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Career and Education Questions: June 02, 2022

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I'm finally almost done my undergrad, thanks covid, and I'm interested in grad school but my GPA is shot. I would like some advice from maths professionals on the best way to apply. I published at a conference in 2016 (an actual conference too, not just an undergrads first conference) and again last year on a research project, but my GPA is about 2.1. Is having published as an undergrad enough to make up for an abysmal GPA or am I just fucked on my dream of getting a masters so I can teach at a small college somewhere?

I know the uni I'm doing my undergrad at has a GPA requirement of 3.0 for masters students, so I'm open to suggestions on institutes in Canada for pursuing a masters if anyone happens to know of a maths department in cryptography or algebraic geometry that doesn't have a GPA requirement.
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I'm almost done with my 4 year PhD in TCS and honestly I don't know what to do next. All of my friends who are doing post doc say that there is just so much stuff unrelated to research (they expected that there are things unrelated to research but not that much). Also I kind of didn't socialize enough (and COVID didn't help) so I feel like I'm not cut out for academia. My research profile is also not very good because I'm really slow in publishing.

At the same time I'm not sure if I should go and find a job in the industry (I have some backgrounds in ML/Computer Vision). But it's really hard to land a research position nowadays, especially if my PhD topic is not about ML/computer vision.

Sorry if this sounds like a non problem but I can't figure out what to do next, and because of that I don't know what I should prepare for (should I grind more papers? Socialize more with other professors? Practicing job interviews? Do an open source github project? Etc.)
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I will be a second year Computer Engineering student next fall. I personally like math a lot, so I will be taking Real Analysis sequence in my school that uses Baby Rudin. Luckily, I have a good amount of friends in the math department that are taking this with me, but I heard rudin is really hard. What should I study over the summer to prepare for it?

Also: Does studying Abstract Algebra help to get better at Linear Algebra (which is arguably more related to my major)? Or vice versa?

Do math majors study probability? What about statistics?
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I'm currently an electrical engineering master's student but for various reasons I've decided to pursue a PhD in math. I've heard that plenty of people with an EE background have gone on for math doctorates at well-respected schools (it's even explicitly mentioned on several programs' webpages), but it's hard to find anything more specific about their background/applications. Mainly I'm asking for some advice on how strong my applications would be and any potential weaknesses. I'm interested in studying analysis, especially in relation to signal processing/machine learning, so areas like harmonic and functional analysis, PDEs, and stochastic stuff. I'm from the US and would be applying to programs there.

A brief summary of my background:

- Double majored in EE and math in undergrad, did very well (~3.9 GPA). At same school for master's, focusing on signal processing/communications
- Taking graduate math courses for master's breadth requirements (1 semester of measure theory/complex analysis each and 2 semesters of algebra)
- Good engineering extracurricular stuff: undergrad research, several summer internships, design team work, but nothing math related
- I've worked as a graduate research/teaching assistant thus far and should be able to continue until I finish my master's

As for recommendation letters, I have both EE and math professors I could get good ones from. Not sure how much a math admissions committee would care, but my thesis advisor (EE prof) is very well-respected and I'll certainly be asking him for a letter. My school isn't really known for its math research though. I know that the reputation/connections of your letter writers can hold a lot of weight, so this is what worries me the most about my application.

Overall, how do I compare against applicants with more traditional backgrounds and experiences? What tier of schools could I aim for? Any advice or insight would be greatly appreciated.
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I love research and I love to teach but if I have to pick I would rather work in a university to teach university level math courses with research on the side.

Is it bad that my goals are to get a Phd in Math but not really aim for a tenured position in any research university? What are the job prospects for someone who simply wants to mainly focus on teaching Math? (In and out of the US since I live out of the US)
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I am currently thinking about the choices I have to make for the next semester.
I want to specialise in geometry or something interesting that has to do with it (here I'm open for suggestions). Till now I have taken Real Analysis, Linear algebra, Probability theory, Abstract algebra, Measure theory, Topology and geometry (and some other applied math courses) and I plan to do Analysis on manifolds and Functional Analysis next semester (algebraic topology is another option which I plan to do a bit later).
But I have no idea if it's the right thing chosing geometry later as main area or it's better to get more into analysis (and PDEs). I don't know the research situation or if there are other combined areas that include more probability theory for example that are more research-active.
I'd be very grateful to any suggestion.
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Failling college. Should I give up on the Math Major?
  


This is truly off my chest.
  

  
I don't know what to do anymore, this is an atypical situation actually. I was studying Engineering in one of the best universities in my country, getting good grades such as As and Bs\*. I decided to change to another university and major in Math, the problem is that the transfer period of this university is fucked up, totally. I ended up missing one month and half out of \~4 months (shorter semester bcuz covid) due to the transfer period and I am failling everything, I am so devasted and lost.
  

  

  

  
4 days after I got to go to my first class in Abstract Algebra I had an exam, that obviously I failed. All the students spent more than one month studying for this exam and I had less than 3 days, basically I asked the teacher if he could give me another exam because I came from another university and I watched only a single class, but he simply didnt give a f\* and told me to go to the exam, I tried to talk to the chairman, but he couldn't solve anything. And worse, the teacher got mad with me after that and took me out points on questions that I got right - I googled the questions to verify when got home and received my grade.
  

  

  

  
That same week, I had more exams, in Physics, Calculus, another math subject and experimental physics. I tried to learn everything from all 5 subjects in 1 week to take the exams and obviously failed. I have severe ADHD, so I can't concentrate at all and my As and Bs are going away. I also have to admit that I don't have a study habit I don't write anything down in my notebook at all and I started to get lost, but I already was.
  

  

  

  
Not only, the average of my class in that calculus exam was 2/10, in my country it is normal that \~80% fail or drop the course (\*so Bs and As are considered pretty rare) and seems I am going to the same path of Fs. I am so so sad, I used to help my peers in math, I LOVED math and I am failling tremendously I dont know what to do, I am so lost due to the transfer, lost due to ADHD (not medicated, but I do have a formal diagnose) and seeing that maybe I have zero future in Math and should just give up, but I dont want to give up. Jesus I am failling everything and I dont know what to do, everyone, including my family, thinks I am doing so well and thinks that I am so happy at this college, but I cry all day and dont know how to get out of this...
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Hi guys. I am starting a 1-year math master's program as a part of a combined BS/MS program and I am thinking about applying to math Ph.D. programs. I know the answer is subjective, but do you guys think I should take the GRE? I really do not want to; I have research experience in REUs and also in a senior thesis and eventually in a Master's thesis.
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Econometrics, operational research, data science, financial math, and financial engineering, which one of these areas will be suitable for someone who loves math and economics. They are kind of the same for me. This is for a master's degree
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In my junior year of high school, I dual enrolled for Calc 1 and Calc 2. I earned a C in the former and withdrew from the latter due to the fact that I could not balance it with the rest of my high school courseload. I'm entirely certain that math is for me; that year was just too packed with other classes and extracurriculars.  
I plan to apply for Applied Math PhD programs at Princeton and MIT, and I know that their applicants will have stellar grades, many of which who will have A's all across the board. I fear that I may never be able to compensate enough to avoid being filtered out by the AdCom. Doing bad on two of the core classes is an extremely bad sign and given the fact that I don't already go to an extremely prestigious institution narrows my chances even more.  
As I'm officially entering undergrad, I intend to compensate for this by acing all my classes and taking as many graduate courses as possible. But most importantly, my focus will be on producing quality publications, because I know that my ability to do research is most valued at these programs.  
Given these two bad grades, is it unrealistic to think that I have a chance at these programs, or would it still be possible provided that I ace the rest of my classes and produce stellar publications with good LoR's?  
TLDR:  
C and W on Calc 1 and Calc 2 (Dual enrollment from junior year of HS); attending a T30 state school with a low math ranking. Do I have a chance for PhD admit at Princeton/MIT?

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