for something more than a teacher/student relationship?  Is something more pleasing about them? What's causing the problem, and can you reduce the factors that lead up to it?
I suppose the other alternative is to find a place where you teach only one gender.  Then you don't treat your students unequally.  Personally, that seems like taking a short cut.

Overcoming biases is extremely difficult. In order to reduce your bias, you need to identify when (not necessarily why) you give extra attention to the female students. Once you know when you give extra attention, you can work on being fairer. Some possibilities are:

If you preferable schedule them for office hours, you can use a first-come first-serve sign-up system (online or paper based).
If the bias is related to answering question after class, you could require students to make an orderly line and address people in order (i.e., take your choice out of it).
For question in class, you can use a "clicker" device so that people get addressed in order (and not when you see them).
If you spend more time on each question from females, you could either time your answers, or make sure you finish your answer with "does that answer your question"
If you grade differently based on gender, you can use anonymous electronic submission.

@User001 clickers are not only practical, they can be super useful: https://www.cmu.edu/teaching/clickers/ Most LMS systems (e.g., blackboard and moodle) allow anonymous marking. You say the rest are obvious, but don't say if you are already doing them.

should I quit teaching?

Maybe, due the fact:

I couldn't change my attitude. Now, I think that male students might have noticed this and they may make complaints against me to the principal.

Ans: Quit is not a solution. If you do not fix your attitude you can make the situation equally bad (i.e., people complaining to the principle, as mentioned in the comments) in other professions too. However, if you start fixing yourself from now onward, things can easily get right even in the teaching.

So what changes can I make? While teaching how should I give justice equally to both female and male students equally?

If this all is due to opposite gender attraction overwhelming you (as I understood):

The problem is that while teaching I have soft corner towards female students. I don't understand whether it is due to opposite gender attraction or due to female students asking more doubts than male students. I help female students more than male students.

While, you know (but you can't help yourself):

I know that it is against moral ethics of teacher's profession.

And, you've  mentioned "unmarried" in the following (if you mean this as one of the factors deforming your attitude):

I am 27 years old unmarried male teacher. I have been a teacher (lecturer) for the last 6 months in an Engineering institution. My students are 4 to 5 years younger than me.

(while being the lecture seems to be a new chapter in your life)
I would suggest you to try to remove "un" ASAP.
OR
Try to get tharapies that would help you control yourself getting into such situation.
Left unchecked may lead to serious implications on your professional life at least.

Wait, am I read this right in that one of your suggestions is this person gets married as soon as possible?  Highly doubt that would change anything.  Married men don't stop being attracted to women.

@Andrew Whatever As a side note, "being attracted to women" shouldn't be a problem.

Yeahhhhhhhhhhhh this is about more than attraction, it kind of sounds like he's looking (consciously or not) for some kind of response from his female students.  Maybe lonely and desiring female attention, in which case finding someone and getting married MIGHT help, but... it's not like a lot of married dudes don't do the same thing.

@AndrewWhatever In my opinion, (though culture/country specific) tougher social and legal implications for married people (especially for men) can bar them or at least help them mend their ways. Which can also help a man stay content and concentrate on the right things to become a better professional.

I wonder if there is any research on this.  I haven't seen much evidence that people who like female attention stop liking it once married.

If you want to do justice to your profession then I would suggest a few tips:

Divert your attention to weaker male students and arrange sessions for them.
Always maintain direct eye contact with the male students and not with the female students (eventually you should, just avoid it for some time).
Motivate men and talk with them whenever you talk to women. (I.e. just devote equal time to both males and females.)
You can sometimes give favours to men instead women so that they are more inclined to you for any sort of help whenever it is required.
Remind yourself consciously that you have to pay equal attention to all.

Hope this helps.


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Should I ask my teacher before using speech-to-text software?
Should I ask my teacher before using software of speech-to-text in classes ? The software in question does not record (the audio) at all, just "hear" the input and output text.
What about using it in conferences and lectures ? And is it OK to share this with other students ? I'm more worried about legal issues than anything else (European Union and U.S jurisdictions).

Related questions: Is it okay to record audio for a lecture? and Under what circumstances would a professor be offended at students taping or recording his or her lecture?

I do have problem with what you say "The software in question does not record at all,".  When it outputs texts, do you display it? Do you store it? Please clarify.

@scaaahu Sorry, I meant that the software doesn't record AUDIO, only the texts. The texts are then stored in google docs

@Freedo Then YES. Really, really, YES. How would you take to having your words recorded and put online without permission?

@JessicaB Well, google docs is "online" but it is not public at all, so what is the difference of having it locally on your phone/pc ?

@Freedo No data has ever been accessed without permission from a 'safe' online space...

@Freedo FYI, when you put text on google docs, you grant Google a worldwide license to use, host, store, reproduce, modify, create derivative works (such as those resulting from translations, adaptations or other changes we make so that your content works better with our Services), communicate, publish, publicly perform, publicly display and distribute such content. (although The rights you grant in this license are for the limited purpose of operating, promoting, and improving our Services, and to develop new ones.)  So "not public" is debatable.

@JessicaB, you should mark sarcasm more clearly, some people have the respective sense completely absent.

The only possible answer is that it is not allowed to record what is said without explicit permission. Same, just stronger, applies to sharing it. As  @FedericoPoloni's comment states, you are sharing with Google and giving them wide permission to use the recording, and that is an even bigger no-no.

Yes.
It is always polite to ask anyone for permission before acting towards them in a way that clearly differs from what is generally taken as the norm.
I'm curious what you see as the argument against doing so, given you ask about etiquette.

I suspected that the teacher wouldn't want records of what they spoke without a lot of preparation like you do in lectures, and worried that I could leak it for revenge or things like that

@Freedo Exactly.

@Freedo For an extreme case, I could imagine a situation where a medical lecture is teaching about a very rare condition, and they are allowed to discuss cases within the lecture because it's necessary to protect people with the condition, but that private information should not be generally released because that could identify someone's medical history.

@Freedo that is an excellent reason for asking them in advance. The answer may be no, but the consequences could be worse if they discover you were recording them without permission.

I think that you should indeed ask. Depending on your country / institution normally either the lecturer or the University owns the copyright to the oral presentation, and I suspect it is immaterial whether you record his voice signal or the spoken words.

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Is it reasonable to start a PhD during the Master's dissertation semester?
I would like to start my doctorate in the same university during the last semester of my Master's. Do you think it is wise to do this?
Think that I will have to start writing my Master's dissertation, meanwhile taking PhD courses (both starting 2016's fall and finishing by mid 2017's spring) and right next to start my PhD thesis (2017's fall).
So, what is your advice?

It depends on the department and university. What does your Masters thesis/departmental advisor say?

@Luigi I think they don't mind about it. My question is more related to intensive track pressure and to short time gap between one program to another.

Depending on how your university deals with things, courses you take in 2016 may count towards your Master's and not your PhD.

It really depends on country and culture. In most places you are rather busy to do even one, so doing both can be too much.

I would like to start my doctorate during the last semester of my Master's -- Why?

I think it's an extremely attractive proposition, but not necessarily realistic. For a start, your master's degree/dissertation result most likely won't have come in by the time the PhD term starts (and your master's dissertation will give your institution a good idea of what your PhD performance will be). For my own institution, I submitted my dissertation mid Sept and my mark came in early December. There's no way I could have started a PhD a week after submitting my dissertation! But your deadlines may well be different.
Secondly, how you would have time to do a well-thought out PhD proposal while you are doing your master's dissertation is beyond me. Don't do too many things at once. Bear in mind that when your master's dissertation finishes it's a good idea to start thinking about your PhD topic pretty soon afterwards anyway. Work through the proposal carefully and thoughtfully during the Autumn and submit before Xmas/Jan - especially if you are going for funding. Then you will have to work on your supporting statement.
Thirdly, it may be a good idea to collect yourself and have a year between master's and PhD. I'm currently at that point and while I do miss academic responsibilities, I do have a couple of things to involve myself with in my field. Join your library, do some reading. You may also appreciate a year [well, it's less than a year] to have a little time out before your full-on PhD.
Summary: while it's extremely attractive as an idea to do PhD straight after master's I don't think it's practical. You need mental and physical space to do things well and to commit to both properly. Don't push yourself too hard and don't be scared of your year in between the two. As you must know from your time in master's, it's better to pace yourself rather than to rush things.

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Do I need an introductory paragraph in SOP?
I'm about to write a SOP. I have sketched some points that I want convey through it, then I will develop them to their own paragraphs. Here they are:

I believe that I was born for scientific research.
I think I have been familiar to the scientific activities.
I want to shift the discipline to biology after spending 4 years in physics.

And I want them to stand in the beginning of their paragraph so that the readers can know which point they are reading. For my personal taste, I want to find another way to connecting the paragraphs without using transition words. For me, everything seems to be ok, I don't find any trouble to read it (I'm the one create it, of course). However, when I gave my sample of SOP to my mentor, she said that she didn't see the connection between them and made her feel lost. I have asked in writers.SE How to indicate the topic has been changed without using words?, and Chris Sunami suggests me to...

...include an introductory paragraph that summarizes your overall structure

While this is a great advice in general, I don't think that it will be applicable in SOPs, since you don't have enough space to write one.
So, do I need an introductory paragraph in SOP?

I just had to say: including the idea "I believe I was born for scientific research" is a terrible idea. Did no one tell you to avoid cliches? Try to change that to "I have done / am doing X, Y and Z, all of which demonstrate an aptitude and passion for scientific research" instead.

Didn't you already write your SOP like two months ago?

@Johanna we have, in fact, more than once (e.g. here, here)

None of your points are especially interesting to an admissions committee. The point you should be trying to convey (if you want to be admitted) is: "I would be extremely successful and productive in your program" (followed by specific evidence supporting that assertion)

@Johanna I have opened a separate question instead of asking in here. Hope to see you there.

Three things.
(1) From the little information you have shared I believe the problem may lie with your structure; either in your individual sentences, your overall essay or both.
(2) The reasons you have provided for applying into the programme you're interested in are not strong enough. Inadvertently, I t might decrease your chance to get into the programme. My suggestion is to demonstrate (a) passion (b) initiative you have taken to deepen/affirm your interest in the programme and (c) why specifically that programme at that university.
(3) Finally to answer your question. Essays generally have three basic components: introduction, body and conclusion. So yes you need an introduction. To say that "there is not enough space" is to say you've not been critical to your essay and cut 'fat' sentences.
I hope this helps.


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I have an article in the field I am just interest and has no overlap with my major. Should I mention it my SOP?
Related questions:

Should one mention multiple, albeit somewhat unrelated research interests?
Should I talk about a unpublished paper in my SOP?

Besides physics as my major, my other interest is linguistics, and as you can see, there is no overlap. When I was in high school, I wrote my first article in linguistics. It hasn't been read by any professor or published in any specialize journal, not because it was rejected, but because I haven't tried to do so. I had a graduate student in linguistics review it for me, and it seems that she finds it interesting. As far as I know, there is currently no material on the topic I researched available on the internet, which indicates that the topic is new.
Because (1) it is the first article I have ever wrote, (2) I did it when I was 16 or 17 (although I have updated so much it lately) and (3) the topic is new so far, I consider it my proudest scientific activity. I think putting it in the SOP will make a steady point that "I was born for scientific research." Will it be useful if I do that, or just mention the latest article in physics I wrote?

Are you applying to graduate programs in physics or linguistics? If physics, it might be too irrelevant as its not published or peer reviewed.

I'm about to apply to... biology, but the branch is relevant to physics (theoretical biology). Many physicists collaborate in it.

Not directly an answer, but one of my personal passions is disproving the claim "these interests are unrelated." The acoustics of vocalization and related physiology is an active, fascinating area of research which obviously requires both linguistics and physics. The study of information transmission can apply the concepts of thermodynamics to linguistic domains. I'm certain there are dozens more examples.

@Tim Maybe. However my linguistics article certainly does not affiliate with physics.

https://xkcd.com/793/ :-)

I wouldn't mention it. As Chris C states in the comments, it is not peer-reviewed and is not directly relevant to your area of future research.
My answer would change if the article were peer-reviewed and/or published in a journal, however. I think demonstrating that you have the ability and motivation to submit an article for publication is a positive attribute for a potential graduate student, regardless of whether the paper is in your field of research or not. For example, my first publication was not in my current research area, but several reviewers of my application later told me that just having a published paper set me apart from other applicants.
Since you claim that at least one person in the field finds it interesting and that the topic is new, why don't you want to publish it? Is there a way to at least submit it for publication before your applications are due?
In my opinion, it is a little dangerous to put unpublished articles on a SOP or CV. A reviewer might arrive at the (potentially false) conclusion that you're trying to pad your CV or SOP with articles that may never actually be published, which can hurt you. Others might wonder why you feel that the article is important enough to include on a graduate application, but not be important enough for publication.
Overall, I think the safer thing to do is omit it for now. If you end up moving forward with disseminating it further, then I would consider mentioning it.

Thank you so much. The reason I haven't tried to do so is because of procrastination. I always find that I have something more urgent to do. However, I do want to publish it. If you say so, I will consider to find a person to review it. But it will take times, and maybe it end up after my application are due.

Also, do you think should I spend a paragraph for it? How much should it be?

That is a hard question. I would probably address all other aspects (like your preparation for your chosen field, etc.) before addressing this. If you do address it, I would keep it short because it isn't very developed right now (largely unreviewed and unpublished). Again, it's a tough call.

Let's assume that it is reviewed by some qualified reviewers and on the process to publish it (I'm not say that it will eventually be accepted). What is your suggestions?

With the caveat that I don't have all the particular details of your application, I would say just mention it as an example of your research ability.

I have take my risk and add it to my SOP. I write my experience as my answer. I notify you if you are interested.

Before continue to read this answer, I think you should read Florian D'Souza's answer first.
Well, after consider many aspect, I decided to take the risk and included it into my SOP. My motto is "Do whatever that doesn't harm". The hardest part is to know the distinction between the good things and the looking good things.
Note: this answer is my own experience
Turn out that's a good idea. In the interview room, at first of course the interviewers wanted to focus on my "on-topic" research. After they satisfied with my answer, they couldn't hide the curiosity about my  "off-topic" one. I think it's reasonable since I come from the natural side of science, applying to the STEM scholarship but have my first research in social science. They still kept their critical thinking, asking me about the assumptions, the model of collecting data, the explanation, the result, etc. But I think that they also got entertained with my presentation.
Unlike what I was cautioned before, they didn't care if the work was published in any journal or not. In fact, all they care was the research itself. I think this is because they were not linguists, so they couldn't evaluate the value of the work.
But to be fair, they also didn't ask whether my "on-topic" research was published elsewhere or not. I think at the level of mine, a published paper is not expected. But making a research outside my field is also unexpected.


text:
Unprofessional to write (in a paper) that something is "really cool"?
Is it unprofessional to write (in a paper) that something is "really cool", for example, when describing a colliding black hole simulation?

If you simply want to transfer to the reader the experiment is cool you can use other words. Conider explaining why it is cool. It may make you paper more robust.

Would it be okay to write that colliding black holes are groovy?  Keen?  Fab?  Gear?  Phat?  Spiffy?  Ace?  Grouse?  The bee's knees?  The cat's pajamas?  Totally bitchin?  The new hottness?  Hella wicked?  Da bomb?  Off the chain?  All that and a bag of chips?

You could say that something is "cool" if it has a relatively low temperature, "really cool" if there is some possibility of doubt but you can prove that it is true.

Similarly, you could say that something is "groovy" if it has a lot of grooves.

@JeffE I am now trying to think of experiments in which I might reasonably be able to work in one or more of your terms.

It sounds unprofessional and unscientific. Imagine also your readers in 30 years, what will they think? They may not even take the paper seriously. Indeed, current potential readers may not take the paper seriously.
What would you think if you read an old paper that describes a black hole simulation as "groovy"?

I can see where you are coming from (thanks for the answer by the way). However, isn't the appreciation of the 'coolness' of 'theory x' independent from the scientific rigour that 'theory x' is subject to? How could one convey, in a more professional manner, that something is cool? Or is this best avoided entirely as being too 'emotional' for academic (esp. scientific) publication?

You could write in a way that conveys your enthusiasm. Most stuff we do is intrinsically cool, albeit to a small group of people (sometimes just one person).

@User17670 My go-to word for "really cool" is elegant. 'This elegant simulation of the dynamics of a black hole captures...'

You're off here. The word cool has been cool for generations, and will probably remain so for quite some time. It has staying power. That doesn't mean it's appropriate in a scientific paper, but the probability is that it won't date nearly so badly as groovy.

@TRiG: Yeah, sure.  Tell it to the Marines.


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What to do if a referee plagiarises the result after rejecting a paper?
I find myself in an awkward situation. Nearly two years ago I submitted a paper to a reputable mathematics journal. After 15 months it was rejected with the rationale that there had been papers published (most since the submission date) that contained results that I should have referenced. I found that a little spurious, but moved on and put my work together with some colleagues and got our new paper accepted (pending some language issues) by a different journal.
However, one of my co-authors has found that my exact result (barring some small notational changes, but with the exact same language; I can recognise it as mine, I slaved over finding just the right words!) from my original paper has had the proof published in a book by one author of the references that caused the paper to get originally rejected!
My assumption is thus that the paper was sent to this person to referee and they liked the result so much that they kept it for themselves, which also explains the delay in refereeing... I believe that this author has also presented this result at a conference as their own work. They have a number of papers published on the topic in question from their doctoral thesis.
My question is what steps can I take now to re-assert my authorship?
I believe that it would have been simpler if I had also submitted it to the arXiv, but I wasn't sure (at that time) how that would be seen by the journal. I did give a presentation of my results at a local conference, so I would be able to produce credible witnesses to back up my claim, if necessary. The book published containing my work is largely the doctoral thesis of the author, so I am attempting to find a copy of the thesis since it was deposited before I submitted my paper to the journal. Can anyone suggest any other recourse?
My co-authors would prefer to err on the side of caution and include a reference to the result in our revised paper, but I would really like to reclaim my work...

The American Mathematical Society has a Committee on Professional Ethics that can assist with cases like this.  I imagine the Canadian Mathematical Society does too, but I don't know.

Any updates on this?

Our paper containing my result has been published with wording that I was happy with. A followup paper seemingly went to the same referee (it was the same style of reply, anyway) and it was refereed in a reasonable amount of time. There were just a few things in that paper that we needed to fix, but hopefully that paper will be published soon...

I would not waste a microsecond in blowing the whistle on this. In the future, when you produce an important paper, send a copy to yourself by mail for the effect of having it postmarked. Do not open it. At a later date, you can prove that the text existed in your possession long before the publication date of the plagiarized text, and that in fact is the oldest copy which carries some kind of authenticated date: evidence that you are in fact the author. There are other ways like having the paper certified by a notary public.

@Kaz The postmarked envelope establishes nothing. How would you prove that you didn't mail yourself an empty, unsealed envelope to get the postmark on it, and then insert a document and seal it at a later date?

@DavidRicherby You're right; if it's important, just spend some money and get it notarized.

@Kaz: Somehow your advice, which is very appropriate for 1972, has gotten transported in time to 2014.  Nowadays: just put your paper on the arxiv (or some other preprint server with a timestamp).  Problem solved.  This has some collateral effects, which are also beneficial to you.

Do you have anything timestamped from your submission? In any case the journal ought to have a record.

@Kaz All decent publishers now operate electronic submission systems which archive everything relevant to the review process, especially if the need arises to prove/disprove accusations of fraud (e.g. encouraging self-citations by journal). As a member of editorial board, I am even discouraged to send any mail directly to any of the parties in a review process. So proving that the certain reviewer had access to the manuscript should be trivial, if the publisher/editor cooperates, and they should without any further consideration.

I suggest that you write a formal letter to the journal editor who handled your submission.  (Make sure it is the same editor.)  Give all the relevant details, including dated copies of all correspondence (whether electronic or printed).
The editor should know who refereed your paper, and although the editor will not reveal their names to you (I assume that blind refereeing was done), he or she would be in the best position to act on the matter.
Perhaps the best thing that could happen is the editor agrees that some unethical behavior occurred, the editor helps you file a case against the erring referee, the erring referee gets penalized, and proper attribution is given to you.
Perhaps the worst thing that could happen is the editor does not believe your story, thinks you are just looking for trouble, and tells other editors and referees that you are a "bad, crazy person."  Or the editor does believe your story but is a close friend of the erring referee and so acts as if he or she does not believe your story.
Either way, at least they know that you are aware of this unethical behavior and this will perhaps discourage the erring referee to continue with the unethical behavior in the future.

Thank you, I just sent off an email, will let you know the outcome! If anyone has any other suggestions, I'd be glad to hear them, but hopefully this will work. I'll accept this answer formally this time tomorrow as per the FAQ...

I just heard from the editor after less than a week; the answer was supportive of me and I will be kept informed of the outcome of their actions, so far as the anonymous process allows.

I'm curious: did you get your work back?

I am also curious here at the end of 2017, could you give us a general update @jp26?

I have had no similar problems, but have made a point of explicitly asking any journals that I submit my research to to not use this individual as a referee, and no journals have minded doing that.

I love your answer; however, if the editor file a case against the referee, then he is breaking the anonymity of the referee. This is because most cases are publicly known, and by simply searching for the cases I will be able to fig-out who is the referee.

There are some useful resources at http://www.siam.org/journals/plagiarism.php (especially if you submitted the paper to a SIAM journal, but some of them are more broadly useful).

My co-authors would prefer to err on the side of caution and include a reference to the result in our revised paper, but I would really like to reclaim my work...

I strongly agree with you on this.  You have a right not to share credit with a plagiarist, and you also don't want to seem to be treating it as independent work.

I am attempting to find a copy of the thesis since it was deposited before I submitted my paper to the journal.

That sounds valuable to me.
Joel's suggestion of contacting the editor seems like the best way to start, especially since the editor may have critical information (if the plagiarist was indeed the referee, then the editor would have proof), but there are also several other ways you could follow up:

You can ask a professional society you are a member of to investigate.  For example, the American Mathematical Society has a Committee on Professional Ethics.
You can complain to the publisher of the book.  A respectable academic publisher should seriously investigate the complaint, but unfortunately some publishers are not respectable.
If you discover any evidence of plagiarism in the dissertation as submitted to the university, you can bring it to the attention of the university.  Even if the dissertation was submitted prior to your paper, it could be worth doing some web searches to look for other plagiarism in it.  If you can document previous plagiarism, it will establish a pattern that may help make your case even more convincing.  I'd be surprised if this is the first or only time this person has plagiarized.
If the plagiarist is employed at a university or research lab, you can complain to their employer (since plagiarism is a form of professional misconduct).

Unfortunately, you may never reach a really satisfactory conclusion (see http://www.siam.org/journals/plagiary/index.php for a case study).  For example, it may end up with the plagiarist using flimsy excuses ("I copied the text by accident when I mistook my notes on your paper for my own research", "my undergraduate research assistant copied it without my knowledge", etc.) and basically getting away with no serious consequences.  However, if all goes well you should end up with an authority figure, such as an editorial board or ethics committee, agreeing that your results were stolen.
When you reach that point, I'd recommend publicizing the case, for example on your web page.  Of course whether to do this is a personal choice, but I think it is a valuable service to the community to let us know about a plagiarist to watch out for (and it may deter or uncover other instances of plagiarism).  You could even publicize it now, although of course if you do so you should make sure to present a compelling case and avoid speculation.

The flimsy excuses you describe are too flimsy: if you happen to believe them, you may feel that the person in question plagiarized without malicious intent, but anyone who says that is certainly admitting to plagiarism and should face all of the consequences of that.

Exactly, there is no value to these excuses, but they are distressingly common.  What seems to happen is that some universities are unwilling to admit that they are letting anyone get away with deliberate plagiarism, but they are also unwilling to actually punish anyone (maybe they don't think the behavior is so terrible, maybe they would rather cover it up, maybe they know it is a systemic problem they don't want to face, maybe it is bureacratically difficult to do anything), so they push for a flimsy excuse and then pronounce themselves satisfied.

Sunlight is the best disinfectant. So long as it gets swept under the rug, nothing will happen. If you publicize the issue, then often the university will have to respond. Besides, this isn't a simple case of a few sentences or a paragraph being lifted—this sounds like a whole paper (thesis chapter) was lifted wholesale. That's a much bigger issue, and one no self-respecting university administration can ignore.

This exact situation happened a few years ago, and the result was:

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/our-business/policies/article-withdrawal).
This article has been retracted at the request of the Editor-in-Chief of Results in Physics, the original authors and journal, IEEE Transactions on Energy Conversion.
The paper constitutes a case of plagiarism of the article “Fault Detection of Eccentricity Based on Multi-Physics in the Permanent Magnet Synchronous Motor” by Doo-Young Kim, Dae-Kee Kim, Hyeon-Jin Park, and Jung-Pyo Hong that was submitted to IEEE Transactions on Energy Conversion. Ferhat Çıra served as a reviewer of the original paper and recommended it to be rejected, then used the same material in his offending paper in Results in Physics.

You can guess what happened: after the paper was published, the original authors raised a complaint with the original journal and possibly the editor-in-chief of the new journal. The complaint was investigated, found to be valid, and the offending article was retracted. Note the paper was retracted at the request of all three parties, hence they were all involved.
I can't tell from the outside if the authors complained to the new journal, or if they complained to the original journal who then contacted the new journal. Still, if I were an author, I'd notify the new journal as well and tell them that I have also contacted the original journal, just as a heads up.

This happens. Quite often, in fact. You can get somewhere by pursuing this formally with the editor, but first carefully consider the political lay of the land. I should not be saying this, but it is the truth: if the editor and the plagiariser are buddies, and if one or both of them are "big shots" in the field, you are not only likely to get nowhere in this particular matter, but to have your reputation sullied in the bargain. Discuss this with your co-authors, especially the ones that have been around the block once or twice.

This is just a layman's perspective, but  here's what you can do:
1) Keep copies of all official correspondence.
2) If you have not touched the file at all, take a screenshot of the file explorer displaying the file name and the "last modified" date.
3) Get a signed statement attesting to your character and to the fact that you spent long hours putting your essay together.
The key is to gather enough evidence to conclude that the editor probably plagiarized. If you were to sue the author, all you'd to do is prove that there is a > 50% chance that the guy plagiarized your work.

A screenshot of the "last modified" date has no value.  (You can alter the timestamp in the file system, it's easy to edit a screenshot, and in any case the file name proves nothing about the contents.)  Signed character references could theoretically be useful, but I've never seen them play a role in any plagiarism case, so I don't think they are worth spending time on.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Survey or original article: Which one is more important to get postdoc or tenure-track position?
There are two main opinions about originality and contribution of ISI (journals which are indexed and listed in JCR report by Thomson Routers)* survey/review journal articles compared to original articles in ISI journals. Some scientists consider survey papers lacking originality while others think the opposite especially for survey articles presenting the state-of-the-art and research challenges. So, I am wondering, in general, which type of article has the most impact on an applicant's success when applying for a postdoc or tenure track position; survey or original article?
*It was asked earlier, so it is wise to put its meaning for clarity.
-Certainly having both of them is the best, but among these two which one has more impact.

In which field?

questions here should be general enough for all readers, but my case is computer science.

In that case: Neither. Conference papers are more important.

@JeffE, are you sure? For instance, publishing original paper in Mobisys is more important than publishing a survey paper in IEEE Communication Surveys & Tutorials or ACM Computing Survey (both conf and journals are somehow equally prestigious)? How?

Yes, I'm sure.  You need to have original research results that are visible to your community; journals are too slow, and almost nobody in CS reads them.  (I'm the chair of the faculty recruiting committee in a top-5 US CS department.)

I see, good to know. But the problem in some Asian university like University Malaya is that conference, even Mobisys got 0 value. Faculty wants only 2 ISI full length journals before PhD viva session and conference here is just waste of time and enjoying life, though I don't agree. Wht don't you elaborate your comment as an answer?

There's no simple answer to this question, because there are a lot of variables left undefined. I think this is what we can call an example of a "false dichotomy." For instance, consider the following examples from physics:

A first-author "original" publication in a journal such as Physica A might not be as useful as a first-author review paper in Reviews of Modern Physics.
Being third author on a review paper in Reviews of Modern Physics might not be as useful as first author on a paper in Physical Review Letters.
The stage in one's career also makes a difference in some fields: a postdoc might not be asked to do a review in some fields, but might in others. (Tenure-track professors are a separate category in this respect.)

So I think there are a lot of issues to be considered in this process. However, if one is a postdoc, this is also a conversation to have with one's research supervisor. In general, such articles would be written with their involvement and participation.

Upvote: great point raised in the examples!

Generally, for the most selective positions, original research is more important.  If you apply for a top-tier tenure-track faculty position, the conversation will focus on questions like: What has their contribution been to the field?  How impactful has it been?  What are their prospects for future contributions?
Survey articles can sometimes have an impact on a field (e.g., if they reframe a problem in a new way or present new connections), but most commonly, they don't offer a major new contribution.  As such, it is unlikely that they will be considered a major contribution.  For a typical job candidate, when people ask about their contribution, the first answer will typically be original research they were involved in.  I'm not saying this is a hard-and-fast rule, and I'm not saying survey articles are pointless (not by a long shot!), but I think it is rare for a candidate to be hired on the basis of a survey article; usually, candidates are hired because of their novel research contributions.

It would be quite unusual to write a survey article in a field where you have not already made significant original contributions yourself.  Indeed, I would suggest that if you have not worked in an area already for several years, you probably do not have the perspective and depth of knowledge to write an influential review paper.  It's not impossible, of course, especially if you have more experienced co-authors.
In order to get a post-doc or assistant professor position, you will need to have made significant original research contributions to your field.  Writing an influential review article is often most beneficial later on (e.g., when you're evaluated for tenure) because such papers tend to be highly cited and administrators who don't know your field will give a lot of weight to citation counts.


text:
How to deal with the frustration of doing PhD at a low-ranked university
Though I did my bachelor's at a top-notch college, because of low GPA I had to settle down for PhD at a low ranked university. Now I see that there is lack of intellectual atmosphere and very few people to discuss academic stuff in and around my area of research. I discuss with faculty, but it would have been nice if there was a good graduate student atmosphere which is lacking. Now I get frustrated often with the fact that it was my low GPA which led to all this. Also in general the graduate student atmosphere is very discouraging.
What should I do to make my life better? Some people tell me to mind my own business and not worry about the environment. But to me no peer level discussion leads to feelings of loneliness.

Is it possible for you to get your Master's and then switch to another university?

What is "low ranked"?  Is it a top 100 public research university (some people consider anything > top 10 "low ranked") -- or do you mean a small private college?  Just curious.

Well the college I am at is iit in india, it is the top college for undergrad in the country but isn't so good for a phd. And I happen to have done undergrad and doing  grad studies at the same place.

Try discussing your work with undergrads. A major result in mathematics was proved by IIT undergrads together with a professor.

One thing I found very depressing about graduate school  is the lack of a 'team' atmosphere.  When I did undergraduate research, my lab operated as a team.  It made things fun, less discouraging, and facilitated motivation.  Graduate school is much like the real world in a sense that everyone is 'out for themselves'.  The concept of a team does not exist which took me a long time to come to terms with.  Its odd because you would think that working as a team could only better science rather than a lone wolf approach.  But that doesn't teach you to be independent either.

While I understand that you seem to be asking about face to face interaction, I find it hard to believe that you can't find any forum/list/community online that is up to whatever academic level you are looking for.  Is this not the case?

Who says you're better than them?  Maybe there are other students at your school who also went to top universities and had low GPAs.  Try hanging out with them.

Stop whining and start kicking ass.
Work hard with faculty (and undergrads!) that you respect, do some awesome research, and then (if you are very lucky) move to a better department, either as a PhD student, a postdoc, or even a faculty member.
Meanwhile, own your past mistakes, but forgive yourself for them.  You put yourself in this situation, but holding onto your frustration and loneliness, instead of doing the best with what you have now, is only going to keep you frustrated and lonely.
(My undergrad GPA was 2.4/4.0.)

You, sir, have made my day!

Agreed, if you want to be noticed focus on your research.  Do a couple conference preceedings and meet some other PhD students.  Expanding your network will get you more heads to bounce things off

Your undergrad GPA is impressively low for someone who went on to a very successful academic career.  I checked though that you got your undergrad degree in 1987 (at an excellent school).  However, I think that times are different now: in 2013 graduating with a 2.4 GPA is perilously close to not graduating at all, and I think that such a GPA would strictly bar you from admission to most reasonable graduate programs.  (I say this as a member of my department's graduate admissions committee.)

I think that such a GPA would strictly bar you from admission to most reasonable graduate programs — Yes, indeed.  Including my own.  (I'm also on my dept's grad admissions committee.)  I got VERY lucky.

More JeffE mindset scholars are needed for the dystopia!

Ok 1st of all I think you're delusional about what you "think" you're missing out on.
Everywhere you go, academia is a very independent vocation.  That is, even at a top notch school, your peers probably wouldn't want to chit chat with you about physics much.  They'd want to go do their own research.  Life at a top notch institution isn't some all-day sitcom with witty exchanges about subatomic particles.
Friendships and conversations can be had with people in other disciplines.
One thing I think you don't understand is
nobody cares about your research problem, not even your peers and equivalents because they are too busy with their own problem.  The intellectual load of academia is such that if you don't narrow your focus, you'll never succeed. Simply because there is too much to know, and if you start exploring too many fields, all your time will be lost.
If they are researching the exact same thing as you, then they are in competition with you.
You may also have a superiority complex that you need to overcome. You very obviously think you're smarter than everyone around you, and you look down on your peers. You have to stop doing that, and instead work independently, chat with peers on break times on common grounds.
Use the Internet for peer discussion.

I generally agree with this answer (and upvoted it). However, it seems a little extreme to say that "nobody cares about your research problem". There is such a thing as collaborators, and "better" institutions (for some value of better) might be reasonable places to look for them. Academia can be a rough business, but I don't think it is totally the law of the jungle out there.

Right. But there are severe limitations in your peers' capacity to help you, given that they must make sure they have their own research ball rolling (which, by the nature of the challenge, should take up close to 100% of their time).

A PhD is often, a very lonely beast. I go to a "top" school but often, I feel that there is no one to discuss my work with at a high level other than my adviser. Often, I feel that everyone around me is much smarter than me and can contribute so much to my general academic knowledge just by having a high level discussion over coffee.
This has nothing to do with my school or my department but everything to do with me. If I cannot make other people, especially my peers understand what work I am doing and have a broad level discussion with them, my science communication skills need to be improved.
As others have already pointed out, if you are indeed better, prove it by being the very best at where you are and you will soon magically see that there are plenty of people to discuss your work with no matter where your university or department is ranked.

If you are indeed substantially better than your cohort, prove it by far exceeding your professors' expectations, and then ask them to support transfer applications to more prestigious universities next year.
In the meantime, make the best of the situation you're in.

nobody cares about your university, the only important thing at least in Europe is your CV. If you can publish paper in good journals then nobody will think about your university.


text:
Are Mathematics graduate programs open to admitting a student out of high school with graduate work?
During my high school career, I had the unique opportunity to take multiple mathematics courses at my local university, and after graduating, I took two graduate level math courses: Measure theory, and a class on topological manifolds. This was a great experience, but it has left me in a shifty situation.
I asked the department head if I could be admitted into the program since I took a full time course load receiving a B+ and A respectively, but it was denied due to the fact that I did not have a bachelors. The only option given to me at this university would be to enroll in the undergraduate program and take graduate courses.
I would be open to that idea, but it has multiple pitfalls. First of all, I am not guaranteed any research opportunities, which view as highly restrictive on my growth as a mathematician. In addition, I am not guaranteed funding opportunities like I would be in the graduate school. This in combination with the fact that I would have to take 50% more credit hours of course work would mean I would end up having to take out more loans than I would like. This is all very disappointing for me.
Instead of enrolling in courses again, this semester I began independent study in algebra and differential topology using Aluffi's and Lee's book respectively on the subjects. In addition, I have been exposing myself to more theoretical physics, such as Yang-Mills theories and Supersymmetry. Because these subjects are capturing my interest as well, it seems natural that I take my studies towards Algebraic Geometry and String Theories. I really want to get involved with a program to help enable me with my studies, but I do not think an undergraduate program would be adequate. For those of you who are still reading, how can I work towards getting into a program which would enable my studies an empower me with supervised research?

EDIT
I did not think my undergraduate work would to be too relevant, since most of it was not rigorous; that is, calculation based. I took undergraduate courses in ODE's, PDE's, probability theory, analysis, mulitvariable calculus, and linear algebra. Unfortunately, I did not do well in the ODE, calculus, and linear algebra courses because they were during the summer, and I had not yet acclimated to the required amount of work. In this specific program, my course work is nearly equivalent to a bachelors degree, sans single variable calculus and a class in discrete math.

It's going to be very difficult to convince a graduate school to let you in on the basis of having a grad class or two, if you don't have the expected background equivalent to a bachelor's degree in mathematics.

I would question a graduate mathematics program that took on a student that did not do well in undergrad calculus, no matter the reason.

@corsiKa Frankly, my high school career was not stimulating enough and I developed some extremely bad habits. Breaking those while taking calculus, linear algebra, and ODE's was too difficult and unfortunately I paid the price by not understanding the material well at the time.

I would question any graduate mathematics program that did not have some form of waiver for someone who did not do well in undergrad calculus for some reason, but was able to prove an exceptional talent in some other way.

If you didn't do well in undergrad calculus or linear because you weren't "acclimated to the required amount of work" why do you think you are ready for graduate study? It's about more than having enough prior education to study graduate-level material; you need to be able to handle an immense workload. You view yourself as more precocious than you really are by doing well in graduate classes, too, because they are not necessarily difficult.

@user14018: then you need to go back and make sure you understand calculus and ODEs before you attempt to progress. Calculus is straightforward and simple compared to the type of stuff you are talking about studying in grad school. Furthermore calculus is used for almost everything else.

An undergraduate degree is an opportunity to learn more mathematics. How could learning more mathematics possibly be harmful to your intended research career?

Actually the fear of not guaranteed any research opportunities while being an undergraduate student is incorrect. Even as a student you have the two external things you need; access to facility so you can talk with them, and access to the library for published material. The rest of it is up to you to provide in mathematics. The access to faculty may require being enrolled a semester to allow yourself time develop a reputation as having mathematical maturity.

@mctylr: What you say is true in theory, but in practice, I believe a student has a much greater chance of carrying out successful research if they can work closely and regularly with a faculty member who does research in a student-accessible subfield. It would take a very exceptional student to proceed on the basis of library resources and occasional chats with professors.

@NateEldredge: Absolutely, the quality of the relationship with faculty does play a large part and I did not mean to imply a solo endeavour. Just that labels are only labels, and not restrictions.

I know of one case in which someone went straight from high school into a graduate program, so it is theoretically possible if you can find a university that agrees.  However, it's almost unheard of, and it would be a bad idea for just about everyone (even setting aside the question of whether undergraduate education provides any benefits beyond preparation for graduate school).
What I assume is that you'd like to do important research and are looking for preparation that will help you accomplish this goal.  The minimal standards for a Ph.D. are actually pretty low, and you can squeak by without knowing much or doing impressive research, but this sort of dissertation will set you up for career failure.  Instead, you need to enter a strong Ph.D. program, ideally one of the top ones, and really excel.
It sounds like you've completed enough courses for a minimal undergraduate degree in mathematics, but probably not enough to be competitive at a top grad program.  The applicants at these programs have generally taken a more extensive and rigorous collection of undergraduate courses (e.g., abstract algebra, topology, complex analysis), and it's not uncommon to have taken more than two grad courses, sometimes many more and in a few cases starting in high school.  Plus it's common to have undergraduate research experience or other substantial independent work, such as a senior thesis.
Basically, imagine yourself in four years.  That's who you're going to be competing against for admission, the other extraordinary high school students who went to college and became even more knowledgeable and impressive.
If you could find a university that would admit you to graduate school now, you'd probably end up going to a second tier school, spending some time catching up on courses, and then writing a good thesis but not living up to your potential.  Your career would get off to an inauspicious start, you'd have trouble on the job market, and in the long term you'd likely end up with a less research-oriented job than you might have had otherwise.
Of course I could be wrong about this: you might have exceptional luck or be the next Terry Tao.  But diving into graduate school at a young age with minimal preparation is an incredibly risky strategy.
This is something that's really hard to discern from college catalogs.  They usually focus on the minimal requirements to complete each degree and move on to the next level, but that's not how people do things in practice.  Instead, the vast majority of future mathematicians spend at least three years on their undergraduate studies, and generally four (in the U.S.).  The operative question isn't how quickly you can complete the degree requirements, but rather how much you can achieve along the way.  Preparing well for grad school is far more demanding than completing an undergraduate degree.
So what I'd recommend is that you pick an undergraduate program in which you'll have really outstanding fellow students, so that you learn from and are pushed by them.  Being part of a cohort like this is probably the single biggest factor in success, and your goal should be to find amazing people to hang around with and discuss mathematics.  You should then take whatever undergraduate courses are needed to fix up your background (if any) and move on to graduate courses.  You should also look for research opportunities during the summer or perhaps the school year, but it's not worth obsessing over this.  No program will guarantee anything, but at the very least you'll surely have some success applying to summer REUs, and it's reasonable to hope for even more than that.  Perhaps you'll finish in three years, and perhaps you'll decide to stay for four, but either way you'll be far better prepared for graduate school than you are now.
It sounds like you're in a great position to do well, with a remarkably strong mathematics background.  However, I'm convinced that the right question is how to get as much as possible from your undergraduate studies, rather than how to skip by them as quickly as you can.

"[Y]ou might have exceptional luck or be the next Terry Tao." Notably, Terry Tao earned a bachelor's degree before going to grad school.

+1 for Preparing well for grad school is far more demanding than completing an undergraduate degree.

the person you knew who went straight from high school to grad school: which field was this?

@MichaelMartinez: Mathematics.  Aleksandr Khazanov went straight from high school to grad school at Penn State.  (His career ended in tragedy when he disappeared in 2001, but he was an extraordinarily impressive young mathematician.)

interesting. so he already studied calculus, vectors, real number analysis, probability, systems of ODEs, PDEs, combinatorics, etc, in high school?

@MichaelMartinez: That hardly follows.  I haven't known many graduate students who studied all those subjects before grad school.

@MichaelMartinez With the exception of real analysis and PDEs, I studied all of those in high school. If I started taking college courses a year earlier, adding on those other courses would certainly have been possible.  (All that to say, the coursework is not an issue for some high schoolers.)

@MarkMeckes. My undergraduate B.S. requirements in Math included all those course (and more)

@MichaelMartinez: That may be, but I haven't known many graduate students who were you.

@MarkMeckes: really? my coursework was standard fare at the school I went to. Everyone I knew took those classes, even non-Math majors (physics guys and so forth)

@MichaelMartinez: In the US, there are only a few courses that are standard fixed requirements for a Bachelor's degree in math: basically calculus, real analysis, linear algebra, and abstract algebra.  Most departments do have more specific requirements (though some have even fewer), but they vary from place to place.  E.g. many departments require courses in complex analysis, logic, or probability, but not usually all of those.  Often much of the math major consists of technical electives, which of course vary from student to student.

@MarkMeckes. The school I went to is rigorous and tough.

@MichaelMartinez: Good for you.  For the record, of the departments I'm familiar with, the one with the lightest list of specific requirements for a BS in math is Stanford.

I am not familiar with math grad programs (your situation would be highly unusual in a CS grad program), but I'd like to question two statements you make about the non-viability of an undergraduate degree:

First of all, I am not guaranteed any research opportunities, which
  view as highly restrictive on my growth as a mathematician.

If you're good enough to take advanced material, grasp it and even approach an actual research question, then you're functionally equivalent to a grad student and many professors would be happy to take you on. The antecedent is important though: the fact that you've taken courses doesn't mean you're ready to do research, but this is precisely what REU programs are for, and faculty often get extra money to support students for UG research.

In
  addition, I am not guaranteed funding opportunities like I would be in
  the graduate school. This in combination with the fact that I would
  have to take 50% more credit hours of course work would mean I would
  end up having to take out more loans than I would like.

You're not wrong here, but there are often scholarship opportunities available, so the situation isn't completely black and white.
A final note: one reason that grad programs might be leery in taking someone without an undergraduate degree is because the UG degree is more than just a credential. It's a proxy for a long sequence of coursework that exposes you broadly to an entire field of study. In almost any discipline, a basic level of breadth is very important for research work: because you need to

understand what questions are important and why
understand how different questions fit together
acquire the ability to see connections among different parts of an area.

Of course you can do an entire undergraduate program via self-study, but then you don't have a "short certificate" proving your command of the material.

I appreciate your advice. It sounds like I would need to find a professor willing to help me getting into a graduate program.

You need a mentor.
Consider your current experiences and gifts as a large and powerful chainsaw.  You may find some immediate gratification at cutting through swaths of wood at a pace you like.  However, you can burn yourself out, wreck the chainsaw, reduce your number of functioning limbs, etc.
(I didn't lose any limbs as an undergraduate, but I got sick of school in my second year and left it in my third.  If I had paid more attention to the people who were there to help me, my earlier years might have been more satisfying.)  If you give yourself the discipline to handle the routine and mundane, and also the time to have fun and work on things at which you excel, you will have something better than an awesome trajectory: you will have a life of enduring and satisfying achievement.  And you can still spend time doing graduate work.
The mentor will have to know you well to tell you what is best for you.  (A team of mentors might be better.)  I can imagine more disasters for you than successes if you try this without at least one.  Also, the Internet is no substitute for a mentor: this kind of life decision, while up to you, can benefit from talking face to face with someone who is interested in your personal as well as your academic success.  As commented elsewhere, hardly anyone cares how fast you did something as much as how well you did it.

I think a very good options for you is to apply to very competitive (private) US institutions for undergraduate (i.e. Harvard, MIT, Princeton, Stanford, Yale, etc.).
I mention these specifically for a few reasons. They all have very well regarded graduate programs where you will have the flexibility to take very advanced courses. They have extraordinary peers with similar advanced backgrounds (my brother, who was an undergraduate at MIT, took many years of graduate math coursework in high school). Finally they have very good financial aid opportunities. I will say from my own experience (at Yale), that strongly prepared undergraduates are known to jump straight into graduate coursework and research freshman and sophomore year.
The most important thing to do if you are interested in mathematics (or physics) professionally is to interact with great professors and go to a great graduate program. I am extremely skeptical that the top notch of graduate math programs (the past list + Berkeley + University of Michigan + Cambridge + etc.) would take you right now. People apply from undergraduate with graduate coursework, research experience, and letters of recommendation from very well known people in the field. The last point is especially important for these top notch programs (math is a fairly small community). By going through undergraduate, you will make these connections early on, find a subfield, position yourself for the very best program in your interested subfield, and get into an excellent program.
Another thing to note is that assuming your "local university" isn't a large, well-regarded state-school (or international equivalent), these courses are simply not up to the level of those you would take at top-tier university. Generally, in my experience taking courses at my local university in high school, theses course are very computational and those that are proof-based aren't nearly as challenging as those I found at Yale.

Don't focus on the letters you'll get from your first degree.
It is very likely that you will need to get a bachelor’s degree before going enrolling for an advanced degree, especially since you sound like you would do best in a highly selective program. But for now, what you need is a university and more specifically, a math department, that is willing to be flexible, encouraging of advanced work, and give you the chance to prepare yourself for a really top graduate program. You need this whether you are admitted as a masters student or an undergrad. Assuming you want to continue to a PhD after your first degree, you need to focus more on what you will be doing for the next few years, rather than the degree you’ll have at the end. You are better off finding an excellent school that will support an undergrad doing graduate level work (fairly common) than an OK school that will accept a grad student with uncertain credentials (very unusual).
To start with, I’d strongly recommend contacting professors at well regarded math departments whose research you find interesting, and let them know your situation. This will mean you are looking at schools as though you were going to grad school even though you will probably be an undergrad. Find professors you think you’d like to work with, and arrange to meet them and meet their other grad students. In person is best, but at least talk on the phone. Apply to a few schools where the math department supports and encourages their grad students, not just a place with a good reputation. I've had a number of friends who have dropped out of PhD programs due to department politics or unsupportive advisors. Start yourself out on the right track.
Many schools have scholarships available, and in some cases, a school will offer a full ride including a living stipend to the most exceptional undergraduates. The math departments and professors may be able to help you out here, too, if they especially want you. Just ask.  Don’t limit your options because of a preconceived bias.

You're not going to get into grad school in Math without going through a Bachelor's first. Just like you won't get into grad school in any of the hard sciences without doing the foundational work first. There's good reason for this: you need the solid background in the fundamentals before you delve into a specialty. The specialties emerged out of the fundamentals, historically, and it makes no sense to try and skip ahead. Also, if you try to do this, you're doing yourself a great disservice, which you would probably realize later on. You'll be approaching your studies without adequate knowledge/experience.
Why would you want to skip undergraduate courses anyway? There's a lot of mathematics to be learned in the undergrad classes, and if you truly love math, then you ought to welcome the chance to learn and explore. You say you didn't do well in calculus and differential equations, but these are foundational for so much mathematics that follows.
So, the main question here is not whether you can go straight into grad school (the answer is no), but what your true goal is: to learn and appreciate math, or simply to get into a field that you think is interesting without truly knowing what's involved.

I went to an engineering school that is well known for the hard sciences and engineering, I've had a lot of exposure to academia, have known, studied and worked with a lot of people in these fields, and have never heard of someone going straight from high school to grad school in physics, math, chemistry or engineering fields.

now that said, once you are enrolled in an undergraduate degree program, you can definitely take grad level classes, particularly once you get the basic prereqs out of the way, once you start showing your interest and abilities, it's pretty easy to take those grad classes even if you haven't finished your B.S. yet. I've had friends who basically worked on both their B.S. and M.S. or Ph.D. at the same time!

Unlike some other respondents, I don't think this is impossible. In fact I have a friend who dropped out of high school for various reasons unrelated to his academic achievement. He spent several years studying math and CS, by himself, to graduate level. He tried in various ways to access a research-based course, culminating in him being offered a place to do a PhD in CS, without having either a Bachelor's or a Master's (which is a usual requirement to start a PhD in Europe).
However, to follow a trajectory like this there are at least four necessary conditions:

You must be very good. Someone who looks like they are going to do a passable PhD and publish a couple of papers before stagnating or disappearing into industry is not going to get this opportunity. Someone who has already published peer-reviewed work might be a candidate.
You must have some good reason to not want to do an undergraduate course. You aren't going to be supported with this just because you don't feel like sitting in a lecture hall for several years, listening to things you already know. Most working mathematicians, including prodigies and household names, did exactly that. Usually you will be advised to do the BSc and study harder things / do research in your own time. Good reasons might include some disability or personal circumstances that make it extremely hard for you to get through the undergraduate system, or the fact that you are already spending most of your time doing professional level research. Money issues might or might not be seen as valid, depending on whom you ask.
You need to show that you are mature enough to be a graduate student. Undergraduate studies involve a certain amount of hand-holding for a reason - many students who have just left high school aren't ready to take full responsibility for their education. Even if you are a genius, a school will be worried about your abilities to perform well in your studies, while taking care of yourself on your own, and not succumbing to mental health issues, addictions, etc. Teaching or TAing undergrads also requires a certain maturity. The exception is if someone is going to take care of you (for example, if you have ASD, and you live with your parents who support you with all the non-mathematical things you need help with).
You need to put your case to a professor in a school you want to work at, including convincing her of the things above. This is key. There are various obstacles put in place to stop the over-confident, the under-qualified, and the insane from getting onto advanced math courses. If you apply in the usual way you will almost certainly be rejected.

Your best bet is to approach someone in a field you care about, write to them directly and explain why it is that you know you are capable of a PhD. Most people you approach will reject you out of hand. (Think Ramanujan - statistically you are likely to be less talented than Ramanujan.) If you get lucky, you might find someone who is willing to hear you out. Be aware that anything that gives the impression of a scattershot approach (standard letter template, not being able to explain why you chose that professor or that school) will rule you out very quickly. You should be looking for someone whom you have read and understood several papers by (if you aren't reading and understanding journal papers on a regular basis, why not?). You should be able to show them published or publishable work you have done, related to their own interests. This person, if they end up supervising you, will have to fight to get you in to their department, and then deal with an unusually onerous burden of formalities and paperwork to have you as their student. They aren't going to do this unless there is some compelling reason why they would want to work with you.

You need to show that you are mature enough to be a graduate student or in my own experience undergraduate studies provides the time and freedom to make mistakes while you are busy growing as a person (assuming typically high-school graduate age or younger).

A very prestigious professor at my school told me that another professor here, whom he named, in fact completed his (STEM) undergraduate degree in two weeks:

he looked through colleges to find the one that had the lowest requirements to graduation
he settled, I believe, on Ohio State, although my memory may be incorrect on the exact college.
for two weeks, he took tests to pass out of enough requirements that he was able to graduate.

So he ended up with a legitimate undergraduate degree in two weeks, and then he went to graduate school. I was told he had been sailing around the world for three years prior to getting his undergraduate degree. However, my school is very prestigious. From this story, I am guessing that the professor was also doing something other than sailing that I was not informed of, and certainly he would have to have some kind of academic contact to achieve the necessary recommendations.

If you give us the name, we can fact check the story.  It would certainly be an interesting one, and I see no reason to think that it is particularly confidential or delicate.  (Actually there are whole books of stories like this about mathematicians.  By reading one of these books, I learned that my former thesis advisor had no high school diploma or undergraduate degree!)  Without the name, this is just a rumor and a rather fishy one at that.  I don't know any reputable American institution that will grant an undergraduate degree just by virtue of passing exams: there are required courses.

As a rule, you don't get into Graduate Programs without Graduating.
Others have already mentioned ways around that etc.
I will comment on ways you can do undergraduate, and meet your goals.
I am going to assume you are brilliantly clever.
in the top 1% or so of people graduating from high-school at the same time as you
Some universities offer a research undergraduate. For extremely high achieving students, thus the top 1%. This normally involves each year a research component. Either in the from of a unit, or on top of all units. Perhaps with a requirement of maintaining a Distinction or better average. My university calls this a Bachelor of Philosophy -- in the same way the a PhD is a Doctorate of Philosophy. It was formerly known as a Bachelors of Advanced Science, and a Bachelors of Advanced Arts.
I thus recommend that you look into Research based undergraduate degrees in your area.
Even if you are not currently performing well enough to get in, you can often transfer courses after a semester or two of demonstrating your high marks at university -- which are valued to admissions much more than similar marks from high school.
I wouldn't recommend cutting out on the board baseline of experience you would obtain from a undergraduate degree, even if you could. (Exceptions apply, see other answers.)


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How to find an appropriate journal to submit to when working in a new, unfamiliar field?
I have developed a new method to form a single-atom chain (break junction) in physics, which so far has results from calculation and simulation but not yet experiment.
How can I find out which journal is suitable for publishing the work?
My advisor is not familiar with my research field. I am exploring a whole new field.

In order to know that the method is new you need to be familiar with the literature; so send it to a journal that you would expect to read it in. If you are not familiar with the literature then you need to become so and to update your text and citations to reflect what you will have learned. Then pick one where you would expect to see the paper.

The one you cite most often.

Having had experience with this type of problem myself, I agree with the suggestions that you have been given in comments: the best way to figure out where to publish is to look at where the papers that you are citing in your related work are being published.
There is an additional challenge as well, however, which is that as a newcomer to the field, you are likely to have a more difficult time getting published because 1) you have not yet established credibility in this area, and so people will justifiably view your work with more skepticism, and 2) you are likely to be insufficiently aware of key concerns and points of debate within the community, which can get you into unnecessary trouble with your reviewers.
I would thus recommend a "publish early and often" strategy: rather than trying to send a major manuscript to a top publication venues immediately, start by sending a couple of more restricted manuscripts to less difficult but still respectable targets.  By doing this, you can gain experience with the community's expectations and start building your reputation as a good practitioner in the area, both of which will later help you to be able to publish in higher impact venues.


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I think that I can have the scholarship. Is this confidence or arrogance?
I will have an interview for my scholarship to study grad school in US next month (taken 30 in total 122). In this month me and other 6 candidates have been gathering together to mock the interview. Based on what I observe and other information, I think that I can have the scholarship. With that thinking, for over a week, I have switched my focus to other priority. However, I'm afraid that I'm just blindly arrogant, and soon I will have to pay a mortal price for this.
Am I?
Evidences that support me

After I finished my turn, everyone got exited and said that I was very well prepare. They said that they could see my readiness and alacrity in my talk. They commented that I spoke a little fast, but at the same time I reacted to the questions fast as well.
The questionnaire is taken from the previous interview questions. I can answer them all fast with little thinking time.
I have seen their SOPs, and most of them have things like quote from famous scientist. I think I'm very lucky that I have ask this before in Academia SE1.
There is a high chance that the interviewers are not from my field. Mine is biophysics and the professor with the closest field is particle physics.

Evidences that against me

This doesn't mean that other people are worse than me. In contrast, some of them seem to be very prominent. They are either more experience or win more contests than me.
My sample is only 6, while the population is 122.
And my weakest point: I have a big hole in statistical physics, the  fundamental knowledge in my major. During my dissertation, most of the time is coding. It does need statistical physics knowledge, but at a very basic level.
Of course I know what I should do. I am filling my hole by self studying. I need to read six chapters of a very good book2 and so far only finish three first ones. I will finish it in a couple months, but finish all now is impossible.

I see my weak points. But I cannot help of thinking positive. Can you tell me if I'm arrogant or not?
1Why shouldn't I quote famous scientists in my SOP?
2An Introduction to Thermal Physics

Honestly, I think that trying to estimate your chances of success (let alone trying to classify your estimate as "confidence" or "arrogance") is kind of pointless. You'll either get the scholarship or you won't, and you won't know which until you're told. Just make sure you're prepared, mentally and practically, for either outcome, and have contingency plans either way.

@NateEldredge my purpose is to know whether switching to another priority before the interview is good or bad

@Ooker Try to look beyond yourself, at how you can make a contribution to science, or something like that.  Also, work on your English.  For example, think about why "me and other 6 candidates have been gathering" is grammatically problematic.  And try to find some differences between positive thinking and arrogance.

The only way you can be certain that you've earned a scholarship is receiving a letter stating "you've earned this scholarship". Anything else is misplaced optimism/hubris/etc and should probably be avoided.
It goes without saying that you should definitely not take any actions at this point that are based on the assumption that you earned the scholarship. To quote Yogi Berra, "it ain't over 'till it's over."

Agree. But based on the evidences, if the question is only "am I good or not?", what would you say?

@Ooker - The relevant question is not whether you're good, it's whether you're better than everyone else who applied. There's no way for anyone on this forum to answer that.

I'd go so far as to say that being better than everyone else is not the question - the only question is if you get the scholarship or not. "Better" has too many different dimensions to quantify here.


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Professor X introduces professor Y to me. Should I CC prof X when emailing prof Y?
I email to prof X to ask about a PhD student vacancy. He refuses because of his retirement, but kindly introducing prof Y to me. When emailing to prof Y, should I CC prof X?
I do this because at the end of the letter he says that he wants me to get him informed of my work. But more importantly, even without this saying, I think CC to someone when they has introduced me to another person is a good etiquette. It shows that I'm transparent.
But what if they are not really close? They may know each other through the work of each other, but hasn't had any conversation? Would this make things become awkward? And if he didn't say anything about informing him, would CC him simply annoying him?
While you can say that this question is a continue of my previous one, the names have been rearranged completely. For the sake of your understanding, please assume that the two questions have no relation to each other.

And by the same poster. @Ooker - really, I think you are overthinking this. Contact prof X, period. Prof Y has given you his answer, and X knows that Y is passing you on (for whatever that is worth). Y is finished in the process.

@JonCuster no. Prof X here = prof Y there. Prof Y here is a different prof

@Ooker. If you're really concerned about transparency, you can CC a thank you. But all in-depth discussion should only happen with those who are contributing. Keep Prof. X informed with updates, but if he's not on the project, there's no need to continually CC him.

I'm quite sure that Professor X is directly communicating your thoughts to all parties involved.

I work with many professors worldwide. I believe that its always good to CC the professor who had introduced you, (avoid only if he is not interested in you to know). Once you are involved with the professor and do some work with him, you are free to communicate independently.
Also do not forget to thank him/her for looking forward an opportunity for you.


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Considerations for applying to postdoc positions and contacting faculty
I am applying for postdoc positions using the Mathjob website. I've noticed that some universities inquire if I've been in contact with faculty members in their departments. I applied for several of these positions and answered the question with 'no.' In such cases, do they reject my application? Should I contact a faculty member and express my interest in doing a postdoc under their supervision? Alternatively, is this question merely informational, with no response indicating that they will assign a random mentor?

I doubt that every university asking this question has the same intent. Some will want to judge your interest in a specific faculty member or sub-field and others just want to know how flexible you might be.
I've even known of places that didn't really assign "mentors" but just wanted the skills of the applicant with a view to a future hire.
I doubt that many would reject your application if you don't contact individuals first, though it could happen in principle.
I don't recommend blind emails to people just to "cover" this question. That is unlikely to help. But, if someone "advertises" interest in a postdoc, by all means, write to them with your interest, assuming your research aligns.

As someone who regularly hires postdocs, I can say that if someone has reached out to me and expressed interest in my work. I am much more likely to look carefully at their application.
We are flooded with applications from people who have no idea who we are or what we do. If we feel that someone specifically wants to work with us and pursue the kind of research we have been doing, that makes a huge difference to the care with which we review their application.

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