Author Topic: Doctoral studies - perspective  (Read 4385 times)

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Offline RinnakeTopic starter

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Doctoral studies - perspective
« on: June 17, 2022, 02:20:15 pm »
Good day,   
 
my brother and I would like to ask for your views on doctoral studies in power electronics. At the moment, we have successfully completed a master's degree in power electronics and control of electric controlled drives, and we are deciding whether it will be worthwhile for us to complete an additional doctoral degree.

If we continued our studies, due to our diploma theses whose topic was the design, construction and control (vector oriented) of the Vienna rectifier, the dissertation would be directed towards power electronics and develop existing knowledge and research on new AC-DC topologies of power converters and its new advanced control techniques. However, we are at a crossroads. We are "reproached" that if we continue to study, we will lose work experience, which is often more valuable for today's employers than the degrees obtained, and the financial side of things will not improve significantly with a PhD degree. From this point of view, continuation seems to us to be an obstacle, but on the other hand, one does not know what will happen in 10 years, if the current activities do not stop fulfilling him and then he could regret not taking the opportunity of this study when it is offered.

According to our findings, a doctoral degree is necessary if we want to remain active in the academic sphere, which does not attract us yet, and also in the research field. The research area is very attractive for us and we would like to get into the development of new products. However, we found out that most of the trained doctors still work in exclusively engineering positions, which surprised us very much. According to some doctors, PhD does not bring other benefits and values and is associated with very low salary. Do you think if it is worth completing this study today? If so, in what form (full-time at school / remotely at company)? 
 
We will be happy for your views on this study and its contribution to future employment.
 
Thank you for the discussion and we apologize if we posted this post in the wrong thread of this forum.

EDIT: I live in Czech Republic (sometimes called Czechia).
« Last Edit: June 17, 2022, 03:14:29 pm by Rinnake »
 

Offline Slh

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Re: Doctoral studies - perspective
« Reply #1 on: June 17, 2022, 02:54:43 pm »
I work in a research focussed power electronics company. I work with some very good people with PhDs, some very good people with only a bachelor's and have worked with some rubbish people with PhDs. I have also interviewed a lot of people with PhDs....

A lot of the time, all a PhD shows me is that you can complete a PhD. The PhD often doesn't give them particularly useful skills above and beyond what they gain from their undergraduate degree. it's essential for academia but  not for industry.  Most of the PhD candidates that I get would be suitable for a graduate role. Not all of them realise this... Unfortunately, often the post doc roles don't improve things enough either.

Most of the PhDs I work with don't work on stuff directly related to their PhD. I suspect they would also do a great job if they'd gone straight into industry.

If you want to do a PhD, then do a PhD. It's unlikely to get you more money.
 

Offline Peter Taylor

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Re: Doctoral studies - perspective
« Reply #2 on: June 17, 2022, 03:03:25 pm »
I have spent half my life at university only to find that all I did was learn. I started a business seven months ago, and at 55 years of age, it was the best thing I have done. The three D's of life. Do, Do, Do. Do what makes you happy.
 

Offline RoGeorge

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Re: Doctoral studies - perspective
« Reply #3 on: June 17, 2022, 03:56:01 pm »
Go get your PhD.

First, you'll get a few extra years of youth freedom to live.  This alone would be enough.  Then, the thread of life is not only about money.  You won't get rich in your first years as an engineer.  Don't get so eager to get yourself a job and a boss.  You'll have all the rest of your life for that.

Then, right now the economy is not in its best shape for engineering jobs, so you might end up not even finding a job at all in engineering.  Instead, during the next years you can finish your thesis, while the economy recovers.  And you'll end as a fresh PhD in a booming economy, instead of starting now as a fresh engineer in a recessing economy.  Your choice.

You say you like research.  Do you want to spend the next years doing research for your PhD thesis, or you want to stay in a cubicle doing repetitive tasks as a fresh engineer?  You might never get the opportunity to do research again for the rest of your life, so do it now.  And if you think in terms of employment advantage, of course you'll get an advantage as a PhD, a lifetime advantage.

Companies are looking for PhD in EU, especially the small ones, especially in EU.  Sometimes, small companies have to prove their expertise when bidding for contracts, and one of the things they do is to list the number of PhD they have on their payroll.

If you can, then go get your PhD.  :-+
« Last Edit: June 17, 2022, 04:08:41 pm by RoGeorge »
 

Offline m98

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Re: Doctoral studies - perspective
« Reply #4 on: June 17, 2022, 10:27:00 pm »
Go get your PhD.
First, you'll get a few extra years of youth freedom to live.
Not sure if having extra youth freedom would be an accurate characterization of the PhD Students I work with. Quite the opposite, actually. Relatively bad pay for the skill level, still having to live in a WG, having not one, but at least two bosses, regularly stressed out and working overtime, hard constraints on what they can actually work on, as papers and conference proceedings need to be constantly pumped out, etc...

Can't really give any view on the career perspectives, but I don't think it necessarily increases your chances of landing an R&D-Position compared to just applying for one with a Masters degree and some relevant work experience.
 
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Offline Benta

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Re: Doctoral studies - perspective
« Reply #5 on: June 17, 2022, 10:53:18 pm »
You now have:
MSc degree in power electronics, right?
The PhD will bring you prestige somewhere, but that's about all. No money.
You need to look outside the Czech Republic. Czech engineers are highly regarded in Europe, and exactly power electronics engineers are sought.
I won't say you can decide your own salary, but you're in an extremely good position.
Look to the wind or solar power companies or Siemens or Alsthom or power transmission or...
You'll be welcomed with open arms.

Good Luck to you both.
 

Offline Someone

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Re: Doctoral studies - perspective
« Reply #6 on: June 18, 2022, 01:02:35 am »
but on the other hand, one does not know what will happen in 10 years, if the current activities do not stop fulfilling him and then he could regret not taking the opportunity of this study when it is offered.
There are always PhD positions available, they can be much easier to obtain and complete as a "mature" student with industry experience. Do not feel pressured into doing it continuous with other study.

...the financial side of things will not improve significantly with a PhD degree...
...According to some doctors, PhD does not bring other benefits and values and is associated with very low salary...
Remember it is very industry dependent (most posters on here are not professionals, or in electrical industry). Below is a cumulative histogram for income of electrical vs electronic engineering in Australia (2016 data) broken out with masters and PhD against the industry overall. Electrical engineering pays higher and has more scope for upward growth, but any earning difference between masters and PhD disappears at the top end. A PhD would likely get you a good entry level income and first few years but beyond that is all your own work and little to do with qualifications.

Contrast to electronics where there is a "bias" against having a PhD at lower jobs, but it has some weight at the higher end.

Median electrical engineer paid 15% more than median electronics engineer!
 

Offline jeremy

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Re: Doctoral studies - perspective
« Reply #7 on: June 18, 2022, 06:24:16 am »
I have a lot of (maybe too much) experience in this area, not only because I have a PhD but the other details I’d rather not go into it too much. However, most of the following comes with respect to Australia, it may or may not be relevant to other countries.

My opinion echoes a lot of what is said here already.

1. If you want to be in academia, you need it as a “tick the box” measure; most universities I have been involved with simply won’t hire you if you don’t have one. There isn’t really much choice here except in a few areas like architecture and design. I don’t think this is the case for pretty much any other workplace.

2. If you do a PhD as a way to earn more money, you are probably going to be disappointed. In Australia the most competitive scholarships still earn less than minimum wage. Like you could be kicking butt on cancer research or something that is really obviously good for society, and you’ll be earning less than if you worked at McDonalds. At least in Australia, graduate degrees don’t appear to be valued that much by employers except in very specific circumstances (I don’t agree with this, but it is what it is). It can be an impediment to getting a job because HR will say you are “overqualified”, and in Australia we are very strongly influenced by “tall poppy syndrome” - having a PhD makes you a target for this. I think Europe is much better in this regard.

3. A person doing a PhD between the age of roughly 35-50 years old seems to be getting rarer (anecdotally). Given the price of houses/sizes of mortgages today as well as the age people normally have kids, that kind of makes sense. Most people seem to do it immediately, or closer to retirement for financial reasons (I was in the former).

4. A good supervisor/colleagues is extremely important. I’m not necessarily talking about research pedigree, I mean more in terms of interpersonal skills, how friendly/helpful people are, etc. The last thing you want to be is a PhD student for a “superstar” researcher with a well recognised name, but who has 50 other students and 10 postdocs as well as an executive position elsewhere, etc. There are also supervisors who just want PhD students so that they can use them to teach their classes.

What I usually tell people is (at least for engineering and most science): the only reason you should do a PhD is because you want to go deep, deep down a rabbit hole. Because my own experience is that you would need to do so, right to the point where the number of people in the world who can even understand what you are working on begins to move towards the single digits. That’s not to say that it makes you a “genius” because you know more than everyone else (you definitely don’t/won’t), but rather you would like to really persist in something intricate that you want to learn about. This could be GaN FETs as much as it is the breeding patterns of hummingbirds in a specific town in the US, or optimising the way you make dyes out of crushed beetles.

The reason it can be tricky to get a job with this sort of thing is that it can be tricky to convince an employer that this depth is useful. For example, if you did research into MEMS devices, but then went to work for a power distribution company, your knowledge of MEMS is probably not going to be all that useful even though it may be considered Electrical Engineering and your employer (perhaps rightfully) would not want to pay you extra for that knowledge. Certainly you could argue that your time management, organisational skills etc are demonstrated by having a PhD, but you could have done a PhD in lots of other things and still be able to argue that.

PS: “going down a rabbit hole” is an idiom in English which basically means to strongly persist in investigation, regardless of how weird/complicated/difficult it gets. It is a reference to the original story of “Alice in Wonderland”.
 
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Offline Someone

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Re: Doctoral studies - perspective
« Reply #8 on: June 18, 2022, 08:20:41 am »
In Australia the most competitive scholarships still earn less than minimum wage.
At the same time, there are a small number of highly competitive scholarships paying well above the minimum wage:
https://scholarships.unimelb.edu.au/awards/john-monash-scholarship
before adding extra scholarships/prizes, and in Australia scholarships are non-taxed so you can work in other jobs or have other income and make some bank. Doing a part time postgraduate project while working is a great option for those with employers who will support it.
 

Offline rstofer

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Re: Doctoral studies - perspective
« Reply #9 on: June 18, 2022, 04:26:21 pm »
Around '76, job opportunities for PhDs in Silicon Valley went to about zero.  They changed the law on job applications allowing PhDs to omit to mention that degree and stick to MSEE.  You couldn't lie about what you had but you didn't have to state all you had.  "Overqualified" came up a lot.

Completely off topic: 

These days I wouldn't spend much time on electronics but given the amount of math I had to take to get to an MSEE, I think I would add a couple of courses and head off into Machine Learning.  Anybody that can handle partial differential equations (on a massive scale) will be right at home.  Linear Algebra rules!  Some of the AIs talk to hardware so there is still an opportunity to use the EE component.

There are even opportunities for Fortran programmers.  The NVIDIA toolkit contains both a C++ and Fortran compiler.

I have to believe that ML is a sieve.  There are very few people that can handle the math and there are even fewer that can interface the math to physical hardware.  ML is an area that I think will grow without bound over the next generation.  Everything else is just more of the 'same old stuff'.  How many ways can there be to build a power supply?  How many NEW ways are there to build a power supply?

Who wouldn't love a 10,000 x 10,000 matrix of partial derivatives?  Fortran rules!







« Last Edit: June 18, 2022, 04:32:24 pm by rstofer »
 

Online CatalinaWOW

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Re: Doctoral studies - perspective
« Reply #10 on: June 18, 2022, 05:08:10 pm »
Even though some of the advice here seems contradictory, from my point of view it is all correct.  This decision is very dependent on you and where you want to go.  There are a few careers where a PhD is a required check box.  Academia and some large corporations and some government jobs.  Beyond that it is wide open.

It has been my observation (I have worked with, managed or observed literally a few hundred PhDs and other professional people over my career) that very good people do well financially regardless of degree and narrow or weak people don't do well, also almost regardless of degree.  Success at getting a PhD is only loosely correlated with being well suited for a particular career.  Collecting a PhD involves several factors.   Obviously being good at academics.  But also putting up with BS, luck in advisors and academic committee members, persistence, creativity, writing skills, academic politics and a long list of other things.  Success at post PhD career depends on how well the mix of skills you brought to the table applies to the rest of your life.  Perhaps fortunately, perhaps not, all of those skills help some places and times.  Only you can determine your satisfaction with that result.
 
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Offline Tomorokoshi

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Re: Doctoral studies - perspective
« Reply #11 on: June 19, 2022, 02:36:27 pm »
In Australia the most competitive scholarships still earn less than minimum wage.
At the same time, there are a small number of highly competitive scholarships paying well above the minimum wage:
https://scholarships.unimelb.edu.au/awards/john-monash-scholarship
before adding extra scholarships/prizes, and in Australia scholarships are non-taxed so you can work in other jobs or have other income and make some bank. Doing a part time postgraduate project while working is a great option for those with employers who will support it.

I know a person who did just that. It takes a good combination of employer, advisor, and student. The project was applicable to work. Perhaps one day per week was dedicated to the project.
 

Offline RinnakeTopic starter

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Re: Doctoral studies - perspective
« Reply #12 on: June 26, 2022, 03:11:41 pm »
Thanks to all for your help. At the moment, we are finally thinking about whether we have not studied a less promising field (power electronics and control of regulated motor drives), when cybernetics, control and information systems, artificial intelligence, embedded systems, etc. are coming to the fore today ... We are beginning to think that those who would doing doctoral studies in cybernetics would be much more in demand nowadays.
 

Offline rstofer

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Re: Doctoral studies - perspective
« Reply #13 on: June 26, 2022, 05:44:47 pm »
AI in general and ML in particular are starting to fly!  The techniques are being applied to just about everything and one requirement is a strong background in Linear Algebra and, if the model is to be applied to something, there needs to be some kind of interface.  It's one thing to derive the model, it's quite another to actually drive an automobile.

There have always be suboptimal schemes for controlling production lines. Somehow, we're willing to accept a small discard rate.  Maybe ML can play into this and somehow provide guidance to the Programmable Logic Controllers (PLCs).  I have no idea how this works.

I would spend a bunch of time at NVIDIA learning how to use the Jetson Nano as a stepping stone to larger systems.
 NVIDIA is SERIOUS about AI.

https://developer.nvidia.com/embedded-computing

So is Google:

https://coral.ai/docs/dev-board/get-started

And so is PyImageSearch (for money, of course)

https://pyimagesearch.com/2020/03/25/how-to-configure-your-nvidia-jetson-nano-for-computer-vision-and-deep-learning/

Computerphile has put out some videos that are easy to watch:



I don't know where the stumbling blocks come up but that's where the PhD comes in.  Figure out a faster algorithm and the world will flood you with money.

I love MATLAB and they have some nice tools for ML.  At extra additional cost, of course.  I buy the Home license for MATLAB plus several add-ins so it runs a couple of hundred $ per year.  I like their digit recognition example because it shows a convolutional neural network as just a bunch of predefined blocks stacked together.  There's a lot of magic in the blocks but I don't need to know that.  I just chain them together and magic happens.  No, I don't truly understand what I am doing but I'm really good at 'cut and paste'.

Or Python with additional libraries or, in the case of NVIDIA (at least), C++ and Fortran compilers are available. 

The number of CUDA cores on the graphics card becomes an important consideration.  I bought an HP Laptop just because it has an NVIDIA RTX 3070 graphics chip with 5,888 CUDA cores (and it was affordable...).  That's a lot of parallelism!

Good luck!


« Last Edit: June 26, 2022, 05:48:03 pm by rstofer »
 

Offline Benta

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Re: Doctoral studies - perspective
« Reply #14 on: June 26, 2022, 07:09:02 pm »
Thanks to all for your help. At the moment, we are finally thinking about whether we have not studied a less promising field (power electronics and control of regulated motor drives), when cybernetics, control and information systems, artificial intelligence, embedded systems, etc. are coming to the fore today ... We are beginning to think that those who would doing doctoral studies in cybernetics would be much more in demand nowadays.

Yes, and that's where everyone is applying today. Those are the "buzzwords" in fashion. You'll be one of the herd.
I remember from 30...40 years ago the buzz about "everything's going digital, so analog engineers will no longer be needed".
B*llsh*t. Good analog engineers are the best paid people today, because not many good ones are out there. The same can be said of RF engineers, PE engineers, sensor technology etc. All those fields that operate on the interface to the real world.
Digital engineers and progammers are a dime a dozen and can be hired cheaply in India or other low-wage countries.

The bar is much lower for AI etc. candidates. They just need a PC, which is why everyone is flocking to it.
Analog, RF, power, sensors need a million-dollar lab to just get started. If your university has that, use it to the hilt. You'll come out on top.
And VERY IMPORTANT: you need a Mentor. Can be a professor, but also from industry.

Very personal opinion, but from the heart.
Good Luck.

« Last Edit: June 26, 2022, 07:12:51 pm by Benta »
 
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Offline Slh

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Re: Doctoral studies - perspective
« Reply #15 on: June 26, 2022, 07:24:45 pm »
Personally I chose power electronics because it gave me a chance to play with magnetics and analogue. And when I get bored of those I can do a little basic digital to relax :). As a bonus it appears that everyone else also thinks that it's either hard or not interesting so there's plenty of jobs out there. Shame I'm actually hiring...

There's a lot of research going on in power electronics. SiC appears to be taking over in the stuff I work in and GaN is something for the future. Lots of new topologies, some of them even useful...

Power is required for everything, even in all of the new buzzword fields like AI. Smaller, more efficient, cheaper - the usual challenges.
 
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Offline RoGeorge

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Re: Doctoral studies - perspective
« Reply #16 on: June 26, 2022, 07:26:14 pm »
We are beginning to think that those who would doing doctoral studies in cybernetics would be much more in demand nowadays.

Fake worries.  The actual specialization or PhD theme is close to irrelevant.  You wouldn't expect whatever is hot right now to still be the fashion in 10, or 20, or 30 years from now, isn't it?  The world is keep changing.  By the time you finished your PhD, the theme will be halfway obsolete. 

What really matters is the process, and also the title.  These will stay with you for the rest of your life.  Other than that, yes, the grass seems always greener in the neighbor's yard.  Right now, power electronics is at all times high demands because of the trend to switch to solar energy, electric cars and so on.  Go get your PhD no matter the subject.
 
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Offline rfclown

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Re: Doctoral studies - perspective
« Reply #17 on: June 27, 2022, 01:32:44 am »
It's very interesting that you are two brothers pondering the same journey. One thing that I'm sure everyone responding here would admit... our journey wasn't completely planned. One never knows how circumstances and opportunities will arise. My journey started with a fascination with electronics as a youngster. I looked at circuit boards and wondered, "How do they know what parts to put together? I want to learn how to do that." When I was told that the profession was called Electrical Engineering, my course was set (about 10 years old). I was good at academics... if I cared; and the only things I cared about were math and science. It wasn't until I got to college that I really excelled, because I was finally getting to my goal. I loved my time in college. When I finished my B.E.E. in 1983 I wasn't in a hurry to leave. I was encouraged by my university to continue, and received a research fellowship which more than paid all my expenses. Here's were circumstances come in. I got engaged. I needed to be a provider, so after getting my M.S. I took a job with Motorola. Great job, but after time, I wanted to be back in research (like during my graduate work). I was looking to go back to school (which would have been REALLY hard since I had two kids and one on the way) and had inquired at two schools... and then a research position opened up at Motorola that I was able to get. That turned out to be a dream position (George Fisher CEO at the time), until former CEOs trashed the company (Ed Zander...) and decided that research wasn't needed, and they'd be followers instead of leaders. I've been very fortunate that I had a fantastic education (Auburn University) and the privilege of working for Motorola from 1986-2009 were I learned from many great engineers. I've been able to excel in 7 jobs since then. Do I wish I had the PhD at this point? (skip the Moto research opportunity and go back to school?) It's so hard to say. You have decide on opportunities as they arise.

Just a rambling from my experience. That said, if you think you might want a PhD, and you are in a position to get one... you most likely will not practically have to opportunity in the future to do so. I'd say grab the ring and do it.

Nothing like getting a PhD... but I decided early on go get a Profession Engineer license. It was not needed in the job I had, but it was going to be MUCH easier to do when my academics were fresh in my mind, so I did it. Has it benefited me in my profession so far? Not one bit. Do I still keep up the continuing education requirements and pay the fee every two years to keep it current... yes. Because I don't know what opportunity might arise tomorrow.
 

Offline jeremy

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Re: Doctoral studies - perspective
« Reply #18 on: June 27, 2022, 02:01:26 am »
The majority of money I have earned in the last 5yrs has nothing to do with my PhD specialisation/topic, it is more around electronics in general. Pretty much the only people that matters for is if you stay in academia, or you have a very, very specific job in mind (ie you want to research neural networks at Google). But the latter is a very risky choice, as you are betting the farm that you can actually get that job and that your skills will not become obsolete overnight. If/when the next AI winter comes around I am not quite sure what all of the AI folks will transition into, as it seems the skills are so domain specific that they will be not really all that transferable. I am told that this was a problem for a lot of people in genetic sequencing when automated PCR machines hit the market.
 

Offline rstofer

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Re: Doctoral studies - perspective
« Reply #19 on: June 27, 2022, 03:11:52 pm »
I would think there is quite a similarity between the math required for AI and that used for data mining or optimization of cost functions in a more general, and business related, sense.  The branch of math called 'big data', for lack of a better term, is becoming increasingly important at every level of business.  Everybody wants to collect data and they need math types (particularly statistics) to do something with it.

Neural networks, despite the heady title, are really just another way to find a minimum of some cost function.  It's just that the networks take so many inputs (tens of thousands, perhaps) and, at best, find only a local minimum.  I expect that finding the true global minimum is the holy grail of AI and is still quite elusive.  Where else could you say "Jacobian Matrix" and not get a bunch of blank stares?

My interest in optimization was always related to scheduling with constrained resources and everything was done in Fortran.  Those were the real 'good old days' circa 1970.



 

Offline HighVoltage

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Re: Doctoral studies - perspective
« Reply #20 on: June 27, 2022, 03:22:07 pm »
One of my nephews just got his PhD in physics and had high hopes for a good job and good pay, here in Europe.

He finally got a job....

The company who hired him, had applied for EU money grants but one requirement to get the grant was to have a full time PhD on staff. He is getting paid as much as he got before on his Masters degree. But instead of working in the field of physics, his main job is now to fill out forms and sign them with his title.
There are 3 kinds of people in this world, those who can count and those who can not.
 

Offline SiliconWizard

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Re: Doctoral studies - perspective
« Reply #21 on: June 27, 2022, 07:17:27 pm »
Yes, there are numerous programs, especially in Europe, to fund "highly-qualified" staff with various public grants, so private companies can pay very little for someone with a PhD. So they'll hire you not just because you are highly qualified, but because you will cost them little while they'll be able to show off your title.

To add to what jeremy said, apart from academia or very specific jobs, and the point just above, having a PhD will also help to get access to the higher spheres of R&D management, especially in large corporations.
 

Online coppice

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Re: Doctoral studies - perspective
« Reply #22 on: June 27, 2022, 07:33:05 pm »
To add to what jeremy said, apart from academia or very specific jobs, and the point just above, having a PhD will also help to get access to the higher spheres of R&D management, especially in large corporations.
It can work both ways. The man who was in line to become the head of an R&D lab in the UK some years ago had only ever worked in R&D roles. The charter of the lab called for its head to be someone with solid project management experience, so they had to find him a substantial project team and project for him to run for a couple of years, so he could fulfil that criterion. A task he was poorly prepared for, and for which he seemed to get a lot of assistance and mentoring.
 

Online ebastler

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Re: Doctoral studies - perspective
« Reply #23 on: June 28, 2022, 11:33:16 am »
One of my nephews just got his PhD in physics and had high hopes for a good job and good pay, here in Europe.

He finally got a job....

The company who hired him, had applied for EU money grants but one requirement to get the grant was to have a full time PhD on staff. He is getting paid as much as he got before on his Masters degree. But instead of working in the field of physics, his main job is now to fill out forms and sign them with his title.

While I have no reason to doubt your specific story, it is anecdotal evidence at best -- and an anecdote which decidedly lacks colour too...

What field of physics did your nephew specialize in? Which type of companies and jobs did he apply for? In which countries; was a language barrier getting in the way? What experience does he bring beyond his university courses and thesis work -- stays abroad, industry work experience, technical hobbies?  Does he communicate well and get along with others? etc.

If your story was meant to imply "don't bother with a PhD, it's worthless", then I wholeheartedly object.
 

Offline HighVoltage

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Re: Doctoral studies - perspective
« Reply #24 on: June 28, 2022, 12:41:07 pm »

If your story was meant to imply "don't bother with a PhD, it's worthless", then I wholeheartedly object.

Definitely was not meant like that at all.
It just happened like that a few weeks ago and was meant as awareness of what is out there. It is just one example of what can happen to a highly educated graduate.




There are 3 kinds of people in this world, those who can count and those who can not.
 
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