TakeruK

In addition to what was said above, sometimes people say things like "the job market is good/bad this year" and have nothing substantial to actually back it up! There's a lot of confirmation bias, and sometimes if you actually count the opportunities posted, it might surprise you compared to what you hear. Also, the number of openings doesn't tell the full story: what if there are more applicants now too? I would say you want to listen/pay more attention to specific observations instead of people's guesses/estimates of the goodness/badness of market (not that the gut feeling isn't useful, but be wary of the limitations). For example, in my field, things that might matter: 1. How much funding Congress has allocated for NASA and Planetary Science. 2. Whether or not big missions are reaching important milestones where a ton of data is about to come up (e.g. In summer 2015, the New Horizons mission reached Pluto, and so a lot of postdocs were hired in 2014 to provide support for this mission). Similarly, when a big mission ends, it means a lot of people are going to be looking for new positions! 3. Faculty shuffle. In the past 12 months, my field saw a large number of faculty members, especially at top schools, switch around, but the schools that lost professors did not always gain the same number. For those postdocs applying to faculty jobs, they would be on the lookout for new faculty position postings! 4. Prize fellowships in my field generally announce the number of fellowships they expect to award when they make the solicitation. Comparing this number to trends from previous years can give an indication of overall funding level and interest in the field. One of the big postdoc fellowships in my field is only offering half as many awards as a typical year this year!

Maybe more details would be necessary? In North America, a post-doctoral fellowship is a position that pays for research work done by someone with a PhD (hence "post-doctorate"). So, it sounds a little odd to have this offered to you when you are not even in a PhD program yet. Most postdoctoral fellowships require you to have completed your PhD before you can start, but they may be offered to a graduate student who is about to finish. If this offer is coming from a Canadian school or a UK school and the wording is actually "post-graduate" instead of "post-doctoral", then I think it is a fellowship/award for graduate studies. In Canada and the UK, "postgraduate" means Masters and PhD students (post-graduate means past your graduation from your Bachelors degree).

Usually not. You can look at ratemyprof, but I wouldn't hold much weight to the reviews there and they mostly review undergraduate courses. Many schools do publish student-written reviews of their own courses, but that's something that you can only access if you are already a student. However, this information is not really relevant at this point (I'm assuming you are in the application process?). There's no need to review courses prior to applying to a graduate school. If you want to see what courses are offered at each school, look up the catalog or the department website. But be warned: many graduate classes only happen every once in awhile (e.g. a course might be listed but it may only happen every 2 years or even only once every 5 years). So don't count on any classes happening unless it's a required class. Even so, I want to reiterate the point that you don't really want to be using this as a criteria on choosing which schools to apply to.

3 days is not very long at all. Wait about 1-2 weeks have passed. Then email again and this time say that you will be in town on X dates and offer to drop by office hours to discuss it further.

The test went okay. I scored at the 50th percentile on the Physics GRE. I'm not good at standardized tests (my earlier attempt was 44th percentile). I still got into my top choice schools though. I don't remember how long it took for the paper ticket. There is a number you should probably call to ensure you have the right information. I registered for the test in June 2011 and I found that confirmation email. My test was in November 2011. This is what it says about the admission ticket: Admission Ticket------------------------------------------ A paper admission ticket will be mailed to you in approximately 3 weeks. If you do not receive your paper ticket at least 10 days before the test date, you can view and print your admission ticket online at www.ets.org/mygre or call GRE Services at 1-609-771-7670 or 1-866-473-4373. So I must have gotten the paper ticket sometime in July or August? Have you checked online yet? If it's not there either, maybe call them (check to make sure these numbers from 5 years ago are still valid!)

I very much doubt that there is any benefit in getting a large number of people to apply. However, it is very very rare for someone to say "Don't apply to my school". You would have to know the person well enough to know if it's something they are saying because they personally really want you there, or they are saying it because they don't know your full profile so they want to see it (i.e. you need to apply) before they can make a decision. However, it's unlikely you would know someone well enough to judge this when you are applying. So, don't get caught up in these mind games and what-ifs. If the program interests you, then you should apply.

I wrote the GRE at McMaster too! But that was back in 2011. In 2011, they mailed everyone a paper admission ticket. When you registered, did they say this to you too? The paper admission ticket told me which room/building it was in. I had to travel from Kingston, which sucked since that meant I had to go to Hamilton the night before and stay in a hotel. Two things to keep in mind: 1. All the subject tests take place in the same room at the same time. You said English Lit GRE here, but all the subjects will be the same place (unless something drastically changed) so if you see other GRE test takers on campus looking for the room, you might be heading towards the same place. 2. The room was changed at the last minute. I arrived extra early (7am, for 8am test) and at first I couldn't get into the building of the test room since it was a Saturday morning and everything was locked. But when they did open the door, there was a sign (inside the building only) that the room has changed!! And it just gave a building name and room number, with zero information on how to get there. I didn't have a smartphone so I had to find a campus map and figure it out. Made it with a few minutes to spare. So watch out for that! (Luckily, it turns out that the test takes forever to start---we didn't start until 8:45am. So also basically plan to spend 8am-noon with the test).

My student met, in person with the professor & me, only about 6 times during the whole summer. It's more than your contact but not that much more. I also had a previous experience where I worked in a biophysics lab for 8 months (full time, 40 hours per week) and the PI was on sabbatical in Germany the entire time. I worked with the lab manager every day. The PI only visited in-person for 3 days during a mini conference. There were group meetings every 2 weeks where it was 10 people in a room and the PI on Skype. I only spoke maybe 2 or 3 sentences each time (the lab manager generally reported my progress to the PI). There were also a few situations where I emailed the PI (copying the lab manager) about a few questions. I still got a letter from the PI, which is almost certainly written by the lab manager (arranging for a letter was part of the exit process of this lab). For your specific situation, sure, maybe your other choice could be a lot better. I would recommend discussing this faculty in your department. Maybe start with your current PI and see what they think. Then, you could discuss it with your former PI or the other letter choice and see what they think too. You don't know what kind of notes your former PI may have on file already for you.

Indeed, the airline rewards only work well if you are willing to stick to one airline and actually have reason to use the tickets. My calculation is that I spend about $25,000 per year on my credit card, which, including the spending points bonus, corresponds to about 35,000 bonus airline points in purchases. I would guess that about $2,000 is spent on United flights (for work travel) so that's another bonus 2,000 points. What's 37,000 points worth to me? It's about 1.5 round trip tickets within North America, which I value at around $500 per round-trip ticket, so that's $750. If I were to use a cashback card, assuming a 1.5% cash back rate, then $25,000 is $375. Even at 2%, it's $500. However, this is $500 that I get right away, no matter what. I only realise the benefit of my airline points if I actually use it to get a flight that I normally would have to pay for. If I redeemed my airline points for gift cards, 37,000 points is about $370 value, not as good as cashback. Also, even if I gain 37,000 points in one year, I only have enough to redeem one single ticket. Airline rewards forces you to redeem at set intervals, which may not be as good for you. (Some cashback cards require you to redeem $50 at a time, but that's still much more frequent than a $500 flight). If I am only looking at the points benefits, after considering the $95 fee, the airline rewards are just marginally better than cashback and if I didn't use some of the other benefits, I would have just used the United card for the first year, collect the 50,000 points (which we used towards a dream vacation in Australia) and then cancelled. But I like the other benefits enough to justify paying for it, at least for now. In particular, I am traveling a lot this year and next year for job applications, so I appreciate the little extra perks. Another strategy that others use is to just rotate through the various airline cards. You can sign up for the United card, collect the bonus, cancel after a year, then sign up for AA card for a year, collect the bonus, cancel etc. If you want to do this, you need 3 different cards because in order to qualify for the bonus, you need to not have the card for at least 2 years. However, all of these opening and closing of credit cards can be bad for your credit score---not likely to be worth a couple of free flights each year in the long run. One way to mitigate this is to ask the bank that issues these rewards card to transfer your line of credit to a free card and then just not use it. You still get dinged for opening new credit, but at least you don't have a series of very short credit histories.

There's no single answer for this because it will just depend on who you are living with. Normally, many of the things you ask here are discussed with potential roommates before moving in. In an ideal situation, if you are moving into an apartment with people already living there, the current residents will probably want to meet with you and chat to see if 1) you get along and 2) you share similar ideas on things like privacy, food, etc. This is a common way people find roommates. Another way is to find the person you want to be roommates with first (e.g. other students in your program), meet them, determine that you will get along and then look for a place together. So, what I'm saying is that these things should be sorted out before anyone signs any lease or other binding agreement! For food, a common arrangement is that you only eat your own food, unless a person has indicated something is up for grabs (e.g. maybe they have a made a lot of it and it would go bad otherwise). Typically the refrigerator and pantry would be divided up into areas that are for sharing and areas that are for personal use. Some roommates will go grocery shopping together (and split the bill) so staples like eggs and milk are shared, while other roommates prefer to do everything on their own. In almost all circumstances, it would be incredibly rude for a roommate to go into their roommate's bedroom without permission. Even so, it's important to have discussions like I mentioned above when considering moving into a place with roommates. Depending on the apartment, you may not be able to actually lock your bedroom door from both the outside and inside. So, this is why I think it's really important to meet your potential roommates and see if you trust them / feel comfortable with them. For your last Q, there are other things you should keep in mind when selecting roommates. One big category is the etiquette/agreement on having guests visit (both having friends come hang out and having someone spend the night). Some roommates may have rules on whether or not it's allowed, how often it should happen, whether it's limited to certain days or certain times, and whether both roommates need to agree to it (e.g. if you want to have a party etc.) Other categories of things to be discussed are things like whether pets are allowed, how to divide up the chores/cleaning of common spaces, whether there's quiet hours for the apartment/house, what kind of utilities/services you want (e.g. TV? Internet? phone?) as these costs are generally shared by everyone etc. And finally, I would say that you shouldn't let others take advantage of you, but it's important to be patient and flexible where reasonable. Living with other people is an adjustment and there will probably be times where your limits will be tested. You may have to make full use of your conflict resolution skills. One thing to keep in mind that sometimes it makes more sense to give the other person the benefit of the doubt at first, and then escalate if necessary since it's easier to escalate than to de-escalate.

I also recommend reverse-chronological order (actually, this is the only ordering I've ever seen in a CV but maybe other fields do it different ways?). If you don't want to write about your past though, reverse chronological order also allows you to start at the present and only go back until you stop having experiences you want to talk about. Note that most schools will require you to write all the schools you've attended (or received a degree from) in the application form, however, I think it's okay to leave it out of the CV if you think it's irrelevant and don't want to discuss it. (I'm not saying that the non-traditional background is good or bad, I'm just providing another option).

Yes, whenever I am away from a project for some time, it takes awhile to get back into the swing of things. I think this is normal. That is, you are not lacking in intelligence or ability because you aren't able to jump right back into your work at full speed after a few days off. Typically, when I come back from the weekend, Monday morning is a little slower for me. But knowing how you tick helps you set helpful schedules for yourself. For example, because I take time to "get back into the work", I don't try to get into heavy duty coding on Monday mornings. I tend to just make more mistakes that way. So, Monday mornings are good times for me to write emails or prepare materials for my TA work. Or sometimes I have to do lower level thinking work (think "look at data and classify it") so I schedule that for the mornings. Also, I often work on multiple projects simultaneously. To avoid the startup lag, I try to work on the same project for at least 2 or 3 days at a time before switching. Usually, given my other non-research commitments, this means I only work on one project per week.

I don't think it will be a red flag because as you said, it's been more than 2 years since you worked with this PI. However, if you are asking us to weigh the merits of one letter vs. another, my default answer would be that the PI from 2 years ago is probably still going to be a better letter than the professor you worked with in two of your courses. If you want further advice on this, perhaps you could indicate why you think the course-professor might write a better LOR than your previous PI? (But you don't have to if you don't want to). Also, regarding the hands-off nature of the PI---this is normal. Was there someone else that you worked with closely instead of the PI, such as a grad student, postdoc, staff scientist, lab manager etc? If so, perhaps this person could work with the PI to write the letter (and the PI would sign it). When I supervised an undergrad student, I worked with them almost every day and the student only met with the professor once every 2 weeks. However, at the end of the summer, I wrote a summary of everything that happened and a list of accomplishments/strong points that the professor uses to write LORs for the student. So, especially in labs/groups with hands-off PIs, the letter might be written or partially written by someone else and signed/submitted by the PI. Therefore, I would not worry about the hands-off part of the PI, unless there is no one that can help the PI with the content of the letter.

My graduate student friends with cats generally have friends or hire a cat sitter to look after their cats when they are traveling. I think roommates actually help with this, as long as your roommates are okay with pets too and you have a good relationship with them. Most of my friends tell me how great it is when their roommates have pets because they generally get all of the benefits of having a pet around in the house, but none of the responsibilities and vet bills. So, many of them are often willing to cat-sit for a week etc. My friends with cats usually use a cat sitter + friends combination. The cat sitter is paid to do the necessary stuff like feeding and cleaning the litter box while friends come to spend time playing with the cats. This way, friends get to do the "fun" stuff and no one feels like they are creating a burden for their friends and/or feel like they are obligated to do extra work because of their friends. Another way is to take your cat to a pet hotel for the week, but that can be pretty pricey. As for housing, generally finding cat-friendly housing could be more expensive. At my school, all the grad student subsidized housing (owned by the school) have strict no pets rules for allergen reasons. So, few students have pets because it means renting from the private market and costs are about 30% higher than the subsidized housing. However, we live in a very high cost of living area, so I think in general, most apartments and other rentals will be okay with cats as long as you are willing to have a higher security deposit.

I only got this card about 2 years ago, but I love my United Chase Explorer card. The first year is free and there is a $95 annual fee afterwards. I originally was only going to get it for one year, but I decided that I will pay $95 each year for the benefits, especially the car rental loss/damage waiver benefits (see below). The reasons I love this card for academic travel: 1. You gain 50,000 bonus points if you spend $3000 (or was it $2500?) in the first 3 months. This is very easy to meet if you put all purchases on this card---I spend about $2000 per month on the card (the only thing I don't pay with the card is rent). If you just directly sign up for the card, the bonus offer is only 30,000 points. In order to get the 50,000 offer, you should sign up for the United Mileage Plus account first, and then within a week, you'll get an offer in the mail for the 50,000 points bonus. 50,000 points gives you two round-trip tickets anywhere in North America. 2. You accrue points very fast (1 point per dollar spent, 2 points per dollar spent with United). 3. You get two free checked bags for you and a companion if you book with the card. 4. You get priority boarding for tickets purchased with the card (Boarding Group 2 out of 5). 5. You get two passes per year for the United lounge. 6. No foreign transaction fees! Great for conferences, because I don't have to add these numbers into my reimbursement requests. 7. Car rental loss/damage waiver benefits. The card covers the loss/damage waiver for car rentals, which saves me about $10-$15 per day. Coverage is also primary, so the card's coverage applies first and your own insurance won't be dinged. This was super helpful for me because I got a flat tire with a car rental and the company charged me $400 including a $80 processing fee for the damage. The card covered all of the costs, even the processing fee. 8. There are lots of other benefits I haven't had to use yet, like purchase protection and lost baggage (with any carrier). One downside is that the interest rate isn't the best, but I always pay the balance each month so it's not a big deal for me. I really like the above benefits because it makes traveling a lot more convenient. I live in a United hub city so it's always easy for me to get a United flight. Yeah, United isn't the best airline, but the benefits and points gives free flights! It also works well for me because my school reimburses me for my flights for work and then I use the points for my partner and I to take vacations etc (or if the conference is in a cool place, we use points for my partner to come with me after the work is over). Note: I'm sure the other airline cards are also pretty good, but I like United because its membership in Star Alliance means I can also use points for Air Canada and trips home (I'm Canadian).

I agree with you that in an ideal world, the anonymous student and the TA can have a conversation and sort things out. Maybe the student had good intentions but very bad delivery and therefore just needs someone to guide them the right way. But, maybe the student really is just a bully and/or a troll. In my opinion, this is a situation where the TA has a lot more to lose than to gain. No one (not my professor, not my students, not my colleagues) should expect a TA to open themselves up to further bullying because there might be a teaching moment there. I do admire and see the appeal in trying our very best to reach out to every student. However, because certain demographics receive more bullying than others, I believe that the attitude that TAs should suffer these offenses in order to teach our students results in unfair distribution of this extra teaching load. Groups that are more often on the receiving end of these types of emails are going to disproportionately spend more of their time teaching/mentoring in this way. So, I think advice like the one you are giving is harmful to academia, because it increases the disparity between the majority and the minority groups.

I also want to emphasize a couple of things about these two points that are related to @Bumblebea's response. First, you mention twice, in both points, the partial accuracy of the student's comment/observation. However, whether or not the student's comment was accurate is not relevant to either of your points. That is, whether or not the email was out of line has no relevance on the accuracy of its contents. Whether or not the OP was performing their TA duties has nothing to do with whether or not the student is accurate. I think in academia, sometimes, people tend to value the content of the message over the way it is delivered. Delivery matters and being accurate/correct doesn't make up for the fact that someone was rude. It is 100% inappropriate for a student to call out any TA like this. Period. I wrote my first response without knowing that the student's email was anonymous, but with this information, the only action I would recommend is to ignore the email and not give in. That is, I would not change my behaviour at all. Carry on as if it never happened. The most likely interpretation of the intent of this unsolicited anonymous "feedback" is to bully the TA and make them feel like they do not belong here. Unsolicited advice disguised as "feedback" is a type of micro-aggression and does not belong in our workplace.

To balance out this advice, I'd like to present a more idealistic view: many students cannot afford to buy their own copies of the essential literature and some professors recognize this. I know that whenever my advisor suggests that a student (especially an undergraduate student working on research with us) references a certain key book, my advisor always offers to lend their own copy, or in some cases, even buy a copy for the student to borrow. I have noticed that on many occasions now that my advisor is deliberate in making this offer immediately after suggesting the book, before the student feels the need to ask for help in obtaining a copy. I think it's important for academics, especially those in positions of power, to remember that not everyone comes from a background where they are able to buy their own textbooks and have a healthy library. So, those who recognize this will try to avoid giving advice or making passing remarks that could come off as "If you don't have your own version of this book, you're not a real scientist/historian/sociologist etc.". I want to also emphasize that I am not disagreeing with Sigaba here, and I'm also not trying to undermine your advice!! I know we do not exist in an ideal world and Sigaba is right that the "critical glance" is something we should be wary of and Sigaba is spot on that it's really important to frame your request appropriately. The only reason I put my response here is to provide an additional viewpoint since I would advocate that academia in general moves away from the ivory tower and become more open and understanding of the diverse backgrounds of all researchers. That is, I acknowledge the reality that academia is not like this, but I want to also nurture the hope that we can do something to make a difference in the future.

Is your school in Ontario? If so, have you added the OGS (Ontario Graduate Scholarship) to your list? In general, for the US and Canada, the number of fellowships that everyone would be eligible for are small. It's just a half-dozen or so major fellowships. By "major" fellowships, I mean things that will fund most or all of your stipend (i.e. awards at the $15,000 level or higher). So, there isn't a need for a directory for these. There are a larger number of small fellowships though, that fund at the few thousand dollar level. Usually these are very specific---only for certain topics, fields, or work at specific sites or requiring an affiliation with a specific institution or organization. Because the number of people that are eligible for each fellowship would be pretty small, there isn't a directory (as far as I know) because the majority of the directory would not be useful. Instead, from my experience in both Canada and the US, the best source of fellowship information is from your own department. Organizations that wish to fund students generally email the admin staff for each department and then the department forwards them to their students. You'll likely see more chances and opportunities once you begin your program. In addition, the national organization for your field of study often compiles relevant fellowships and also emails them to their members. I would recommend joining your field's national society in Canada (and also the US if you want to maintain ties there). Finally, one other source of funding that you might want to know about is Mitacs (https://www.mitacs.ca). In particular, they have an "Accelerate" program for graduate students. You can read more about it here: https://www.mitacs.ca/en/programs/accelerate. Mitacs is not a field-specific organization. Instead of funding for a specific field, their priority is to foster connections between research and industry. I don't know what you will be studying/working on so I don't know if this is relevant for you. But take a look at their Accelerate program and see if it's a good fit

I didn't realise the mathematical sciences had very little research in undergrad (I guess my undergrad school was a little different, or maybe my friends in the math department had different subfields). I still think it would be a good idea to develop a deeper relationship with your topology professor. Especially if you want the letter to show that you haven't reached your mathematical ceiling**, your conversations with him now can show that you are still actively thinking about mathematics and that you know the relevant literature etc. I think a letter from your German advisor is better than the German department head, however, I would be hesitant to put it as a 4th letter. I understand the appeal of putting everything about yourself in your application, but I caution against this approach in academia in general, especially for other applications later on in your career. As I wrote above, the more information you provide, the less each piece of information will be weighted, so it's better to say less and focus on the aspects that the committee will care about instead of just giving them every piece of information about yourself, regardless of relevance. The evaluators will read your application for just a tiny fraction of the time you put into preparing these applications. Again, I am not saying you should avoid discussing your German studies---this is a great thing to discuss in your SOP and it will show that you can think and excel in other fields/modes of analysis, but I wouldn't add it as a 4th letter. ** With regards to the concept of the mathematical ceiling: I wonder if this is a concept shared by all mathematicians, or just the ones you have interacted with? I know that in academia, there is the "growth mindset" and the "fixed intelligence" mindset, and the whole idea of there existing a mathematical ceiling sounds very much like a "fixed intelligence" mindset. My impression of academia is that more and more people are moving towards the growth mindset model. I am obviously an outsider to your field, and maybe this doesn't apply here. But I wanted to point this out because as students (both undergraduate and graduate), we are just beginning to interact with the academics in our field and I have made the mistake before of assuming that an idea is common because everyone I talked to preferred that one.

I agree with @avflinsch. For many programs, they are not going to admit someone just because they cost less. Even if part of your stipend is covered by your funding source, it will cost just as much time and energy to train you as a grad student with no external funds. I don't think the Statement of Purpose is the right place to put this information. I don't know if you have started the online application forms yet, but almost all of them will ask if you have applied for any awards and if you know any of the results. Many students in the US will be applying for things like the NSF GRFP (national level graduate student fellowship) and many other external awards from the US government. In this area, you should put your awarded that has already been confirmed and also mention the awards you are applying to. If this is not one of the questions in the online form, then usually the last question is "Do you have anything else you want to tell us?" or "Special considerations" etc. This would be another good place to put the information.

Ah okay, I misunderstood your post. I thought you were making a more general statement about not commending people for just doing their job. But I see that you mean that you know this specific person wouldn't appreciate that action. Sorry for the confusion.

This is an interesting perspective. I always ensure I thank everyone even for normal behaviour. e.g. When I ask the admin staff to process a reimbursement for me, although it's part of their job, I always thank them for it. I thank the bus driver when I get off the bus, even though it's part of their job. To me, I don't see a problem with recognizing people and commending them for doing what they are supposed to be doing. I know that when I get a thank-you for doing my job, it feels nice that my work is being acknowledged. And, maybe openly recognizing and commending/rewarding good behaviour (even if it's expected of you) is probably the best way to encourage certain actions in academia, since we're not in a setting where disciplinary measures are taken to ensure good behaviour.

The point of reference letters is not to demonstrate that you have high level understanding of the material. There are many other ways that the admissions committee will get this information, such as your transcripts. Getting a letter from someone that taught you a course isn't very helpful. So, on the flip side, if you didn't do amazing in it (A- is still a good grade), it won't hurt you either. Ideally, you want professors who can write you letters attesting to your ability to do good work as a researcher in graduate school. The best letter writers are those who have supervised your research in the past. I am assuming you might already have this lined up for your first two letters, and you don't have a third supervisor so that's why you are seeking a third letter? If so, then my advice is to get in touch with the grad level topology professor from last fall. Do more than just ask for a letter---also reconnect and renew your previous relationship with him. A good way to do this is to let him know that you are applying to grad schools and that you would like to pick his brain for his thoughts and then also ask him to write you a letter. Do this fairly soon since deadlines are only 2 months away. You will get a much better letter from him if he knows more about your motivations and your grad school plans. Through discussions with him, he will gain insight into you as a new researcher and this information can be conveyed into his letter. This will make it a good letter, instead of a bland "this student did well in my class and understands the material", which isn't a very useful letter. The other advantage is that you took a graduate level course from this professor so he can discuss your preparedness for graduate work more directly. I would advise against asking for a letter from the head of your German department. If you did do research in German then maybe your research advisor would write a good letter. If it's a letter about your research ability, then the actual field of research doesn't matter (although the closer it is to your planned PhD field, the better). I agree with @avflinsch that having diversity and breadth is very good and very important, but the LORs is not the right place to show that. The committee will be impressed by your breadth through transcripts and probably a notation on your degree that indicates you have studied German. And you would presumably write about your experience in Germany in your SOP as well. I would also caution against getting a 4th letter of reference. In many programs where they specifically ask for three, they only want to see three. Even if there is an option to upload a 4th letter, I would advise against it because your 4th letter from the German department isn't going to be as strong as the other three letters. The admissions committee is going to only want to read three letters, and sometimes, when students submit more than 3, they might just read the first three in the pile. In addition, they are going to form an opinion about your application's LORs after reading all 3 (or 4) letters and coming to some impression. This impression will be averaged out over all the letters, so you would be better off if they read 3 strong letters than if they read 3 strong letters plus 1 okay one.

I agree with the above advice. I know several people who accidentally lowballed themselves and ended up with a salary that was much lower than they should be earning. Since annual merit/cost of living raises are going to be some percentage of your income, having a lowballed salary can add up to significant losses over time, as rising star said. Also, if you move on to different positions, your current salary factors into how much you'll be offered at a new place. Fortunately for the people I know, after a year of work, they were able to renegotiate their salaries and got big raises that year (ranges from 25% to 40%) so that they are now back on track with expected earnings. They still missed out one year of salary though! I'm not saying that this is the right way to go about it, just saying that if you did happen to lowball yourself, it's not always irreversible. So, I second the advice to get data, especially from any contacts you might have in the field (maybe those working at different companies). The other way to think about answering this question is what is the most you could be qualified to earn? It's unlikely that any offer you might get would be higher than whatever you put here. So, instead of putting the lowest amount you're willing to take, put the highest amount that you could be reasonably offered. Finally, just as a starting point, the data I've seen for PhDs in your field moving onto industry jobs after graduation suggests that starting salaries are in the $100,000/year ballpark. I think someone with a PhD and 5 years of experience would earn much more than that. I agree with all the advice to check the data, but I think you might be severely undervaluing yourself if you were going to put down $50,000.