TITLE: First job in industry for a pure, pure mathematics folk
QUESTION [36 upvotes]: this is an "almost" Ph.D. in pure maths who's got a few reasons to look for a job in the industry.
I know that many choices are out there for a math guy: finance, consulting, industrial research, big data analysis, machine learning...
My main problem is that I have a very theoretical background, mainly in metric and geometric topology. In the last years, I've been decently active in learning a few programming languages (mainly C++ and Python) and some fundamentals in both supervised and unsupervised machine learning.
I would love to find a job in this interesting area, and I believe it is a sector which is quickly expanding, given its many applications. Research jobs in the industry would be appealing too, but I believe they would require a bigger amount of knowledge in probability and partial differential equations, which I do not know.
Any job which makes use of maths in a creative and stimulating way, to solve real-world problems, would be appreciated. 
Looking for job ads, I realised there's not much choice for people who have such a theoretical background as me. I would be interested in any advice regarding how to switch from a pure maths position to an applied one. Unfortunately, I can't go through more courses, as I need some financial support and I could not afford paying for an additional master or any other specific course in applied maths.
Ideally, I guess I'm looking for a company which is willing to allow its employees some period of training, before they start with the actual work.
I'm currently based in the UK, but I wouldn't mind moving to a different european country. 
Thank you in advance for any recommendations you might suggest!

REPLY [6 votes]: As a graduate in pure math after a masters from Cambridge with top grades and having recently come through the road of getting a great first offer from industry I feel obliged to give my advice.
Zero: if you're indeed extremely smart and is motivated by money (who isn't to some degree?), you might like to try for things like Jane Street, Optiver or Citadel which doesn't need too much/any experience. If not...
One: if you don't have much previous experience in industry, you must expect the process to be very painful and be mentally prepared. I had over 10 rejections before my first offer (and that's rejections after getting through the first stage of the assessment process, the number's more like over 20 if you count the submitted applications). At first I felt depressed because I had spent so long learning so many difficult pure maths concepts only for it to all go down the drain in terms of industry requirements. Because I had attended a careers presentation by a PhD graduate who said exactly the same thing, it made the experience much easier to handle. When you get rejected always ask for feedback and ask yourself what you could have improved. I think this mental aspect is most important, don't fool yourself into thinking "I've got a PhD so I can walk into a great job in industry without extra effort". You have to do something extra. 
Two: it's good that you mentioned data science. That's what I ended up focussing on as well! One great thing is that you can take free courses online. E.g. the Coursera machine learning course, and that takes only two or three days to complete if you do it full time. Also you can prove your skills on Kaggle which seems to be industrially recognised. Other MOOCs of note: Udemy, Udacity, KhanAcademy. The former two cost some money but way less than a masters say. 
And good luck finding your dream job!