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Professor not responding to my mails after earlier discussions
I have applied to a professor from another university - and from another country, in case that is relevant - about doing my undergraduate thesis under him.
He said he liked my profile and asked me for some documents (transcripts, recommendation letters, etc). After I sent him these documents, he stopped responding.
Before this I used to keep him updated about the process (when I will get my transcripts, when my recommenders will send him the letters, etc) and during this time he would always acknowledge the receipt of my mails. After my recommenders sent him their letters, he stopped responding. I know how this might look, but I have no reason to suspect that my recommenders might have anything bad to say about me. I have used their recommendations to get a scholarship previously.
This hiatus in communication took place in December last year, so this might very well be because he was on leave during this period. I verified that his university began its semester last week and mailed him, again to no response.
How do I interpret his silence? There is of course no certain answer to this. So the more important question is, should I keep politely following up - say, dropping him a mail every week or so asking if he's made a decision yet?
Note: This question on Academia.SE has a comment which says that "treat a non-response as the (reasonably expected) negative response" about emailing a professor at a foreign university. However, I don't think that applies in my case as the professor had initially expressed his interest in hiring me, so I thought he would let me know if he had later changed his mind.

Christmas, New Years, holidays, semester just started... I would give him another week or two. I just came back from the holidays and did nothing but checking e-mails for a day and I´m not even a Professor.

@JayFromA You make a good point, I guess he might be swamped with emails.

@Veljko89 Yes, patience is the mother of all virtues :) But unfortunately if the prof says says then I need to arrange for my visa, which can take anywhere from 3-4 months. And since I am starting my thesis this May, that is a major point of concern for me.

@Veljko89 Thanks for remembering :). I wrote him an email saying I am under a deadline due to visa and other college procedures, but unfortunately he still hasn't replied :(

@Veljko89 in case you're still interested, after I mailed him one more time he replied saying he doesn't have funding to call me there. I guess that's probably why he wasn't replying earlier, though it would've been nice if he had told me so earlier. I had thought he didn't like my application.

This happens a lot to the super busy profs. They are too famous and receiving too many emails in their mailbox. They could easily forget about them especially if they are old. Sometimes when the email is hard to response (in your case, the decision is really hard to make), things will be getting worse. They will think about it for a moment, then something else comes up like a telephone call, and then they totally forget about your email.
Two things you could try:

Ask him exactly what you need, like an appointment
Ask his assistant about appointment
Do not over estimate yourself. When talking face-to-face, many profs are always saying positive things about you just because they are polite.


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Paper with lots of Greek letters
I developed a system, and wrote a paper about it.  It includes formulas and pseudo-code.  During the course of development I used Roman letters in the formulas.  I eventually ran out of meaningful letters (letters that I could associate to some extent with what they represented), and started using Greek letters.  The development went on until somehow I ended up having about 8 Greek letters and 2 Roman letters used in the final formulas and pseudo-code.
Now that the paper is written, I wonder if having all of these Greek letters is unusual.  Would it be better to replace them with Roman letters?  Would it be better to use Roman letters with subscripts, such as t for time, and t_scaled for scaled time, instead of using Greek letters for that?
EDIT: To clear things up a little, my general question is: is it preferable to use Roman letters or Greek letters in a technical (engineering) publication, and is it acceptable or even preferable to use letters with word subscripts instead of entirely new symbols to label related variables or constants?

That is not a lot of notation at all; it may even be more readable than $t_{mathrm{scaled}}$ and such because these blow up formulae.

This depends entirely on your field, and specifically, what the norm is in your field. In mathematical fields like statistics, economics, physics, and math itself, and to a slightly lesser extent in chemistry and computer science, using Greek letters as variables is exceedingly common - in fact, it's unusual to see a paper that doesn't use a few, and there are many quantities for which the well-established standard notation involves a Greek letter. In other fields, perhaps that's not the case.
If you're still not sure after examining the norms in your field, I'd just go ahead and do it. Given that mathematicians use Greek letters all the time, it stands to reason that when you are doing math in another field, you should be able to do so as well.
However, I would caution you about one thing: try to make your variable names descriptive. That is, it should be easy for the reader to make the association between the variable name and what it represents. So when there is a standard notation for some quantity, use that; when there isn't, subscripted symbols like "t_scaled" are one good way to do it. They do take up more space on the page, though, and can make formulas look unwieldy, so you have to strike a balance between aesthetics and clarity of meaning.

it preferable to use Roman letters of Greek letters in a technical (engineering) publication, and is it acceptable or even preferable to use letters with word subscripts instead of entirely new symbols to label related variable or constants?

In addition to the excellent answers that have already been given, I would like to stress the fact that your original question cannot be answered in the generality that you are apparently looking for. By and large, Greek letters are OK, as are Roman letters, as are either of those with sub- or superscripts. What is preferable depends entirely on context, the established conventions and notation in your field, and personal preferences.
When it comes to notation, the 3 golden rules are:

Make it intuitive. Don't use epsilon to mean "a really large value". Don't use pi to refer to a constant value of 8.5. If you, for example, have instances and timestamps, don't use "t" to refer to the instances and "i" to refer to timestamps (real-life example I recently reviewed).
Make it consistent. Use the same notation in the entire paper. Use the same notation patterns throughout the paper (if you use capital Roman letters for a constant, use capital Roman letters for all constants, etc.).
Make it minimal. Never introduce notation that you are not actually using.

Also, avoid overusing a given letter just because it happens to be a convenient mnemonic for many things. Having two numbers n and N is probably OK; adding a list of numbers n_1, n_2, etc. may work, too, but please don't make the list end at n_n, no matter how clear the notation might be to yourself. Also, different fonts do not make good substitutes for different letters; if you find yourself needing to use script or, worse yet, blackletter fonts to differentiate multiple uses of the same letter, you're probably overusing that letter. (Yes, these are also from real-life examples.)

The writing style is really something very individual, and may vary a lot. There is nothing wrong with Greek letters per se, but it is slightly concerning that you use them because you ran out of meaningful Roman letters. That could indicate that you are using really a lot of notation in your paper, and from a point of reader it might be difficult to keep in mind what do these letters mean.
The use of semantics, i.e. notation like n_cars or t_scaled, may really help to reduce the number of "independent" symbols and improve readability. You may also wish to structure the use of variables, e.g. use Greeks as integers and Roman as everything else. It is very good idea to stick to some classical notation worked out in textbooks and major articles in your area of research. Ultimately, you may wish to present a table of all your letters with their meaning after the first section of your paper.

Greek letters are generally fine. In fact, some things are conventionally reffered to by greek letters e.g standard deviation is sigma.
xLetix's rules are excellent advice. I would just add to please put explainations of your variables close to where you use them. There are two things people do that annoy me in this respect.

Putting a glossary at the beginning of the text and then don't explain there symbols. A glossary itself is fine but please put explainations in text as well as I don't want to have to flick back to the start to know what every symbol means.
Similarly, people often put an explaination when they first use the symbol (often in the introduction) and then use it again several pages later with no explaination. This is fine if you have a few obvious symbols but when many with unclear names are used it is difficult to keep track of them. Just writing the name in words generally suffices.

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How to proceed after academic dismissal from PhD program (plagiarism) and successful completion of master's?
I was dismissed from a (Canadian) PhD program on the charge of plagiarism. I had muddled up sources, and the professor insisted I deliberately did it to get higher grades.  My student advocate informed me that plagiarism is plagiarism, whether intentional or not, whether only on a single line or not, and regardless of the professor's motivation. So, I admitted to the charge, while looking for ways to avoid a repeat and rebuild my reputation.
I did inform the tribunal that this was a single sentence in a 22-page document, and that I was traumatized during this period as the state had taken custody of my two children.
The tribunal upheld the charge but recommended that the provost should consider a minor punishment. My advocate suggested I should not contest the recommendation of the tribunal. However, four months later, the Provost decided to dismiss me because I did not appeal the decision, and because I had failed to inform the professor of my personal challenges when I took the course.
When I was dismissed, I completed a master's program at another university with a GPA of 4.0/4.0. I discussed the plagiarism incident with my master's supervisor.
Now  I want to apply for a PhD Program in a separate, but related, area (my current supervisor does not work in this area and so could not supervise me), and I am wondering how to go about it since I am required to disclose all the post-secondary education attended. I would appreciate any suggestion on how I can navigate this muddy waters.

"whether only on a single line or not" Interesting, here we tend to follow a different definition for plagiarism. Mistakes are human and a single line cannot prove intentional behavior beyond doubt. An error to give credit in a single case therefore is a mistake, and not more. I doubt that anybody who is working in academia can claim to be free from such unintentional errors.

As mentioned in the comments, I do not think that you will be able to find a supervisor who does not know you well already if you have a record of dismissal for plagiarism.
You could try:

Telling the truth about your dismissal (lying or omitting that you were dismissed would likely be grounds for getting dismissed again).
Explaining, with evidence, why it will not happen again.
Do not mention the nature of the trauma you experienced.  Academics are not likely to consider any kind of trauma to be an excuse for plagiarism.  And they are likely to have strong opinions about how children are raised.
There is no need to give the details of the process leading to your dismissal.

@artificial_moonlet: Probably this is relevant to the OP's comment, "I was traumatized during this period as the state had taken custody of my two children", at the end of the OP's first paragraph. FYI, I didn't notice the OP's comment about children the first time I read the question, and I only noticed it after seeing your comment and being curious myself.

You should concisely discuss this in your application. In the US, the Statement of Purpose would be the appropriate place for this (I do not know about the Canadian system). Since you have already completed a degree since being expelled (and are switching areas), there is no need for a lengthy post-mortem, and this shouldn't be a dis-qualifier.
More concretely, I recommend:

Briefly (i.e., no more than one paragraph) explaining what happened
Including (in that one paragraph) the mitigating factors. Namely, that this was a single plagiarized sentence, in a 22-page document, during a child custody investigation. I would not mention your theory that the professor was biased against you (if true, that should have been raised at your appeal).
Considering getting someone to corroborate your account in their letter of recommendation. In particular, that this was all about a single sentence -- that's the part that is hardest to believe (the odds of 'accidentally' plagiarizing a single sentence is pretty high, so it's hard to believe you could be convicted based just on that).

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What should I (a professor) do if a student keeps answering other students' questions before I start explaining?
I have a student who keeps answering other students' questions before I could even start explaining. What should I do in this case? Should I ask them to come meet with me? If so, how should I convey that it is not ok and it is not their job.

As to the ok-ness or not, I'd wager that it's more an aggression (and possibly a show-off) than a wish to be helpful. So it should be discouraged, yes. But privately, not publicly.

Just to add some context. This happened to me (as the student). I was naive and it pained me to hear silence for a few seconds if the other student didn't know the answer. My lecturer took me into a side-room after class quietly and explained how it wasn't helping the class and he appreciated that I was aware, but to let the other students answer the questions. He advised that I don't answer any questions in the class, which actually changed my attitude for classes ever since that talk and I always took a back seat unless I was stuck/unsure.

If a question gets answered that's good. Even more so by an engaged student. What would be your lesson to the student to stop answering questions? Respecting your authority? If that's the only reason for you to call him into a meeting, you should rethink your motives. Authority has to serve a purpose.

Following from @image, students can give better answers than professors, because they better understand their peers' knowledge.

@user2768 The way I understood the question, the professor wants to explain the context and required knowledge, so the student and his silent compatriots know, why the answer is correct. And the interrupting student only seems to be shouting out the factual answer, without explaining any underlying goings-on. Aside from the interruption of class and possible interpretation of the other students, this leaves a lot of learning on the table.

@Minix Only the OP can clarify, but they seem to believe it is not ok for a student to answer...other students' questions before they've gotten a chance to answer themselves. Also, the OP seems to believe the responsibility of answering question is theirs, and only theirs. I believe a professor can best enable their students with help from their students. (I don't see any suggestion that the professor wants to explain the context and required knowledge nor that the interrupting student only seems to be shouting out the factual answer, without explaining any underlying goings-on.)

@user2768 "because they better understand their peers' knowledge" ... ummm.... no, not really. Is my peer quiet because they are shy? ignorant? know the answer but are letting other's answer? ... I don't know my peers thoughts. I may think a peer is dumb as a rock and can't even grasp the simplest of concepts... and that same peer has had meetings with the professor letting the prof know they are on the autism spectrum and don't answer out loud in class. It is NOT a student's job to assume knowledge of the inner mental workings of their peers.

I was a student who did too much answering in classes. At the time, my overly-literal interpretation of the situation was the the instructor has asked the students a question, and it is therefore my role to answer it if I can. (subconsciously, I no doubt got a kick out showing I knew) It took me years to learn that was suboptimal behavior, and to reign it in. I have never been formally diagnosed as asperger, but my son is formally on the spectrum and I recognize many traits in myself. Friendly but explicit guidance is appreciated by such folks.

@paulgarrett I had a similar experience to Dean Meehan. I was home schooled and genuinely thought that if I knew the answer, I should raise my hand, especially during a series of lectures in middle school during which no other students were volunteering any answers or raising their hands at all. I remember being confused when that very lecturer said he saw my hand but wanted to let someone else answer. No one else was volunteering, so why didn't he just call on me so we could move forward? Now I understand how obnoxious that behavior was, but it wasn't intentionally show-offy.

@Minix seems like the professor could simply follow up on the answer given with any missing context in that case.

@CGCampbell You don't think students understand what they all find hard? What some find hard? What a some find hard? When I was a student, we discuss such things. It is NOT a student's job to assume knowledge of the inner mental workings of their peers Many students know these things.

This would, I think, depend a lot on how the "answering" student goes about it. Just interrupting a request to the professor is disruptive, but some people do this sort of thing by reflex. But yes, a quiet word is in order. Ask them to meet with you. But decide first on what you would like them to do to correct the action.
If the answers they give are generally correct then it is a different situation than if they are mostly irrelevant, I think.
One thing that such a student fails to understand, of course, is that often the best answer is a minimal answer. An answer that lets students develop insight, not just get answers. Saying too much in answering a student question may be worse than saying nothing.
One option is just to require them to remain silent, but another is to ask (require) them to raise a hand before saying anything and first getting permission. But yet another, that might be useful, depending on the student, is to require them to write out an answer when they feel the need, rather than to blurt it out verbally.
But the behavior can be a symptom of many things. Some are insecurities on the part of the student; a need for affirmation. Some would just be showing off for the professor. Without knowing what it is, it is difficult to formulate an exact solution.
You have a right, of course, not to have your course disrupted by outbursts, but think a bit about whether the disruptor has needs that also need to be met. So, as part of your quiet word with them, ask first why they think it important to do that. Depending on your view of the student, the question might be direct, or you might want to be a bit more subtle about it.
And sometimes it is actually useful to have students volunteer answers to the questions of others as long as you maintain control over the process. If one student is dominating a conversation, it might be counterproductive for others.

This student's answers are generally correct. She comes across as very arrogant. Though. she is retaking my class because she got very low score last time.  I overheard that she had studied this material from a teacher from School X (a top school) and it was way better than what's been done in this class.

Arrogance is painful, of course and reflects badly on her, I expect. I might lean, in such a case, as requiring a "hand up" first with explicit permission to speak.

One thing that such a student fails to understand, of course, is that often the best answer is a minimal answer. An answer that lets students develop insight, not just get answers. Saying too much in answering a student question may be worse than saying nothing.

Buffy, I like your approach. A premature answer also robs me of the need to explore the question. Who else doesn't know? Why, are they missing context? Other audience members are less likely to admit to not knowing if the answer has already been given.

@user119361 That seems suspicious, so they have so little confidence in your teaching that they were able to take material from a class they weren't even taking at a completely different university and understand the material way better?  If so It is not in the students best interest to not answer these questions because clearly they are gaining experience and study in what ever subject you are teaching, even if you feel it is best for the class.  I thought it was just an overeager student, but given this new information I'm afraid you may have inadvertently caused this.

Buffy and TvZ’s comments here are crucial. The use of questioning is important for scaffolding to an accurate understanding in many contexts. A twist on Buffy’s third paragraph would be requiring the answering student [A] to write down a question, or sequence of questions, that would guide the original asker [B] to the answer A has. This is a much more challenging task that will ideally help A understand how teaching well is a complex task and also improve A’s conceptual understanding. The rationale for the conversation is then shifted from “interrupting” to “helping you learn deeply”.

One thing that such a student fails to understand, of course, is that often the best answer is... I really think that comment should be incorporated into the answer. If the other student is literally just giving answers then that might not be as productive as a professor who can be more engaging - ask follow up questions, get clarity on why the student is asking the question, and then lead them to the answer.

@dwizum, done. Thanks for the suggestion.

"But the behavior can be a symptom of many things" - indeed it is possible that the student may have an autistic spectrum disorder, at least it is something worth considering.

There are two main components to be handled:

The question
The answer

For (1), you can either choose to say

Please ask your question after I finish this part

or take the question right away.
For (2), I usually prefer to ask the classroom

Is there anyone who wants to answer this question?

If someone volunteers, and in your case someone always does, then I let the one who asked the question listen to the answer. Then, the important part comes:

Did you understand the answer?

or rather, as @Bob Brown pointed out,

Is there anything I should explain in more detail?

If the answer is understood, then everyone is happy. If not, then I proceed to explain the answer in my own way.
At the end of the day, the most important thing is that the students understand as much as they can, regardless of the person explaining. Of course, it is sometimes annoying for a student to interrupt your answer arrogantly. But you can always turn this situation into your advantage. Remember that there will be a question where someone else wants to answer, and then your lecture becomes interactive. Interactive lectures, in my opinion, are the best to follow and the most enjoyable ones.

I've found that "do you understand...?" is almost always answered with a yes, even when it's not the case.  I don't have a good replacement question.  The closest I've come is, "Is there anything I should explain in more detail?"  That, at least, turns "you" into "I" and sometimes elicits a further question.

As a student I always very much disliked having my questions answered by the class know-it-all rather than the professor. I could have an enjoyable interactive session (it wouldn't be a lecture) at the local coffee shop. I'm paying tuition to hear material from a real professor.

@CCTO You pay tuition to learn the promised material, as the tutors see fit. Other than that, your own motivation of paying money does not matter, unfortunately.

“What questions do you have about that?” or “What questions do you think a classmate may have about that?” are also good alternatives to “Do you understand?”

There's not enough information in the OP to know if this is the case, I'm adding my answer in case it may help others.
I was forced to take a class for a subject in which I was already proficient (introduction to programming). As the course progressed, I noticed my teacher would answer other students' questions with answers that were correct, but long-winded with lots of background that ended up confusing some of the other students.
E.g. on a question about why 3 / 2 returns 1 (instead of 1.5), he began talking about floating point numbers, and how because of the way they're represented in memory, you can end up with errors, including a tangent on binary numbers (which wasn't on the syllabus). While it was interesting context, he never ended up answering the original question, nor explaining what the student could do to solve the problem. We'd often run out of time in class.
Some of the students would ask me the question again in private, confessing that they didn't understand his response. Even though I knew it was rude to do, I'd sometimes interject before he had a chance to respond so that I could explain the concept to the whole class at once, instead of multiple times individually.
A very convoluted way to agree with @user2768's comment that sometimes a fellow student is a better judge of the level of knowledge the other students have. It might be worth paying attention to the answer they gave compared to the answer you gave / were intending to give.

In my situation, I did try to talk to the teacher about it, but he was adamant that there wasn't a problem.

In many classes, there are a few students who participate way more than others. I would recommend doing two things in this case.

Have times when it is appropriate for students to answer each
other's questions. It wasn't clear from your question whether your
class has that, but if it doesn't, consider adding it. Everyone
benefits -- some students get their questions answered, others get
to think through the material more deeply, and everyone realizes
that they can think and learn on their own, without everything
coming from you.
Make the student into an ally. Pull them aside after class and say that you appreciate their enthusiasm and engagement. Then, make your request -- in your case, say that you need a chance to answer student questions without them jumping in. Don't sound like you're asking for a favor, just making a polite request, preferably with a reason. "I need you to not jump in when another student asks a question. It's important that I can address some subtle issues that can arise." End on a positive note, maybe appreciation or recognition of their interest.

Regarding #2, I think you're better off giving a polite directive rather than making a request, which is how your "I need you to not jump in..." reads to me anyway. Maybe change "make your request" to "give your directive" (or some synonym of  "directive"). I think emphasizing courtesy and explaining yourself is good, while still gently asserting your authority as prof. If it really is phrased as a request, then authority isn't being asserted properly which could backfire. Assertion of authority should be polite and show appreciation for the student, and be constructive, but it is needed.

@bob I'd say "I need you to do X" from an authority figure is a polite directive (imagine hearing it from your boss), but that will depend on cultural context.

I agree. I'm just thinking someone could misinterpret "make your request" as something other than giving a polite directive, so that's the part I was suggesting to change; I think the actual wording you suggest could work well for the situation.

I used to be that student. @Buffy's answer covers most of it, but one scenario she has not mentioned is much simpler, and was the reason I did this: impatience.
When the question was trivial and the answer obvious, I wanted to move the course along so I would blurt it out in hopes to nip it in the bud.
Of course I now know how misguided that behavior is, but it seemed logical at the time.

I have had this problem, and I was vaguely warned beforehand.
Nevertheless it came as a surprise that the pupil was one I knew before. She still hadn't got a job. No wonder why.
And the warnings were about "being too talkative", "taking over class discussions", "irritating the other pupils".
So, here it goes, refering to this pupil of mine:
Your student may be "on the spectrum". Highly intelligent, with a dash of Asperger. Brain the size of a planet. A know-it-all who can behave in an unknowingly arrogant manner. (And "Hi IQ Aspians" are often likely to have an uneven study motivation).
However, unlike others they may be more receptive to getting the situation if you describe it not as a struggle for being the top dog, rather "I prefer you let me lead the lessons, as you interfere with the other's learning process by taking over both student and teacher role. I know you know this subject by now, so just let's just roll through this course".

There's nothing wrong with students answering each others' questions. It helps them "own" the subject rather than see it as something you dispense. However in this case it seems to be unhelpful to the other students as well as to the teacher.
The disruptive student seems to be frustrated that the pace of the class is too slow for her. She seems to be well above average ability and quite capable of studying on her own, and may have failed the class first time because of boredom.
I would set her some extension work to do during class, with a view to entering for the examination early or entering at a higher level.
I would compliment her grasp of the material during class. This acknowledges the effort she has made and lets other students know that her answers are reliable.

I have been a teacher in university, so I completely understand what you are saying.
And I have also been the average student annoyed by "that kid" who is always showing off and answering everybody else's questions to the teacher. I would have loved if someone made that kid shut up.
So please, do something about it, not only for you sake, but also for the happiness of everyone in your class.
One way to approach this is talk to the student privately and ask her/him to, instead of talking, first raising her/his hand and ask: "Professor, may I answer this?". So each time you can make the decision.

I remember a situation where this happened in class. The teacher put down the interrupting student in class for everyone, rather angrily. He told the student something along the lines of "Sure, you might pass the class without problems, but that doesn't mean everyone here will".
I think a more charismatic, friendly approach could work, even if you do it publicly in class. Let's take a very structured nonviolent communication approach:
1) Observation: Hey , i can't help but notice you keep answering questions i pose to other people.
2) Feelings: I understand this feels like you are showing commitment, but to others, including myself, it can come across as disruptive
3) Needs: Other students need to be allowed to take the time to process questions, because that is a vital part of their learning process. If one person answers everything, this doesn't benefit the course.
4) Request: So while I appreciate your active participation in class, can you please try and tone it down a little when I ask questions to other people?
If you feel like this type of issues is something you have difficulty with in your class, I recommend trying to find a NVC course in your neighbourhood.

It stands for 'nonviolent communication'. To pluck a definition from the internet: "A way of thinking, speaking and acting that contributes to mutual connection and cooperation." I am not an expert in any sense, but it is basically a set of techniques that can help you communicate about conflicts (among things) in a way so that relations between two parties is strengthened instead of weakened.

Let them keep answering IF the student consistently gets the answers right. It helps the student learn and spurs class participation. Learning happens best when it is a two-way street.

There are a few things that one can do live, in the classroom setting, to mollify this situation; these are things that I do with success.
One is that in certain situations where it is natural to do so, you can direct your question, and your attention, to a specific student. Your eager student may want to jump in, but when your attention (i.e. your line of sight) is directed to a specific student, it may be more obvious to the eager student that they should hold back. If this is too subtle for the eager student to perceive, you can also be ready to glance at them and, with a friendly expression, make a little hand gesture requesting that they hold back for a bit. As this scenario progresses, it may well happen that no-one else can come up with an answer, and then you can redirect the question towards your eager student.
Another issue here is that directing questions to specific students can be done in a way which makes it really obvious that THAT student has the floor. For example, perhaps you first say to the students "Which problems on the homework assignment do you want to hear about?" And after Joe Schlobotnick says "problem number 1 please", during the discussion of problem number 1 you can direct your questions to Joe: "What would happen in this step if you tried that?" Your eager student might still try to jump in, so you might want to be prepared with the "glance-smile-hand gesture" strategy.

Recruit them as extraofficial help. Task them with answering questions in the online fora (official or non-official). Talk to them and work out some etiquette on answering questions in class: give others time to think the problem through, let others answer first, in general, be polite to co-students.

Ask them/ tell them to sit at the back of the room.
It's always more effective to change the situational dynamics rather than to try to change the person. Some people will automatically try to join a conversation if they are in the middle of it. When out of the line of sight, they are less likely to interrupt.
It doesn't always work. But telling people to be silent doesn't always work either: this is an alternative strategy.

I suspect that would be discriminatory if they had a learning disability, such as ADHD or Aspergers etc.  It also doesn't seem like a "golden rule" approach.

Just put down the interrupter.  Well thanks Hermione.  Boy somebody likes to jump in an answer. Well now, not everyone is taking the class for the third time. Stuff like that.

IMO this may (probably) come off as arrogant and things such as not everyone is taking the class for the third time are disrespectful to the student even if he or she is annoying. I'm not sure this will help OP resolving this simple problem.

PLEASE don't do this. If one of my profs did this to another student, it would instantly destroy my imagine of that prof permanently. And it might open the prof up to professional, civil, and even criminal complaints (e.g. FERPA violation). But beyond that, it's bullying/abusive due to the power differential between student and prof. Student disrupts class: small wrong against prof. Prof humiliates student publicly in front of their peers at a vulnerable social stage: MUCH larger wrong. Like a 300lb person punching an 80lb person's lights out over a slight irritation. PLEASE don't do this.

Are you the user Guest? If so, I normally enjoy your answers (they are often better than most of this site's regulars) but this answer is just horror.

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


text:
How do you study a graduate-level textbook that doesn't have any exercises?
I am trying to self-study a graduate-level physics book that was recommended to me, but it doesn't have any exercises. Also, it's a specific enough topic to where I can't really find any other textbooks that cover all of the same topics. What are some good ways to learn this book besides just reading it?
Update: this is the book. I do have some colleagues in condensed matter generally, but none in this specific field.

Are you studying alone (self-learning) or are there others you can work with? FWIW, I find this an immensely difficult question to answer. I remember trying to learn Fortran from a textbook and making all sorts of intuition errors about the meanings of things. (Long ago and far away). It had exercises, but I had no way to execute the code.

Mod's Note: Please understand that the asker is about to earn a PhD in physics, and the book is a highly technical, graduate-level book. Answers proposing basic study strategies are not responsive and may be removed. Please avoid writing answers in the comments.

When I was in grad school, we would be so happy when the professor assigned a Dover book as the class text.  Dover sells prints of older textbooks that have fallen out of copyright and so cost about $20 a pop.  It's never bad to have different authors' take on the subject, especially when it comes to graduate level topics.  I don't think it would be too hard to find a Dover book that has useful problems to work.

(I'm in mathematics...) My advice is to not think in terms of "exercises", in the traditional sense of posing some sort of "challenge" which can allegedly be "responded to" using the ideas of the preceding chapter. :)
Rather, I strongly think that it's better to think in terms of "examples" ... of the phenomena discussed, not only in the "chapter" or other body of material at hand, but also phenomena that may not fit exactly into a limited range that is perfectly addressed by just one particular method/idea.
In my own little world, I've often found it extremely illuminating to try to conceive of the simplest-possible version of a general issue, on the principle that if a "trivial" (in math-style talk) version is not solvable or comprehensible, the fancier versions are ridiculously out-of-reach. Further, in the kind of math I do, there are often no alternative understandings for relatively fancy things, so it's hard to do sanity checks... while for "trivial" (math-talk, again) examples, there can be alternative viewpoints that do provide sanity checks.
And, from a teaching viewpoint, beyond a certain point it's really hard to compose exercises that are do-able without considerable run-up beyond "theory". That is, again, examples.
And, seriously, the intellectual model that exercises "are a thing" is a bit odd. :)

What is your last sentence supposed to mean? Exercises are a bad idea? It is very hard to understand.

@toby544, I mean that thinking of a subject and one's knowledge of it in terms of exercises is a strange approach. Breaking something into tiny pieces and randomly fooling around with those pieces, as a supposed way to understand the whole?

"Breaking something into tiny pieces and randomly fooling around with those pieces, as a supposed way to understand the whole?" --- well, yes, exactly, how else would one learn a new piece of mathematics?

@JohnPardon, well, it is often very difficult to guess the purpose or intended function of a small idea if one does not see how it interacts, or is intended to interact, with other things. What are the goals? Often many small details are most easily explained with hindsight, in my experience. That kind of thing.

I've found that writing up detailed notes on a topic I've been reading about is invaluable for exposing what I do and do not understand about a topic. It also sometimes has the side benefit of letting me come back to something more quickly after I've been away from it.
For this to work, these must be topic notes, using your own organization of the topic informed by what you read, not notes on a particular item you're reading. If you find that the organization of your notes directly parallels that of a book or paper, you're not doing it right and will likely come out little better than if you'd just taken a highlighter to the document you were reading.
(Another warning sign may be being able to write the notes very quickly for a topic, unless you already feel qualified to teach that topic. For complex topics that are new to me I typically spend at least twice as long writing and reworking the notes as I do reading the source material. This time may include devising and performing small experiments or simulations to help me confirm that certain things I've written down are correct.)
It's of course hard to give concrete advice on how to build an organizational structure for your notes; doing this is similar to sketching an outline for a textbook. (That this is difficult is exactly why the technique works.) If you're having difficulty getting away from the organization imposed by the particular document you're reading, it may help to find a couple of other documents that have at least some coverage of the same area, sketch out the organization of all three (or more), and then combine and change those until you come up with a new organization for your own notes that subsumes all the information from all three documents. What you should eventually find is that, despite coming from different sections of the source documents, these separate but related pieces of information end up together, illuminating each other, in your notes.
I certainly don't have any examples from chemistry, and it's hard to say how well examples from other fields will work for you given that they have to be fairly technical and moderately deep in order to actually to demonstrate the process. But in case it helps, you can have a look at my notes on analogue video as an example. The information here comes from at least twenty different sources and most or all of the sources from which deep details came were specific to a particular video format (NTSC, PAL, RGB, etc.). I had to identify the "high-level" commonalities between all of these and then come up with new sections for each of these, integrating the information from various parts of the source documents.
For example, all the video formats have logically separate display and synchronization information, and the synchronization signals are always logically separate horizontal and vertical signals. However, some formats transfer horizontal and vertical sync over separate wires, others combine the two, and the sources for the latter often discuss the combined version as just the "sync" signal, without really going much (if at all) into the logical separation between the two. In my organization I have separate sections for horizontal and vertical sync containing all information I have about each (whether the information came from a separate sync or combined sync source), and yet another section describing how the two are combined (and any implications of that).
I don't know how much that helps, but perhaps you can at least take away the idea that taking apart source information and putting it back together in a different way is the key to this technique.

Invent your own exercises sparked by what you've read, then try to solve them. When you read something, try to ask yourself what it's good for.  What can you do with this that you wouldn't be able to do before?  Can you demonstrate it?  I'm not a chemist so I can't answer in your domain but if it were in mine in computer science and I was perhaps reading about a new algorithm, I might try to code it and see if I could make it work.
Think of it as if you were going teach this material in a class where you can't just assign problems out of the book, you need to create projects and write your own exam questions.  You would just dive in and do your best to create some interesting problems.

Maybe, but it is often harder to come up with decent exercises than with the text itself. A start, anyway.

Only slightly different is to try to write an exam based on the chapter /paper etc. Especially if you include a range of Bloom's Taxonomy type questions eg 1. Define x, 2. Contrast y and z conditions, 3. Evaluate the effect of changing a, B, c criteria. Specifically aim to capture any premises of the chapter /paper, the boundaries of the field (where this effect does /does not apply)

@CiaranHaines, yes, but a sort of hyper-analytical approach to things can lead to the kind of over-analysis of acquired intuition, so that it becomes impossible to walk, because it's simply toooo complicated. :)

+1 I feel like at the graduate level, one should definitely be able to write their own exercises, although the words “example” (used in another answer), or “thought experiment” might be closer to the mark than “exercise”. If the text presents formulae, invent or find  real world numbers to plug in and see how things change. Build a computer simulation of concepts described in the text. And so on. Part of the joy of teaching oneself is learning how to teach and learn.

Setting your own exercise (as already mentioned) is a good method.
Also consider more generally the Feynman technique:
https://en.wikipedia.org/wiki/Feynman_Technique
In order to truly master a topic, you need to be able to teach it. So try and produce your own teaching materials, such as a summary, a diagram, an exercise, etc.

Many textbooks come with examples of implementations of the concepts covered, for example a dynamics textbook will likely show a step by step derivation of the dynamics of a double pendulum. My suggestion is to try and follow those steps and replicate the examples on whatever platform is suitable (for dynamics you could use matlab, mathematica or python, or even pen and paper!)
You can then check your output against what the textbook shows and see if it matches.

One question would be what level of a student are you, and why are you reading this particular book? Based on an earlier question you've asked, you appear to be an experienced undergraduate or a beginning graduate student. So, what are you expecting/expected to learn from it? Further, how are you accustomed to learning?
Since the book does not provide exercises, I can well believe that the book is not a textbook, but rather a monograph ("a detailed written study of a single specialized subject or an aspect of it"). Not surprisingly, one uses a monograph differently from a textbook, and undergraduates rarely encounter monographs as a learning tool. So, you are correct to wonder just how to deal with it.
I would argue that monographs are written for researchers and are approached very differently than an undergraduate would approach a textbook. For an undergraduate class, the textbook is, in essence, the stuff you need to learn, and then demonstrate on an exam, and is written (mostly) by experts in how to teach the material to undergraduates. The exercises are the practice to help you learn the material and learn how to do the questions that will be on the test.
By contrast, the monograph is a whole bunch of detailed information presented by an expert in the field to present it all in one place to somebody new to the field but interested in becoming expert. There is no expectation that, by reading the book through once, you are suddenly an expert. There is no exam at the end of the ‘class’. Instead, the monograph is useful in several different ways, some of which only emerge over time.
So, how do I generally approach a monograph? Remember, I’m not an expert (yet), but am interested in the subject matter, likely because I see a need to understand it for my own research path. Maybe I will end up diving really deep, maybe not. First step is to look over the organization of the book – what does it actually cover, what order does it go in, are there technical (journal) references readily available in the text or as end notes. This step is to evaluate the relevance, and sometimes I don’t proceed from there. Now, in your case, the book was recommended to you, and if by your advisor the ‘recommendation’ is more than a suggestion.
Next, I read the first chapter. Often this is an overview of what the monograph covers, and I may have already skimmed it in my first step. But this is the time to pay a bit more attention. Is there jargon I don’t know, is the point of the monograph detailed, is the subject of the monograph placed in context of the field?
Assuming the first chapter is an overview, it is time to start into the meat of the monograph. But, I’m not reading for all the gory detail, but I’m also not just skimming it. What does the chapter cover, do I get the general idea, am I totally stumped? If totally stumped, then it is time to put the book down and go find a textbook with more basic stuff in it to review. If I’m getting the general idea, great, but may still choose to skip over more detailed parts for now. If that chapter goes well, I continue onward as long as things seem OK and interesting.
At the end of reading, I am not an expert. I do now know the areas that the monograph covers, and where in the book they are covered. Maybe I’ve looked up a few of the papers in the references. Maybe a section or two has really caught my eye as being directly applicable, and those I’ve probably read more carefully already. Am I done now? Perhaps, but it is time to evaluate what the next steps are, based on why I’m reading the book in the first place. Do I need to read more background material? Do I want to go and talk with somebody to clarify something? Did something really catch my eye? Evaluate where you are and what to do next.
Sometimes the book goes on my shelf and is not touched again. Sometimes it migrates to my desk since I keep referring to a specific section in it. Sometimes it gets pulled down a read through again, more thoroughly. It all depends on what your specific need is for the information.
This is, in the end, not all that different from how I approach journal articles. Something catches my eye and I download it. I’ll skim the abstract and the intro, glance at the experimental section and the figures, skim the final section. Often that is all and the paper gets filed away in case I need more info. Sometimes it gets read more carefully, sometimes I look up some references, sometimes I discard the paper.
Ultimately, as you transition to graduate work and research, you start learning differently. You start evaluating for yourself what you need to know, and how deeply. Frankly, it starts being a lot more fun. Good luck.

Once, I took a graduate-level physics course, in which the book had no exercises, and literally what the professor did was to stand at the front of the room and read the book to us.  To this day I'm unsure why I went to class (he wasn't interested enough to take attendance).  There were just mid-term and final exams to determine our grade (I forget whether I got an A or B).
What I found really helpful was, after learning a chapter, to go back and start at the beginning.  Usually, you understand the beginning of the chapter very differently after you have learned the whole thing.
Also, as others mentioned, it's very helpful to make notes that summarize the topics in a way different from how the book organizes them.  Though, in a pinch, even summarizing the way the book organizes it has value.  If you're interested in remembering it, writing your notes works better than typing them.  (I later took graduate courses in Science Education that explained why.)  By all means, feel free to type them after writing them; that's probably even better than just writing.
Here's an interesting idea: once you've studied (not just read) a chapter, look at the Wikipedia entry for that topic, and see if there's some way you can improve it.  That's maybe a more modern version of the Feynman method.  Even if you can't improve it, looking for a way to improve it is a good exercise.

Wow, my sympathies for that terrible class you endured... Pathetic for a prof to be so disinterested, and also immoral/unethical to so-disserve students.

@paulgarrett - Yeah, I would have expected better at an Ivy-league university, if not for hearing worse stories from my friend who went to Harvard.  (He was there for 3 years before he even had a class taught by a professor.)

I'm confused.  You read the book.  You try to understand what is written. You look at the new material and find analogies to what you already know and make note of what is new.
I must say that I nearly never did any exercises that were not assigned (in either undergrad or graduate school, both in Chemical Engineering).  Relying on examples and exercises is really not how I learn.  I respect that we have different learning styles, but reading and understanding is key to formulating the view you you end up having of a subject.  It's the same whether you are reading a book or reading a paper.
I once took an entire graduate class that included exactly two examples in class; and the second one started with the prof saying "Consider a system in N-Space".  It was a class on State Space Control Systems (from the department of Electrical Engineering - hint to others: never take a graduate level Electrical Engineering class without ever having taken any other Electrical Engineering classes before).  I was very proud of that B.

Make your own exercises. Your physics textbook doesn't have them, but it probably has examples? Exercises is just more examples. Change some or all of the parameters, do the math.
A physics book may have one example of a ball rolling down an inclined plane. To make an exercise, change the angle and height of the plane. Consider a ball of different weight, consider doing this on the moon where the gravity is weaker. If the physics is advanced enough to include friction/drag, then change the friction coefficient too. Find out how long time various balls takes to roll down different planes.
Similar for all other problems. They provide one example, your exercise is to work out examples with different numbers. If the book doesn't give examples at all, make your own. Make up problems so you get to use each and every formula a few times.

When I was in grad school, we would be so happy when the professor assigned a Dover book as the class text.  Dover sells prints of older textbooks that have fallen out of copyright and so cost about $20 a pop.
It's never bad to have different authors' take on the subject, especially when it comes to graduate level topics.
Looking at their selection, it looks like the Goodstein book might be a good choice.


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Acquaintance is paying friend to do his coding for an Ivy League master's degree. What should I do?
I'm relatively close to someone who is currently attending an Ivy League graduate program.  He believes he has it all made in life and yet here he is paying one of my friends to do his coding assignments and projects.
It is an online program, so it makes getting away with this even easier.  This situation only benefits both of them, but it's just bothering me.  I just hate the idea of someone bragging about being in an Ivy League graduate just to pay someone else to do his work.  Should I just drop it or report the student?
In response to questions: no, I am not a student myself.

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How are you going to prove it? How is the university going to prove it? Is this just a Coursera course? Does anyone (including employers) actually care about that online course / degree? I can tell you that when reviewing CVs, I immediately ignore any kind of "online courses"; I see them as showing interest and drive in that area, but I wouldn't weight them in as proper certification / education (like a physical Ivy League degree entails). I find it very odd when people fill their "Education" section full of supposedly Ivy League courses that end up just being Coursera in the end...

What would I do? I would report them both, anonymously.
What is my rationale for this? Mainly because it is not a "victimless crime":

There are plenty of employers who weight the reputation of a university very highly (perhaps too highly) in hiring processes. A more-deserving and capable candidate might not be given an interview or an offer as a result of this person having cheated.
To the extent that any university's reputation is well-deserved, this is founded upon other people's judgements of its integrity. i.e. that the degree means something. If that impression of integrity is eroded by unqualified people receiving degrees, that hurts the employment chances of everyone with a degree from the same school.

I feel these two points are basically just statistical. Given enough incidents of cheating either or both seems to be a likely consequence.
Somewhat more subjective reasons:

Bad outcomes are possible when an unqualified person is granted responsibility. Crashed airplanes? Deadly medical devices? Losing money for their stakeholders? Maybe the odds of great harm are small. And perhaps such a person has no actual interest in taking a job like that. But I don't think this can be totally ignored.
More broadly, what other harm are these people likely to cause in life? Chances are that this is not at all their first case of untrustworthy behavior and won't be their last -- as long as they perceive it to be in their interest to act this way. On the other hand they may be early enough in life that a "shock to the system" from being caught could actually be helpful. Or at least a deterrent.

Why an anonymous report? I think this is pretty obvious, but I would not want to take any personal risk (in any sense) from this. People can be petty, angry, etc., and I see no reason to expose myself as any kind of 'target' of those emotions.
On the other hand you might have to trust the institution to protect your identity, it depends on how you can make a report.

A more basic issue with anonymity is whether the friend could guess who reported him.

@Kimball this is a good point. And the OP has to decide if its worth the risk. Whatever evidence they have of cheating (if any) also might be attributable only to them or a small # of people, even if the basic accusation itself would not. I haven't looked but there might be good questions on here about HOW to go about reporting such a thing

One small issue is I do not know who else knows.  I could possibly be pinpointed quite easily and unfortunately this could cause drama as we are all stuck at our location due to military.  I share your point of views and I know that this student will continue to do this in the future.  He is the type of person who only show any form of respect to you if he has something to gain from the relationship.

@youravgguy Maybe you could have a preliminary communication with your university without naming anyone or even mentioning an academic dept. Share your concerns all around and see if their guidance is helpful. (Don't be pressured by them however). While this is probably a first for you, it presumably is not for them.  And/or, a confidential discussion with a faculty member you trust, perhaps your own adviser.

@youravgguy in my last comment I meant to say an "anonymous preliminary conversation"

This is an excellent answer, and I agree with it wholeheartedly! But for the OP, I would like to add one more practical consideration: do you have any kind proof that can convince others (I mean, the university officials) in what you are going to report? I'm not trying to discourage you, but I suggest you carefully build your case and your report. If it's just "my word against his", the university (probably) won't do anything.

Bad outcomes are possible when an unqualified person is granted responsibility like a certain US president.

You're missing an important point here (which supports your case): if they investigate  one specific instance of cheating or put measures in place to make similar cheating more difficult, they may uncover or prevent many other cases of cheating. Your 1 report could very well by itself put a huge dent into the number of cases of cheating.

"integrity is eroded by unqualified people receiving degrees"
--I'm not so sure this wouldn't be a good thing.  Employers are putting way too much stock in degrees, all the while universities continue to skyrocket tuition prices, hand out degrees to substandard students, and turn a blind eye to cheating.  If trust is eroded in a degree, it'll force employers to consider other qualities, and perhaps even end the idea that an applicant must have a degree to be considered.

@user64141 this answer is not pro- or con- the university system itself. But from the perspective of another student and the same university, things which diminish the value of their own education definitely seem like a negative. Maybe the OP shares this perspective (or maybe not).  Also even if the system needs reform (or improvement) I don't think cheating would be an effective way to motivate change. That seems more like a cancer killing from within rather than deliberate change for good purposes.

I have to say, I couldn't disagree with you more. OP, you said this is someone you're close to. I'm not saying don't turn him in-- that's up to you, and if you feel strongly about this, then you should. But if you do, certainly don't do it anonymously. You bring it up with your friend, preferably before you do it. Yes, he may be angry about it, but you can't judge cheaters if you're willing to snitch on a friend without owning up to it. Don't let a fear of confrontation turn you into a rat.

Just my personal view. I think you can do that if it makes you happy, but... it reminds me of an old joke: "I cheated on a train line -- I got a ticket, but didn't ride". Your friend is basically paying for education he doesn't receive. Will it do him any good? If no, he'll just punish himself by paying for nothing; if yes, then something is wrong on a somewhat deeper level of society, I am afraid.
As a teacher, I am trying to identify and punish cheaters, because it's my job, and it keeps our educational environment healthy. But when I think what motivates people to cheat, I cannot find a good answer at my or other students' level of responsibility (okay, it is possible that a certain course is poorly designed, but usually it isn't the case).

The motivation is presumably the degree. Even if you don't actually learn the material, having a degree can give you an advantage against other job candidates. I guess that's the societal problem you allude to.

“If no, he’ll just punish himself by paying for nothing”. Well, no, he’ll also punish the future employers who hire him, future subordinates working under an incompetent boss, future honest people competing with him for jobs and social status, etc. This mindset of “you’re only cheating yourself” sounds very philosophical and deep, and may be useful as a simplistic lesson to teach to immature twelve years old, but unfortunately — and I sincerely wish it weren’t so — it’s factually wrong.

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Considering you asked this in Academia, and Academia is all about objectivity, integrity, trustworthiness and reputation: report them.
However, considering you used the phrase

it's just bothering me

I would like to give an answer as if you had asked in Interpersonal Skills:
I would talk to the one you consider a friend (or both of them). Tell them how you feel about this topic and make the moral implications clear. Explain to your friend how this is beneficial to them money-wise, but hurting their reputation and their relationship e.g. with you. Ask them to stop. If you already had this discussion or it goes badly, you should probably reconsider the term 'friend' for your relationship. Doing nothing or pretending this is ok will likely hurt your relationship anyways, at least unconsciously.
Depending on your relationship with your friend you can also consider informing them about being on the brink to reporting the actual cheater (or both of them) and you may give an ultimatum.
If you are friends, this will likely resolve the issue without further escalation. Even if not, you'll better understand the relationship you have with them, and this will likely make it easier to report them.
However, keep in mind that you cannot report them anonymously afterwards. We cannot estimate the chance of success or their potential level of aggressiveness without knowing them personally.

Bear in mind that challenging one's personal projects/views, even among friends, can be dangerous though. Expect backfire, especially if the other person is under the impression you want to shape them into the way you want them to be.

I like this answer. But note that if you tell your friend that you think what they're doing is terrible, and then anonymously report it, they're more likely to guess it was you who made the report.

@Ben Millwood: I tried to highlight this problem with my approach in the last paragraph. However, I didn't suggest to report them anonymously in the first place.

This is a moral question and each person has their own morals. It seems like you have already decided what you want to do and ask for validation but you need to decide that for yourself and live with the consequences.
I suggest to think about whether "it is bothering you" is enough of a reason for you to report someone or if there are other facets to the issue. Is the life or health of someone in danger if the cheater gets the grade but doesn't earn it? Is the cheater in danger of failing the course or is it just laziness? Would the cheater be deported back to a war-torn country if they drop?
However there may be more options to consider than just the two you listed (report or ignore). You could also talk to them.

Very true.  The government is paying for this expensive program.

I'd up vote this, except your definition of "morals" is wrong. Morals are defined by a community or civilization. Each person might have slight tweaks to them, but they still have to conform to the norm. Cheating on a test or class is not a "tweak" nor the moral norm. Letting others cheat should not be the moral norm. https://www.merriam-webster.com/dictionary/moral

@computercarguy: I looked up the link you gave me but as far as I interpret it, it is consistent with my usage of the word:"Morals often describes one's particular values concerning what is right and what is wrong:
It would go against my morals to help you cheat on the test. " However what you mean is described as "ethics" there: "In addition, morals usually connotes an element of subjective preference, while ethics tends to suggest aspects of universal fairness and the question of whether or not an action is responsible: [...]"

I personally don't like the idea of people cheating like this in an academic setting, but reporting them is a very serious undertaking with a potential to damage lives and should be considered carefully.  I suggest that you proceed through this sequence of questions to help determine if you should report them or not:
1) Is the person who is helping really your friend?  If so, don’t report them out of loyalty to your friend.  Most likely you only know about this because your friend told you, or the other person told you because he knows that you are a friend of the person who is helping him cheat.  I feel that your loyalty to your friend is a higher obligation than reporting them.  Of course, it’s OK to talk with your friend and tell your friend that you disapprove, or possibly even break off the friendship if you disapprove of this behavior strongly enough.  Obviously if your friend was involved in a more serious crime then your duty to your friend would not necessarily be your highest obligation.
2) On a spectrum of “bad things” this is fairly minor.  Have you ever done anything that is this bad or worse than this?  Would you have wanted to have someone report you for that behavior and face the consequences?  You are in a position to help guide both of these people to a better path of behavior and you can potentially do so without reporting them.
3) Do either of these people know anything about you that could put you in a bad light if it was revealed?  You should consider that they will probably know that you were the one that reported you and if they know something bad about you, they might reveal that information after they figure out that you were the one who reported them.  Although this might seem like item two above, it is not.  Item two was concerned about your behavior, regardless of if anyone knew about it or not.  This is concerned with protecting yourself from harm by one of the people that you report.
4) Are you in academia?  If so, you would probably feel a higher obligation to report it and that would be understandable.
5) Why do you want to report them?  You said “I just hate the idea of someone bragging about being in an Ivy League graduate just to pay someone else to do his work.” That sounds like you are resentful that this person is going to get an Ivy League degree.  Did you want to get an Ivy League degree and you were unable to for some reason? If not, what is your reason for wanting to report them?
6) What do you want to accomplish by reporting them?  Is it just to satisfy a moral duty that you feel that you should report them, or are you wanting to see the person removed from the program or some other punishment?
After having been out of school for a long time, I have adopted the philosophy that the real world is an open book test.  For most things in life, it doesn’t matter if you know how to do things, or you know how to get things done (by yourself or others), as long as you can produce the results in the end.  This person could end up being a dismal failure, or he could end up running a company one day.  In the real world, knowing how to get a good or great result is what matters.  Also, a person who bends the rules like this might be more likely to bend the rules in the future about more important things, but there’s no way to know if that will happen or not. I don’t like the idea of people cheating in a program like this because it is an academic setting, and the rules there are different than the rules in the real world, but I don’t see that this situation rises to the level that you should report it.

Thank you for your response.  I am currently in school as well but have no desire to go to any Ivy league.  I used to be very close to this person but as i've gotten to know them deeper over time, I have come to dislike many of their traits.  He has an faux image of being wealthy he tries to maintain to trick people into thinking he knows the markets and knows how to trade.  He gives poor financial advise to people but they listen because the average person seems to trust someone with his image. He is now using money of those around us as he has convinced them of his successful trading career.

If the university is willing to give someone a diploma for someone else's work, then it reflects badly on the university. They should design their programs (in particular online programs) to make this harder: for instance, have live interviews with participants and ask them questions about the work that they have supposedly done, and catch those who can't answer.
But I would not say that you have a moral duty to report this. You are not in charge of defending this university's reputation. (No matter the university, actually -- would this be somehow OK if it were a less reputable one?) I guess you could, if you wish, and if you don't fear negative consequences (e.g., your acquaintance figuring out it's you), but I wouldn't blame you for not doing it.
To answer @UuDdLrLrSs's points to argue that this should be reported:

If employers value degrees too highly, and don't test that candidates are able to perform the work that they're in charge of doing, then I'd say it's their responsibility.
If the university's reputation suffers, it's the job of the university to defend it, and people with an interest at stake (e.g., alumni) can pressure the university to do it.
I think it's the same as 1. I could imagine exceptions for some areas, e.g., medicine, when you have jobs with high responsibilities which can legally only be practiced with people having a certain degree (and with legal oversight on which institutions can grant these degrees). Then I would see a clearer moral imperative of defending the value of such a degree.
In general could see a moral imperative of denouncing criminals that do harm, even when you're not the victim. But when the crime is made possible by the victim's negligence (here, the university not making sufficient efforts to catch cheaters), I think the imperative disappears.

To summarize: it's a broken system if a university must rely on bystanders to report cheaters. If they grant degrees with online programs, they should make the necessary efforts to ensure that the person who's getting the degree is the person who's been doing the work.

I sort of fell it is everyone's responsibility to stand up for the system (if not improve it) not out of moral reasons but because we all rely on it. I don't disagree about a university potentially being negligent, but I also think societal good behavior pretty much has to be cooperative as well.

I understand the point and I even agree to some extent, but I don't care too much about the system I think. If it turns out that someone from famous university X is actually a fraud, I won't shed a tear for the system :) I'll just update my perception of the reputation of university X in the future.

I may be wrong, but I'd assume that no one gives any credibility to purely online programs. One thing is having online classes and another completely different thing is being evaluated online. I don't think I would weigh in any more value to an online Ivy league certificate than I do to the typical Coursera certificate -- next to nil.

"it's a broken system if a university must rely on bystanders to report cheaters."
Agreed.  It's a good thing if this university's reputation suffers.  Their lax policies greatly empower cheaters and people with no moral scruples.   The colleges takes the tuition money (often from the gov't), conveniently ignores cheating, easily graduate these clowns, and washes its hands.   But as more of these substandard students receive degrees, employers will slowly start to get the message -- which in turn, will force colleges too as well.

I disagree completely with the idea of not "rel[ing] on bystanders". This is how most crimes are reported as well as solved. When the police are called, they look for witnesses, and it's become a TV trope about how no one is willing to say anything, so the crime goes unsolved and unpunished. Even Homeland Security has the saying "If you see something, say something." Reporting a crime, or even breaking the rules at a school, is essential to keeping our society working without massive crime and stupidity. So, no, don't hold your friend's beer while they do something stupid, talk them out of it.


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Is it acceptable for a student to connect with a professor on LinkedIn?
Earlier in the semester, I was informed by both an advisor/academic counselor and a professor at my university that it is a good idea to connect with professors on LinkedIn if they have interests in the same area as me.
I sent a connect request to one of the professors I had last semester (along with some other profs, most of whom accepted) and he just wrote back to me saying it is extremely unprofessional to be trying to connect on LinkedIn for a student/prof relationship. I am confused - how is this unprofessional and how can this be handled better in the future?

Mail is the most preferred way to connect, but Linkedin shouldn't be a problem. Its a site specifically made to connect to other people in the field as professionals. It may not be the best place to discuss research ideas etc., but its not unprofessional and definitely not 'extremely unprofessional'. I have contacted a few professors previously on LinkedIn (after mails went unanswered), a couple of them did reply back addressing my queries.

There are a lot of people (including me) who only use LinkedIn to connect with people  who are actually working (as opposed to studying). I would just ignore a request from a student, but I wouldn't consider it unprofessional to ask.

Where/what area is this?  I always thought that, at least in US in math, most professors don't use LinkedIn.

Related: Is it okay to add a lecturer on LinkedIn?

FWIW I had an small bureaucratic interaction with the provost of the University I was attending, she turned up in my suggested contacts so I just clicked on 'invite' and she promptly did. 48k+ students...

Sounds like your professor is quite full of themselves....

@Marianne013 - in a lot of cultures studying is pretty much considered work. I'm in Eastern Europe, and "colleague" is the standardized title for all teaching staff when referring to students.

There are most definitely professors who will connect with their students on LinkedIn.  Not all of them will, but some will (I'm an undergrad, and connected with at least two professors, both of whom are undergraduate advisors and one who I had served as a TA under)

@Davor: But I decide whose connections it makes sense to accept for me. And undergraduates don't usually fall into that category.

Here I quote the crux of your situation, and put in bold font your sentence containing a question:

"I sent a connect request to one of the professors I had last semester (along with some other profs, most of whom accepted) and he just wrote back to me saying it is extremely unprofessional to be trying to connect on LinkedIn for a student/prof relationship.  I am confused - how is this unprofessional and how can this be handled better in the future?"

Here is my answer:

Whether or not it is unprofessional is extremely subjective.
What you did is perfectly okay, perfectly legal, and is done very frequently by many people.
My recommendation: feel free to continue connecting with people as you see fit, but be aware that some professors might not like it. Exercise careful judgement: if the professor has 5 mutual connections with you, and 4 of them are students, go ahead and connect with them. If they have < 100 connections in total and in real-life you are able to see that they are not the type that would ever want to connect with a student, proceed with caution if you think you might want something from that professor later.

"in real-life you are able to see that they are not the type that would ever want to connect with a student, proceed with caution if you think you might want something from that professor later" Why would a student want something from a professor who doesn't want to connect with students?

@JiK Examples: the professor does "admin" work (in the broader sense) and the student needs a signature for getting a project acknowledged or the professor is in some committee that might discuss a request by the student and the student does not want to cause the professor to raise objections.

@JiK That the professor doesn't want to connect with students on LinkedIn does not mean the prof doesn't want to connect in other ways, such as being a formal or informal advisor or whatever. Perhaps the prof just wants to use it to keep track of connections to other professionals working long-term in the field, and not clutter it with links to every student he's ever encountered. (Many people have the same issues with recruiters; if I connected with every recruiter that sent me an invitation I'd have more connections with recruiters than other professionals.)

I would also add to maybe start asking for connections after the main interaction with the professor has taken place. For example, ask after the course is over or the exam is passed, so that there is less possibility that the connection is seen as the student trying to being noticed than as a genuine interest in sharing future professional opportunities.

@cjs Correct, but the problem in question here was after the term and any ways, connection on LinkedIn should not be considered extremely unprofessional if it is just the professor's personal preference

It sounds to me that this is just the reaction of that particular professor, and so there's not much you can do about it. Perhaps the professor only likes to use LinkedIn to connect with other researchers and professors, but personally I don't believe that it's unprofessional or inappropriate for university students to connect with professors. You are both adults and the site is intended for networking in the professional context. I myself added many of my lecturers on LinkedIn while I was an undergraduate, with no problems.
If you'd added him on Facebook, that might have been a different matter, as many people want to keep their work and personal lives separate and would regard such a friend request as overstepping that boundary. However, all you can do now is move on. In the future, perhaps only add professors that you have got to know quite well, as then they will recognise you if you request to connect, which in turn will hopefully mean they are less likely to refuse.

Yea that's rubbish - most academics have huge networks on Linked In. Many of their contacts are former students who have remained active in their field. This is particularly the case among graduate students and academics in their department.
Personally I think if an undergrad made the effort to connect on Linked In I would take that as a sign that they were motivated and keen to continue working in whatever field it was that prompted the connection.
If an academic is chastising a student for trying to build their professional and academic network - frankly I would just call them an idiot.
Don't be deterred! Keep building your network but seek out the enlightened people who thrive on making connections. Avoid the morons that refuse them...

Most academics I know are not active on LinkedIn at all. So I expect this varies by country and field.

It is totally fine to connect with your professors on Linkedin. You don't have to chat with them or comment on every post they upload but it is good to stay connected via social media in a professional way. I used to get requests from my professors on Facebook and LinkedIn, so I knew that they like to stay in touch somehow with good students. But again, try to not chat with them or comment a lot on their posts.

I agree with the answers here stating that LinkedIn is fine for creating a professional connection (as opposed to Facebook, Instagram etc.)
One important point- when sending an invite request, make sure you write a personalized note. Explain that you want to connect on LinkedIn for the purpose of developing network of professionals in your field, which currently (while you are a student) consists of your professors etc. Write some sort of intro along these lines.
This may sound stupid- after all, it's your professor who already knows you! Why do you need to write such a request?
But lots of people, especially students who are just joining LinkedIn, view it as just another social media platform. They don't understand that LinkedIn tries to keep a more professional focus.
Instead you have people who treat it as just another platform, and act like they do on Facebook. This includes negative aspects like trolling, or sharing inappropriate personal information etc.
It's possible that this professor has had negative interactions with students on LinkedIn and therefore is against connecting with them.
By writing a note along with the actual invite request, it shows that you are actually interested in using LinkedIn in a professional way.
it might not help with this specific professor, but in general it's a good way to establish your seriousness and professionalism.
Also- instead of connecting with a professor, you have the option of "following" him/her instead. Especially if a professor shares content on a regular basis, you can start seeing that content and commenting/engaging on it.
When people see that you are taking their content seriously, they are more likely to be willing to accept your invite request. It's another way of showing that you are serious about building actual connections and not just trolling etc.

I get plenty of LinkedIn requests, mostly from companies that want to sell me something, hiring companies and random people. I just ignore them.
So not getting a reply does not mean much.
I would not write back to a student to tell them that this is "extremely unprofessional", for several reasons

such wording is condescending and shows that the demi-god who replied to you is full of himself. Should he want to explain you something, he would have chosen better words
but especially that my opinion about "who can be connected to whom" is very personal: young people may not have the barrier which was instilled when I was a student - that one should approach professors with deference. Times change and the fact that someone lives with their times (and not mine) is not a reason to be unpleasant.

I would not have done what you did. But there is nothing wrong to do that.
I would not have done what the professor did. This is extremely unprofessional, coming from someone who is supposed to teach.
And finally, LinkedIn is crap, do not put too much effort/faith into it. It is just a fancy online CV. EDIT: see the comment below for an alternative view on the usefulness. (interestingly enough, this is exactly what I was complaining about in my answer: to not focus on one's personal point of view but understand that others may have a different approach. Point taken)

I think your last statement is contradictory and as much as I love to criticise "social networks" for not being useful or not really understanding their use, you made a prime use for LinkedIn abundantly clear - which is incidentally one of the only true benefits I see: LinkedIn provides and excellent job listing aggregator if one searches for new employment. Of course it has its fair share of spam, but it is much easier and more convenient than finding companies without. The "Easy Apply" function is nice too as it uses a standard format for the CV which will be the same. ...

...I do not know if I got my current job via the "Easy Apply" link on LinkedIn or sending my CV to the company, but searching for jobs is one function where LinkedIn definitely has its uses. Also if only just to identify companies hiring in your area. (You see a job posting that is interesting, you then research the company.) - So in conclusion, yes, it seems to be really primarily an online CV today. But this can have its uses for job searching (for those without connections). - I'd thus suggest to edit out the judgement in the last sentence.

@DetlevCM: fair comment, thanks. It is true that the usefulness depends of the use someone makes of it. I would never find a job over there and the "blog" part is horrendous (mostly self advertising). This said if it useful to some then great.

While there is nothing utterly unprofessional about it, I'd feel weird to have a LinkedIn connection with students. LinkedIn in my region is for professional work relationships, whereas - unless we're talking Phd students - a professor does not have a colleague relationship with their students, especially undergrads. This holds even more in regions where "professor" means teacher (i.e. covers highschool).
It might also be that your professor considered it a too private kind of connection, i.e. that they could get in trouble for "befriending" you. I don't think that is a realistic fear or at least it shouldn't be.
That being said, since you explicitly were encouraged to connect with professors from an official advisor, you did nothing wrong and the professor is the oddball here. Maybe they have another cultural background. Many social networks are used quite differently across the world - with the US having one of the more social media friendly and "open" populations as far as I can tell.

Well, I would suspect most students would get a job somewhere after their degree. (Whether it is a good one is a different question.) - Especially if you think the student might do well it could even be self serving as you might have a connection in "important places".

@DetlevCM Ah see for me this is not about getting people in any important places but about a) staying in contact with friendly colleagues that are not really friends yet, but close to it and b) having a network of people that can vet for my abilities and where I can vet for theirs. A student especially a low grad student can barely do that aside from a low level of teaching skill evaluation, but otherwise they are far too far away.

I suspect you might be doing the graduate student a disservice there. If someone wanted to know about you as an educator, former students might be good people to ask to see what they thought of your teaching. And if the pool of colleagues is reasonably static, I would actually consider them very bad evaluators. On the other hand, if the colleagues change and come from a diverse background, they can offer very valuable insights. I don't think your point of view of LinkedIn quite agrees with today's spirit of the site which has become a looser network of connections. Effectively we would need...

..two contact tiers. One for the "looser connections" of potentially valuable employment contacts. And a second tier for people we know well personally or have worked with. As it stands, those two functions are mixed resulting in  potentially very inconsistent views amongst users, as seen in this Stackexchange query and its responses.

@DetlevCM I don't think there is a universal way to use LinkedIn, plus I'm in industry now. But most people I know in my sector barely use it (i.e. have very limited circles), but indeed there are some who collect a lot of connections. I've observed similar behaviour on many social media. There are a minority of power users and a majority of casual more "private" restricted users. The minority is obviously way more visible because they are connected to many and thus one comes across them more often. That being said, I'm really really rarely logged in to LinkedIn specifically.

@DetlevCM And personally I don't think we should have the first part of connections. Personal recommendations by someone that really knows me, cool. All the rest is noise that just redirects energy into making employment "friends" and circumvents neutral job selection processes. If I consider whether I want the market to function like that - then no thanks.

"Extremely unprofessional?" Definitely not! Apparently unwelcome in this instance - seems so. That's OK too. Just move on, and proceed as before.
As context, if you connect with someone on LinkedIn, your own LinkedIn feed starts displaying anything they say, whatever they comment on, etc. This is desired behaviour when your connection is someone you worked with, remember, trust, and want to stay informed about. However, as someone who regularly teaches executive education courses and gets (and used to accept) LinkedIn connection requests from many of those students, it does get tiring -- and overwhelming -- to have your feed flooded with random commentary and reputation-building by all sorts of people who passed through your life briefly for a few weeks a couple of years ago, and left no particular lasting impression. I'm proud of my relationships with my current and on occasion former students, but if that relationship has run its natural course, a connection just becomes LinkedIn noise. All of this to say I'd never be so unprofessional myself to "pull rank" and criticize someone I do know from trying to form a LinkedIn connection, but I empathize with a professor who isn't keen to connect with most of their former students, whatever the reason.
Both in real life and on LinkedIn, it's about genuine connections you do make, not connections you don't make. Doesn't seem like this ex-prof of yours cares to be a real connection, so move on.

I agree with all the views that this is fine.
(Of course it depends on what you do with this connection. Treat it as a professional connection.)
To add to the previous comments:
Our subject has a LinkedIn group which contains at present 301 members. Of course with time this changes - people leave, move on forget about it and the last post is from two years ago.
However when one of our former lecturer retired, this was shared via LinkedIn with us for example.
It keeps a small link back to your old university which may well grow fainter as the staff retire and new students come in.
So, just to re-iterate: Yes, connecting with lecturers is perfectly fine. Of course do not spam connection requests. Treat them as a professional connection, ideally add people you know only. An exception may be people you could reasonably approach - say you are working towards a PhD and want to connect with a researcher, then you could equally consider LinkedIn. However for the latter, I suspect that the vast majority of people would prefer regular email for the initial contact.
(Oh, and maybe (conference) networking events? Again, a LinkedIn connection may be easier to create and exchange.)

TLDR;
Social Media is a new media that is still unnatural and leads to ambiguity. There is a greater disparity, in the perception of the etiquette and usage of various social media platforms, than physical communities. It is best, in such cases, to first be sure of the etiquette that a given person adheres to regarding a given social media. In your case, a simple question you could have asked before connecting with the professor is this: "Is the professor connected to other students on LinkedId?". Having said this, you certainly did not do anything unprofessional.
A Probable Cause for Miscommunication
A probable cause of such confusions comes from one basic dynamic of social networking: "People across different age groups and different communities have a different perception of social media etiquette."
This is very common and leads to many cases of miscommunication in social media (more than in physical communities). For example, we have witnessed a difference in the perception and usage of Facebook across different age groups, and how teens may feel embarrassed about what their parents may be posting on social media and how they are using it. (You may look at Prof. Cristian's work to look at more concrete examples of social media miscommunication).
With this hypothesis at our disposal, it is now understandable that some people may consider LinkedIn as a platform to network with professionals who are colleagues or are equal in position. As mentioned in one of the answers, students would not be considered equal by many people, and they may consider them students in the sense of a high-school student. Having said that, it is certainly not "extremely unprofessional" and this was more of an opinion of the said professor.
A General Heuristic
In such cases, a general heuristic that I use is that I first observe if a given professor connects with students on a given social media platform or not, and how friendly and active he is. On one extreme, I have professors who are highly active on Facebook and connect with students there. On the extreme, there are professors who do not even respond to emails and I have to meet them during their strict office hours.
I consider it presumptuous (it's my personal opinion) to assume that a given professor looks at a media the same way as I do.

I feel one of the better connections on linked are your former professors...maintaining those contacts and relationships can prove beneficial in your professional career.  For example, i know many that have engaged their former academic contacts for intern programs as well as for outsourcing/consulting (both near and far-shoring) opportunities.

This might not be an option everywhere (legal constraints, time constraints, company policies) but otherwise very good points.

Final year Undergrads and Masters students do connect with their Profs after graduating, depending on how well they got to know them (e.g. through Project work, or a 2-semester lecture course). Rather than LinkedIn, try 'Researchgate', where you can (passively) follow any Prof and be one of the first to know about their new Research.


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GRE mathematics subject test
I received a scaled score of 480 and it seems it is not a nice score for GRE mathematics subject test. Should I include it or should I not include it in my application for masters in astrophysics in Germany. I have a very good score in academics and I have done my Bachelors in Mechanical Engineering?  So my question is whether to include it or not?

Do German astrophysics programs require the math GRE? If not, why send it (since the score is poor)?

I can't give an answer as to whether you should include it, but note two things.
First 480 is quite a low score, only the 10th percentile.
But, OTOH, the math test is quite difficult, even for those who major in math as an undergraduate. It is very broad.
The number seems low, however, even for an engineering major who should have studied a fair amount of the things that the GRE test emphasizes (Calculus, broadly speaking, and abstract Algebra).
And standards in Germany are quite high, I think, though I don't know anything about how it works in astrophysics.