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1. I want to work in industry in research departments and deep tech products. For most positions, having deep knowledge will not be enough and PhD grade is expe

1. I want to work in industry in research departments and deep tech products. For most positions, having deep knowledge will not be enough and PhD grade is expected: to pass the filter. 2. I want to explore some topics in depth, contribute, and get regular feedback, mentorship - basically, have an advisor. I do not want to stay in university, fight for places there, I do not need grants - I want accredited expertise that can open some doors. It seems like there are quite a lot of people in similar situations, and despite all the progress in online education, increasing academic requirements from many employees, requirements for life long learning our advanced education system cannot support different paths to accredited degrees and research.

ska 7y ago
Something you are missing in (2) is the collaboration & work with peers, as well as baseline coursework (although that varies from country to country and program to program), and some of the other communication parts. A handwavy version of the scope would be 1) core coursework, which makes sure everyone has the same basic competence across a range of topics deemed important 2) comprehensive exams (but vary wildly by program) - the intent here is to set a bar everyone must pass to demonstrate the competence in (1) 3) seminars/journal review groups, etc.: group activities typically which are far less formally structure than (1), but allow students to be pushed technically by a prof and each other, and expand their understanding of current work 4) semi-formal presentations (usually within your group) and more formal presentations (e.g. conferences) - you have to learn how to communicate effectively with your peers and demonstrate it 5) Advisor: one person to guide and mentor you over the course of your study, and help tailor focus and remedial study as needed. Should help you refine your thesis topics etc. 6) Committee members: A group with broader experience than just your advisor, who will periodically review your research plan and progress. May be involved in setting your comprehensives. Will definitely review your thesis and will manage your defense. 7) external examiner : this is a check-and-balance thing, so a department doesn't drink their own cool aid too much. Should be an arms length expert in your field, who will review your thesis and can spike the whole defense if it isn't up to snuff. So things that list are difficult to reproduce in your requested scenario: a) ongoing collaborative work with peers through baseline courses and paper reviews, editing each others stuff, etc. b) non-formal interactions with committee members although if you can commit to regular campus visits you can probably do that. If I were in a position to consider supervising a "remote Ph.D." student like you suggest, I'd be concerned mostly on how to get them really ready for comps, and how to get them the kind of interaction and face time in a group to achieve demonstrate competence outside of a formal exam. The actual thesis part would be more manageable. I'm not saying it couldn't be done. In fact it's not uncommon for someone to go "remote" once they have finished their comprehensives; in some fields this is known as ABD (all but dissertation). At this point you've put about 2 years in and mostly focusing on your own research. It's worth nothing that leaving at this point is also a very common way that people just never finish. It sounds a bit like you envision doing this ABD part, really, but as noted above that's only half of a PhD program, or less than half. Basically the thesis part is a way to hand hold you through the process of writing up independent research and demonstration you can do it properly and on your own. In recent years their has been a move in some disciplines towards paper-based thesis, actually, which I think is weaker but is a response to the demand for publication numbers.
- playing_colours 7y ago
  Thank you for a very detailed answer! In Germany, where I live, PhD process is different from USA [1]. After getting Master, one can apply for PhD that will be thesis / research part only, without mandatory coursework. [1] https://www.daad.de/en/study-and-research-in-germany/phd-studies-and-research/phd-studies-in-germany/ways-to-your-phd/ https://www.daad.de/en/study-and-research-in-germany/phd-stu...
  - ska 7y ago
    Yes, expectations vary quite a bit country to country. I should have mentioned that! In the USA you may be given a masters as a sort of consolation prize if you leave a PhD early, but rarely are required to have one to enter a PhD. In Canada you often have to do both, at full length. Cambridge is more like your system, but instead of a masters there is a sort of in-between course year. Etc, etc.
justincredible 7y ago
If you only want a PhD to get through job filters, you should be networking with people who work in those fields.
stared 7y ago
1. If you goal is to work in industry, don't do pure mathematics PhD. What works, and is doable in 20-30h/week is doing an applied PhD in an area related to your work. I know quite a few people who did it with great success. (Quite a few friends, and some accomplished people like https://ruder.io/. https://ruder.io/.) Also, as a person with PhD - spending 4-7 years in an irrelevant field is going to seriously hurt your industry career. (I speak as someone with PhD.) Yes, PhD is worth something - but it won't come in the place of experience. 2. For the second, you need time. On their side, even if they don't need to provide funding, they invest their time. Talk to people at a local department. You may impress them enough that they are going to work with you unofficially - but the bar may be high. For later - what is the exact area you are most interested in?
- playing_colours 7y ago
  Thank you for your answer and advice! In pure mathematics - I found most interesting topics around algebraic topology. Next year, I plan to look into homology. These fields also have computational aspect and some applicability outside of pure maths: computational homology and Topological Data Analysis. This autumn, I finally looked a bit into category theory (applied) using this good book: https://www.amazon.com/Invitation-Applied-Category-Theory-Compositionality/dp/1108711820 https://www.amazon.com/Invitation-Applied-Category-Theory-Co..., and, unsurprisingly, found it exciting. Regarding PhD in an applied area: I tend to agree with you, and also keep thinking about focusing more on computational / applied mathematics so that my studies could be somehow related to my work. My tech focus at work is around data processing: with interest in distributed databases and computations. Heh, I see that distributed systems, algebra, topology, and categories are similar in mental representation in my head, they cause same kind of excitement when I study them: visualising, analysing, and playing with the systems of structures, connections, defined rules and operations :)
DreamScatter 7y ago
Yes, I am in the same situation, I research graduate level mathematics outside academia. Right now, I am collaborating with top scientists from around the world by staying connected online via a website called https://bivector.net https://bivector.net and am publishing my own research at https://grassmann.crucialflow.com https://grassmann.crucialflow.com As it turns out, I don't have an undergrad degree either, so it is tough for me to find jobs, but I find plenty of interaction!
- playing_colours 7y ago
  I would be interested to learn more about how you approach your studies and research. I see Julia is your weapon of choice and you are active in contributing!

ska 7y ago

Something you are missing in (2) is the collaboration & work with peers, as well as baseline coursework (although that varies from country to country and program to program), and some of the other communication parts. A handwavy version of the scope would be 1) core coursework, which makes sure everyone has the same basic competence across a range of topics deemed important 2) comprehensive exams (but vary wildly by program) - the intent here is to set a bar everyone must pass to demonstrate the competence in (1) 3) seminars/journal review groups, etc.: group activities typically which are far less formally structure than (1), but allow students to be pushed technically by a prof and each other, and expand their understanding of current work 4) semi-formal presentations (usually within your group) and more formal presentations (e.g. conferences) - you have to learn how to communicate effectively with your peers and demonstrate it 5) Advisor: one person to guide and mentor you over the course of your study, and help tailor focus and remedial study as needed. Should help you refine your thesis topics etc. 6) Committee members: A group with broader experience than just your advisor, who will periodically review your research plan and progress. May be involved in setting your comprehensives. Will definitely review your thesis and will manage your defense. 7) external examiner : this is a check-and-balance thing, so a department doesn't drink their own cool aid too much. Should be an arms length expert in your field, who will review your thesis and can spike the whole defense if it isn't up to snuff. So things that list are difficult to reproduce in your requested scenario: a) ongoing collaborative work with peers through baseline courses and paper reviews, editing each others stuff, etc. b) non-formal interactions with committee members although if you can commit to regular campus visits you can probably do that. If I were in a position to consider supervising a "remote Ph.D." student like you suggest, I'd be concerned mostly on how to get them really ready for comps, and how to get them the kind of interaction and face time in a group to achieve demonstrate competence outside of a formal exam. The actual thesis part would be more manageable. I'm not saying it couldn't be done. In fact it's not uncommon for someone to go "remote" once they have finished their comprehensives; in some fields this is known as ABD (all but dissertation). At this point you've put about 2 years in and mostly focusing on your own research. It's worth nothing that leaving at this point is also a very common way that people just never finish. It sounds a bit like you envision doing this ABD part, really, but as noted above that's only half of a PhD program, or less than half. Basically the thesis part is a way to hand hold you through the process of writing up independent research and demonstration you can do it properly and on your own. In recent years their has been a move in some disciplines towards paper-based thesis, actually, which I think is weaker but is a response to the demand for publication numbers.

playing_colours 7y ago
Thank you for a very detailed answer! In Germany, where I live, PhD process is different from USA [1]. After getting Master, one can apply for PhD that will be thesis / research part only, without mandatory coursework. [1] https://www.daad.de/en/study-and-research-in-germany/phd-studies-and-research/phd-studies-in-germany/ways-to-your-phd/ https://www.daad.de/en/study-and-research-in-germany/phd-stu...
- ska 7y ago
  Yes, expectations vary quite a bit country to country. I should have mentioned that! In the USA you may be given a masters as a sort of consolation prize if you leave a PhD early, but rarely are required to have one to enter a PhD. In Canada you often have to do both, at full length. Cambridge is more like your system, but instead of a masters there is a sort of in-between course year. Etc, etc.

justincredible 7y ago

If you only want a PhD to get through job filters, you should be networking with people who work in those fields.

stared 7y ago

1. If you goal is to work in industry, don't do pure mathematics PhD. What works, and is doable in 20-30h/week is doing an applied PhD in an area related to your work. I know quite a few people who did it with great success. (Quite a few friends, and some accomplished people like https://ruder.io/. https://ruder.io/.) Also, as a person with PhD - spending 4-7 years in an irrelevant field is going to seriously hurt your industry career. (I speak as someone with PhD.) Yes, PhD is worth something - but it won't come in the place of experience. 2. For the second, you need time. On their side, even if they don't need to provide funding, they invest their time. Talk to people at a local department. You may impress them enough that they are going to work with you unofficially - but the bar may be high. For later - what is the exact area you are most interested in?

playing_colours 7y ago
Thank you for your answer and advice! In pure mathematics - I found most interesting topics around algebraic topology. Next year, I plan to look into homology. These fields also have computational aspect and some applicability outside of pure maths: computational homology and Topological Data Analysis. This autumn, I finally looked a bit into category theory (applied) using this good book: https://www.amazon.com/Invitation-Applied-Category-Theory-Compositionality/dp/1108711820 https://www.amazon.com/Invitation-Applied-Category-Theory-Co..., and, unsurprisingly, found it exciting. Regarding PhD in an applied area: I tend to agree with you, and also keep thinking about focusing more on computational / applied mathematics so that my studies could be somehow related to my work. My tech focus at work is around data processing: with interest in distributed databases and computations. Heh, I see that distributed systems, algebra, topology, and categories are similar in mental representation in my head, they cause same kind of excitement when I study them: visualising, analysing, and playing with the systems of structures, connections, defined rules and operations :)

DreamScatter 7y ago

Yes, I am in the same situation, I research graduate level mathematics outside academia. Right now, I am collaborating with top scientists from around the world by staying connected online via a website called https://bivector.net https://bivector.net and am publishing my own research at https://grassmann.crucialflow.com https://grassmann.crucialflow.com As it turns out, I don't have an undergrad degree either, so it is tough for me to find jobs, but I find plenty of interaction!

playing_colours 7y ago
I would be interested to learn more about how you approach your studies and research. I see Julia is your weapon of choice and you are active in contributing!