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I graduated in December 2018 with a double degree in math and electrical engineering and have applied to various graduate schools in pure math and electrical engineering and have been offered admission to phd programs in pure math and electrical engineering.

During my undergraduate studies, I have heard many academic mathematicians say that a math degree opens many opportunities for you and mathematicians can get any job, ...

On the other hand, I have also heard people saying that a math degree is useless financially and you can not get a decent job with a math degree; you either need to become a school teacher or work at a bank, ...

Now that I am about to start my phd program, although I enjoy math a lot, I do not want to get a phd in math and after four years find that it did not worth it financially and I have to do a not well-paid job. I can not also hope that I will end up in academia as I have heard academic jobs are very hard to get.

So that leaves me to think that if I want to get a well-paid job, I should do a phd in electrical engineering and not math.

I am so confused and I do not know which paths am I supposed to take? do a phd in math or electrical engineering?

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    If you believe working in banking can never be well paid, you may want to research the position of quantitative analyst (quant) more carefully. – origimbo Jan 16 at 11:22
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    Where do you live? – henning -- reinstate Monica Jan 16 at 12:44
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    "I have [heard] a math degree is useless financially and [you] need to...work at a bank," isn't that a contradiction? The finance sector pays well. – user2768 Jan 16 at 13:03
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    If youre only trying to maximize income you should probably choose the EE PhD and then drop out with a masters. – user101106 Jan 16 at 13:04
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    @CJ59 Indeed, a PhD doesn't generally maximize income (at least not with the figures I've seen), it might even reduce it. – user2768 Jan 16 at 13:06

16 Answers 16

59

Just a personal anecdote, not really an answer, too long for a comment.

I have a master degree in mathematics and now I'm doing physics simulations for visual effects in Hollywood blockbusters. I believe that a math degree gives you a massive upper hand in any field with reasonable amount mathematics in it. However, you have to be interested in that field and study it in your spare time. I studied computer graphics in my spare time and my math background allowed me to comprehend things in computer graphics orders of magnitudes faster and deeper compared to fellow computer science students.

Take it with a grain of salt, master degree is completely different kind of a beast compared to a PhD degree.

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    Btw, the pay is probably not as good as in a bank but the job is lot of fun! – tom Jan 16 at 11:31
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    I don't know if a maths degree would give you an upper hand vs a physics degree fir your specific example, but I agree that a degree in "not computer science but strong in maths" is very helpful in the world of computers (background, I've a masters in physics, and work in computing). Maths and physics also do very well in banking, if the maths preference is statistics rather than pure. – UKMonkey Jan 16 at 14:22
  • Similar here: BS degree was math & physics (the school didn't offer a CS degree back then), but my career has been mostly programming scientific & engineering simulations - in fields as different as meteorology, seismology, and neurobiology. I can fairly quickly learn enough of the science to figure out how to apply the math to it. – jamesqf Jan 16 at 18:37
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    This is definitely an answer, anecdotal though it may be. Per Good Subjective, Bad Subjective, answers should support their claims through evidence or experience, and this answer does the latter. It could perhaps be improved, but it definitely fits as an answer rather than a comment. – user8283 Jan 16 at 21:04
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Where I live, a lot of math degree holders work in software development and are generally doing quite well ... especially since many computer science degree holders are not really good at maths. Other opportunities for mathematicians are simulations (i.e. in engineering) or insurance companies.

In fact, maths teacher is also a quite decent occupation where I live, but that is of course subject to supply and demand.

Were the people who told you you might not find a good job also math degree holders? I have found that non-mathematicians sometimes do not really know what mathematicians work as.

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    There's a big difference between a math degree and a PhD though. While I'm sure that you can get a good job with a PhD in math, I'd wager that for many jobs the PhD won't get you much more money, but will cost you a lot from seniority and simply the 3-4 years that you spend doing a badly paid PhD instead of working in the industyr. – Voo Jan 16 at 16:29
  • You are if course correct. However, on closer reading it seems as if the OP is already sure she wants to take a PhD and is just unsure which one. If that is the case, maths might still be the more logical option. – Jan Jan 16 at 16:57
  • @Voo This is correct, but doing a PhD in engineering (as stated in the question) will be "equally bad" from the point of view of seniority. If then the point is to not do a PhD at all, then I would agree. – gented Jan 16 at 19:45
  • @gented Somehow missed that when reading the question. Agreed that there's probably very little difference between the two PhDs. Mea culpa. – Voo Jan 16 at 21:00
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I'd be more inclined to comment - but I get more space in an answer:

The premise that a degree is a path to a job is blatantly false. Even the best most sought after degree might leave you jobless: wrong region, potential employer doesn't like you, you aren't as good as the rest (some subjects are apparently very competitive, for better or worse).

So you should really pick a degree that you find personally interesting that has a potential of being useful for work. In the case of mathematics this leaves very must two main routes:

  • Pure maths in academia, or close to it, teaching
  • Applied maths in academia or industry

Mathematics is very much the foundation of much of our modern life. Banking, electronics, engineering - BUT this is applied mathematics, not pure mathematics (but even that has its fans). Some people may joke that an applied mathematician is a physicist ;). In your specific case, the combination of mathematics with electrical engineering can be quite valuable. You would possibly be better at the calculation that your peers if they did not study mathematics. Then again, if you hate electrics and love maths, it may not be an advisable choice.

In addition, paths can change. Even a PhD you should chose to some extent by interest if you can - it will make it more interesting.

To bring in a personal note: I studied mathematics. In the PhD I ended up with some limited experimental and analytical chemistry, chemical kinetics, ab initio quantum chemistry and programming. Then in two post docs I ended up programming more and working more with chemical kinetics and quantum chemistry. Unfortunately I am not in academia any more - still, for now a very interesting job. And what is it? Numerical simulations (where my previous experience is useful.)

Now in some countries subject mobility isn't very large (Germany springs to mind, maybe also France). In England you come from subject A and do a PhD on sbject B in the end...

So to bring this to a conclusion: Study what you like - a PhD is also funded. A degree is NOT a "path to money" - follow your interest. Mathematics is the basis of most of the things we need today. If possible, focus on the applied side and there should be many opportunities for an applied mathematician. And don't necessarily reject the pure maths: Developping new functionals in quantum chemistry or new models for say CFD, working on cryptography is well beyong what I would be able to do in maths - especially given that my paths capabilities have been rusting away the past 7.5 years.... Nowadays I do less "actual maths" and more programming, number crunching and data processing.

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    From my experience (BS in Math, MS in Statistics, incomplete Computational Statistics PhD, now working in Healthcare industry), this answer is spot on. I do very little pure math or theoretical statistics, but I apply math and statistics every day. People may not pay you to do math proofs, but the programming, number crunching, and data processing is in high demand. If you want to make the degree a better financial decision, focus on how you can apply math. Practice solving real problems with applications/programs popular outside of academia. – Underminer Jan 16 at 19:25
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    While I agree that the work you do will be more like applied mathematics, I don't think that studying pure mathematics is only a route to academia - I know several who studied pure, but ended up working in meterology, astrophysics, finance, etc. – Stobor Jan 16 at 22:25
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    "So you should really pick a degree that..." —that was an unexpected twist; I thought you'd say, "So you should reconsider whether you need a degree at all or whether you should just start working now." :) Or maybe even, "...consider whether you're avoiding work by studying endlessly." – Wildcard Jan 17 at 3:00
  • @Stobor Of course there are. But there are fewer (obvious) opportunities for pure mathematicians than for applied mathematicians. – DetlevCM Jan 17 at 20:01
  • @Wildcard There are people that think like that unfortunately... - I would say everybody who wants to continue studies due to interest in th esubject should be encouraged. It is an opportunity to learn new things and develop a better understanding. - If the interest is in an area that is useful, even more so. – DetlevCM Jan 17 at 20:10
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The answer depends very much, as already outlined, on the particular job career you choose to pursue. It is generally true that nowadays it might be quite hard to find a very well-paid tenure position in Academia, therefore the chances that one might end up being financially wealthy with that particular choice are not the best; likewise, industry does not seek many pure mathematicians either.

However, mathematicians and physicist are extremely well employed (and probably consitute the majority) in quantitative analysis, machine learning and data science related jobs, not to mention the subset who choose to continue in software development. It is often said (as you yourself stated) that the ideal solution is to move to the financial sector, nevertheless that is not the only one; as already mentioned, nowadays the field of artificial intelligence and data science is particularly filled with academics: the main trait that pursuing a PhD offers is the capability to solve problems, in general, and to apply a broader set of knowledge to investigate different scenarios. Such skill set can be easily applied elsewhere and as a matter of fact most academics do not stay in Academia (at least nowadays); to make a long story short and answer your question

On the other hand, I have also heard people saying that a math degree is useless financially and you can not get a decent job with a math degree; you either need to become a school teacher or work at a bank

a scientific PhD is not financially rewarding if you decide to stay in Academia (for the majority, with the due exceptions); it can be if you move to industry, to the right places. Moreover I do not see a PhD in electrical engineering opening so many more doors that a PhD in maths cannot.

6

With either a PhD in Math or EE, you have a good chance to get a well-paying job. So my advice is: study what you interests you (if neither interests you, a PhD is probably the wrong choice).

To give you some numbers, from the US, the AMS Survey gives data on starting salaries for Math PhDs. You can also get some data from Payscale on average salaries (e.g., Math PhDs, EE PhDs and Engineering Bachelors):

  • AMS Median industry starting salary (2016 Math PhD): ~$106,000
  • Payscale Average Math PhD salary: $98,000
  • Payscale Average EE PhD salary: $116,000
  • Payscale Average Bachelor of Engineering salary with 5-9 years of experience: $83,568

Some words about this data: The AMS data is rather reliable. Payscale does not have have a lot of data on Math and EE PhDs, and I am not sure if the salaries used are all starting salaries. The Payscale Math PhD includes a number of academic salaries which are significantly lower. AMS reports medians and quartiles, Payscale reports averages and ranges. If we compare the Payscale Median EE PhD salary (by eyeball, about $110k) with the AMS Median (about $106k) we see they are not so different (and the latter is certainly only starting salaries).

Ignoring the relative cost of getting a PhD (which is typically relatively small in the long term), it appears that your general salary prospects are better with a PhD in EE or Math than just a Bachelors, and slightly better with a PhD in EE than a PhD in Math.

That said, there are some areas of math that are considerably more marketable outside of academia than others, such as Statistics and Data Science.

5

To give a slightly different take than the other answers:

Employers hire people to do a job for them. Many companies have situations slightly more complex than "hire the best for the job," but at the end of the day they want the person who can meet their need as best as possible.

As a math major, you have a skill set that people want. Unfortunately, they rarely are looking for people with only that skill; they likely also have other requirements. For example, in the United States, the NSA explicitly lists mathematics on their jobs page. The mathematicians they hire, though, are rarely only mathematicians; they also have at least some skills in computer science, programming, and other related areas (e.g., linguistics, cryptography).

Basically, check out jobs you may be interested in and make sure that math isn't the only skill you bring to the table. Outside of academia mathematicians typically need to be polyglots to be successful, but polyglot mathematicians can be successful indeed.

4

Have you considered the ROI of higher education?

If you want to make more money then start working now and building up your work experience instead of taking on more debt and not having several years of work experience. You will also find out from working that maybe you don't like EE as much as Math for example, and this can help you decide.

If you are a curious person and want to learn, then go for the phd in math and lean towards academia.

I faced the same problem when I was deciding my undergrad, I love astronomy and astrophysics and cosmology. I was concerned about the time and money investment and the questionable returns. I have heard how there is a lot of politics involved in securing grants and funding, and also the small number of jobs are very competitive.

Instead of physics, I went into engineering because it would be more practical to get a BS and begin working right after. Now I don't have a lot of debt, a good entry level job, and I can explore different industries and my own interests and continue growing. I would like to continue my education and get a masters eventually but I'm not sure what it will be in yet.

3

This can depend on more than just the mathematics. You don't say where you are, nor anything about the nature of the educational system. But, for the US, at least, a BS in mathematics is a great basis for many careers, both in and out of academia. But that is because the baccalaureate is, in the US, a very general degree. One studies more than just mathematics, which amounts to only about a third of the courses taken.

But mathematics is about thinking and you can apply that thinking, especially thinking in a formal and disciplined way to other things. But if you don't really know anything except mathematics, then you aren't in such a good place, except to do more mathematics.

But any company that needs analysis of things, such as products or strategies or, well, anything, can use people that have a disciplined way of organizing and presenting information. Mathematics helps with that, as long as you also have the more specific knowledge that the job requires. But that knowledge is easier to obtain, in most cases, with the discipline of thought that mathematics brings you.

A degree in EE would teach you to think in a different way, whether that is better for you is up to you, however.

But, to give some perspective here, I also think that a degree in Philosophy is also a good launching point for a career, and for much the same reason that mathematics is. It teaches discipline of thought that can be generally applied.

However, you are starting a doctoral program. Such programs prepare you to do research and they are very specialized. They are not general education in any sense. Most, or at least, many, PhD holders (guessing a bit here) stay in academia since the doctorate is a good preparation for that. There are other opportunities, of course, but like the degree itself, those opportunities are very specialized. But mathematics is, even at the highest levels, still good mental training that can be applied in other domains.

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    Is it really true that most PhD holders stay in academia? I'm pretty sure that's not true within the fields I'm most familiar with, but I don't know if it's counterbalanced by other fields. – David Z Jan 16 at 14:23
  • @DavidZ I was just about to say the same thing. See, for example, this question and its answers here on Academia.SE. – Peter K. Jan 16 at 14:25
  • @DavidZ, It's just a guess, really, but I'm thinking beyond technical fields. I don't have research to back it up. Made a small edit. – Buffy Jan 16 at 14:25
  • It's statistically not possible for most new PhDs to become academics; advisors produce too many academic "children" in their careers to be counterbalanced by the growing demand for education. – Ian Jan 16 at 15:24
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    @Buffy Here I really mean professors. I would venture to say that going from a PhD into an adjunct position is not a very desirable outcome for most people. – Ian Jan 16 at 15:40
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Is a math degree useless financially? Yes, if its just an undergraduate degree.

What about a masters in math? More useful, but still quite useless comparatively to other degrees, unless you back it up with other skills (e.g. I know software developers who've gone into data science/machine learning positions, but that requires self-learning software development on the side).

What about a PhD in math? Much more useful than either a masters or an undergraduate, but mostly for the purpose of enjoying a career in Academia. Since that's not usually well-paid for most people, that doesn't seem to be what you are aiming for (and yes, the fact that Academia is also highly competitive with loads of pressure is yet another reason to avoid that path if you aren't extremely passionated about research. That's the only way you'll be good in Academia, except if you are some sort of genius). There are however other alternatives: you can get a job in finance (again, if you back it up with other skills, like learning financial theory and/or programming), and a job in banking does pay quite well, but if you aren't interested in that sort of thing (don't blame you), then there aren't really that many options left in the industry. People will tell you fairy tale stories about how their math PhD got them a job working with this or that, but the truth is that none of those jobs are guaranteed and your math degree isn't structured for it. At best, you'll still have to spend an enormous amount of time self-studying whatever stuff you need to work in whatever random industry you got hired into. The truth is you won't walk into any industry apart from banking or teaching and be able to dazzle people with your math knowledge. Your math knowledge is and always will remain a nice bonus. Nothing more. You have to be able to offer more.

Personally, if financial gains were my main worry and I wasn't particularly fond of math (which you don't seem to be), Electrical Engineering is a complete no-brainer. Lots of jobs, salary's decent.

Oh, and please don't listen to people who say that a degree in math "improves your analytical thinking" and blah blah blah. As if a degree in Electrical Engineering doesn't do the same.

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    No, a math degree is not useless financially. It will not bring you riches by itself, but you can get your foot in the door in a lot of different areas with a math degree. Generally speaking, the value of a degree is to get your foot in the door. Unless you go to a top institution, and get top marks in a highly sought after degree, financial well-being will largely be based on what you do after your enter the workforce. – The Gilbert Arenas Dagger Jan 16 at 17:54
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    Unless you go to a top institution, and get top marks in highly sought after degree, financial well-being will largely be based on what you do after your enter the workforce. If this were true, then adjusting for people who got high marks in degrees from top institution, we ought to see no difference in the salary earnings of workers when clustered by degrees... but we do. So the only explanation is either a) Mathematicians are just dumber and lazier than others once they enter the workforce which I don't think is true, which leaves option b) math earns less. – Marqui Jan 16 at 17:59
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    @Marqui I think you may be conflating degree with actual field of work... Only a small percentage of people (per Google--slightly less than a third) actually end up working in the same field their degree was in. For the rest, what field you end up in is a bigger indicator of pay than what your original degree was. – user3067860 Jan 16 at 18:22
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    @Marqui Do you have any factual support or sources for your argument that "math earns less?" – TimothyAWiseman Jan 16 at 20:59
  • I know nothing about EE, but what you write about maths seems right to me. – Carsten S Jan 17 at 12:31
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Is a math degree really useless financially?

I guess you mean PhD., as you seem to have already double majored in EE/math.

I am so confused and I do not know which paths am I supposed to take? do a phd in math or electrical engineering?

From a financial perspective...
the path to the greatest in lifetime earnings is probably to get an EE (or math) job now.
That's four (+/-) years more of income and you won't have to pay to go to school anymore.

Normally my advice is follow your passion, but you don't seem to have found your passion yet (from your post at least).

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I am so confused and I do not know which paths am I supposed to take?

Only you can answer this. Whatever path, it has to be one that you will be motivated to stick with through your PhD.

With that said, assuming math is what you enjoy, why not consider combining a math PhD with another subject? In other words, you focus your work on math, but are integrating it with another field that interests you and opens up employment opportunities that a pure math degree might not have. In effect, consider being coadvised by someone in another department where math can be used in a more applied research context (The caveat being that if you are already in a program, you may have an advisor that may not allow it.)

The reality is that math has applications everywhere, whether it's physics, chemistry, engineering, economics, biology, ecology, computer science, geology, etc. In my case, I'm doing the reverse. I'm just beginning a PhD in wildlife ecology, but I've always had a strong interest in math, so I'm actually going to try and take several graduate level courses in math. The benefit being that most people in my field dislike math, yet there is a strong need for people capable of integrating advanced mathematical concepts into ecology. For example, we use things like network theory for modelling landscape connectivity for different species, which has real world uses for conservation, but this integration is only relatively recent in ecology, and is still be developed and built on.

If your biggest concern is financial success, then integrating computer science into your program could really set you up for success. Computer science, like math, has applications everywhere, so the two combined will give you a lot of flexibility. You can look at the type of research being done in computer science to get an idea of the different things people are working on. Depending on the approach you take here, you could probably set yourself up for a nice future as a data scientist.

Or you could do something entirely different. I know someone that was a mechanical engineer working on space shuttle related projects before starting a successful PhD program studying bears. Despite not having a biology related degree, they were probably able to pitch their math and computer background as strong selling point.

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A math degree provides evidence that you are a strong problem solver, that you can grasp and apply logic, and that you are comfortable with algorithms. These skills apply to many areas. You have the opportunity to find what you are passionate about and pursue it. Many jobs say something like candidates must have degree in X, or other related field. Math is almost always accepted in the other related field category based on the skills it demands. However, a math degree in itself may not always be enough, so you should be prepared to develop specialized skills.

What you are asking is really a personal question that you will be able to answer for yourself better than any of us can do. That said, I do would not recommend a PHD in math if you do not know how you want to use it. You need to find your passion. It's OK if you don't know and if you don't get it right in your first job, but by entering the real world you will get exposure to real life things that you like and dislike.

I was a math major and found myself in a similar position. I started out at an actuarial company and switched to a software development. Both paths required time outside of work to learn the specialized skills required by the job, but the problem-solving skills demanded of a math major have provided an excellent foundation.

1

My undergraduate degree is in pure mathematics and it opens many doors. First, remember that there are a lot of jobs which require a degree but are not overly picky about which one. For instance, I started my career as an Army Officer after receiving my bachelors. A degree is a requirement and a math degree in particular opened the door to Military Intelligence.

Math is also an acceptable starting point for many careers that are tangentially related. After leaving the army, I became a programmer and database administrator for a while. I know others with math degrees that went into financial analysis

Math also serves as a basis for many related graduate degrees. I went into law after I decided I did not want to continue in programming.

And that is to answer your direct question about the value of a pure math degree. You said you also have an electrical engineering degree. While a masters is very helpful if you want to go into work as a true electrical engineer, a EE degree opens a huge array of doors by itself. I know many other programmers that got an EE degree to start.

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I got a PhD in pure math, got a job at a financial company, and I am very well paid.

For full disclosure, I did have a small amount of trouble getting a job at a financial company. I interviewed at maybe 5 companies. I was first hired by this company as a lowly programmer (in the last year of my PhD program), then after I got my PhD I applied for a job on the modeling team. You could say I snuck in.

  • Why were (or weren't) you hired? – Xen2050 Jan 17 at 3:13
  • @Xen For most of the companies I wasn't hired due to lack of financial knowledge. For JP Morgan, they wanted a C++ maven, which I didn't qualify as. I was hired at my current company for my initial job because of my Java programming skills. The modeling team then hired me because of my intimate knowledge of the internal system. They were really looking for someone who knew finance in the posting, but they accepted someone who they don't have to teach about the internal system who has a PhD in math as the next best thing. – Matt Samuel Jan 17 at 3:24
0

As already said, the answer is No, it isn’t.

Among the thousand or so software engineers and systems engineers at my first civilian job, many were math majors.

0

I did a PhD, left academia and have worked a career in areas for which that is an asset. Never had to use very advanced maths, but 'mathematical thinking' has been essential.

A key thing to observe is that maths comes under two well known labels:

  • Pure
  • Applied

When in academia this can sometimes seen a trite distinction, commonly with a bit of snobbery thrown in.

Outside of that, 'applied' also means that you have to take a problem and translate into mathematical form. No longer can you 'given such and such' or 'assuming that'. You need to take the data that you are given and determine the conditions it satisfies, or fix it so that it does. You typically need to translate the business problem into abstract form, solve it abstractly, then implement in software. In fact, even to get the first of these involves a ton of talking to people and language skills.

Think of such roles such as:

  1. Data Scientist/ Analyst : A huge growth area. The Analyst very well paid and mathematical
  2. Operations Research Analyst : Cool, but not that may positions available.
  3. Modeller - finance: Still a lot of jobs, well paid, but you may have reasons not to
  4. Modeller - defence: Still a lot of jobs, quite diverse, but you may have reasons not to
  5. Modeller - other: Fewer jobs, can be very interesting and valuable.

So, if you think you'll want exit academia after PhD, the specific additional knowledge a employer will look for then is programming. If you have EE, you most likely already have some knowledge. Continue to build on that during your PhD. Maybe take some courses through institution or online. Learn about OR and Data Science. You'll then be well set up to find a good position on a good entry salary.

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