It seems to me that most of the companies that hire programmers are looking for C++, Python, Java, etc. skills but very rarely I saw in a job post any requirements about MATLAB. Do you know any company which hires people for MATLAB programming (+ research)? This was extremely useful for me in my research as a grad. student (because I could spend most of my time thinking about the problem than writing code) so I guess there have to be also firms that realized the advantages of MATLAB...
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In addition to Andreas' advice, I'd also add that you might what to broaden your search to include the job titles "engineer", "scientist" and "reasearcher". Depending on the employer it may not be considered a "programming" position.
There is also a section of the MathWorks website where "User Stories" are written. They can be reviewed by company, product, industry, application or academia. This might provide some useful data for where to look for open positions.
On a more personal note, I found the book "What Color is Your Parachute" to be amazingly helpful when I looked for my first job out of college years ago. It's updated annually by the author, so it's always up to date with relevant advice for people looking for a new position.
I am smart and I know Matlab so I got my job at the company I'm working for (the details do not matter here). My Matlab skills have been an important argument to hire me and I've programmed 2 lines of Matlab code for my job in the last year. And this does not mean that something went wrong. It means, that the staff department searched for someone, who is able to use computers to solve problems and especially Matlab, if this tool matches the specific problem. But most of the problems could be solved with much simpler tools also, e.g. Windows-batch files, Unix shell scripts, R, PhotoShop and Excel. In the last case, I would have preferred Matlab, but the team had an already working Excel sheet already, such that teaching them how to use Matlab would have been a waste of time. But I could decide against Matlab only because I know Matlab well.
A company, which employes computer scientists, expect them to learn and use new features. I've done my first steps in Matlab 15 years ago with Matlab 4.2 and there are big differences to modern versions (except for the GUIs...). Keeping in touch with such changes consumes more time than learning how to use e.g. the Financial Instruments Toolbox, when you have an education in financial science. Therefore your question sounds like: "I have a 32mm open-end wrench, who will need this?". But the companies have problems like: "We build bikes. Currently one of the steps requires a 32mm open-end wrench, but this will most likely change in the future and there are dozens of other problems to solve also". Anyhow, this does not mean that a professional handling of this tool is a drawback. But it will be only a small piece of your work in the next 40 years.
Years ago, while in grad school I decided that it would be best to learn one programming language very well, instead of a lot of languages at a mediocre level. I settled on Matlab. In the early 90's it was not the behemoth that it has become, so I chose well. Since then, at every hiring I have requested a copy of Matlab. I have never been turned down, and usually they are impressed that I am so attached to a mathematical tool. While I have still needed to produce products that require software or firmware written in C, C++, Ada, Fortran, C#, Perl, etc., my Matlab coding skills have transferred over relatively well, and I usually can get the help I need for the other languages. And I get to use Matlab for all my design and analysis!
If a company didn't get it for me, and I felt I needed it, I would either change jobs, or buy it myself. Consider Matlab as a skill and tool that you can offer a company. Most companies hiring engineers will be glad to get such an asset, even if no one else there uses it.
The goal of (most) companies is to solve problems efficiently, while the programming language is the tool only. Even the costs of a commercial license of Matlab can negligible compared to the payment of the staff members and to the profit. Therefore you should apply for job opportunities even when they ask for C++ skills: "I could implement this in C++ in 4 month, or with Matlab in 2. Therefore I suggest to employ me and buy Matlab." This can be more impressing, especially when 40 C++ cracks apply for the same job.
Well, all these answers sound good but I would like to hear from someone which can say: I am smart and I know Matlab so I got this job at this company (without knowing c++, c#, java, python, perl, and other 25 languages). Anyone?
I agree that the programming language is only the tool, and that's why I never tried to learn 10 different languages as long as Matlab was always enough for my research. I learned in high school C, Pascal, but after finding Matlab I don't feel like I would like to use other languages which will solve the same problem after writing 10 times more code...
Also, Matlab has all these specialized toolboxes. For example all the financial-related toolboxes (Financial Toolbox, Financial Instruments Toolbox, Econometrics Toolbox, etc.). Does anyone on Wall St. (or anywhere else) use those toolboxes? For example at a presentation of Morgan Stanley last week, they said that the first test that you have to pass before an interview is about C++/Java (clearly they didn't mention Matlab). It seems to me that even if I learn all these specialized toolboxes, it is very unlikely to end up in a place where I can use those. I hope I'm wrong.
I think it would be very helpful if Mathworks could create a better webpage with the companies which use Matlab / appreciate Matlab skills / have Matlab-related job offers. This would encourage many young scientists to learn Matlab and to discover its benefits.
There are two "groups" of employers of people with MATLAB and Simulink experience: MathWorks customers - and MathWorks!
For MathWorks see job openings here: http://www.mathworks.com/company/jobs/opportunities/
For MathWorks customers: The point here is if you want to be involed with r&d yourself or be a programmer for the r&d people. In some industries, the r&d people are more likely to have MATLAB & Simulink skills than in others. It would be unwise to specify this hear in the public though.