I don't have former experience or education on finance, but I want to find a job in finance so I can gain more knowledge about it to help secure the future financially. I have a strong background in science, so I think I'm competent on math, programming, and researching. Questions like Where to start with personal finance? or Ongoing things to do and read to improve knowledge of finance? are useful, but I'm looking for a job as well.
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I don't know whether these types of training programs still exist, but in the past investment banks would have extensive training programs that rotated trainees through different departments. This would give extensive experience in the issuance and creation of debt and equity securities. I've heard of some banks, Chase in a particular case I think that did a similar rotation through different departments, but more on the retail side with banking, investments, and loans.
You could also take a job as a financial advisor trainee. You'd study for at least the securities license exams, and depending on the firm you chose, also possibly insurance licensing exams. The exams are fairly poorly written and the study materials sometimes more so. They do not reflect reality very closely. But you would still get a greater background in finance than without studying for and passing them. Your on the job training, depending on the firm, would likely be the most valuable part of learning finance.
All that said you definitely do not need to get a job in finance to learn finance extensively. There are plenty of options from self study, college courses, seminars, community education classes, and possibly free MOOCs where you can learn finance to almost any level of depth you like.
IMO getting a finance related job to improve personal finance is an overkill. It's like saying you want to be an English professor to speak more fluent English in daily life.
At personal finance level, I think you will be fine by just following the common sense principles (don't overspend, save emergency fund, diversified your investment, pay off high interest debt, etc.).
If what you are interested in is a finance career, with strong background in math, programming and researching, but no finance related degree, then IMO the position you want to search for is quantitative researcher or trader. Many firms don't really require a graduate degree or finance related degree to apply for the job. However you will have to demonstrate you really have the skill you claim to have (by doing near perfect on math or coding test if you receive one) in the interview process in order to have a chance.
If you are good at math, you can always apply for quantitative analyst positions in the banks/funds (these are typically fresh grad from physics/math/engineering who have zero experience in finance). If you are good at programming, there are a lot of financial technology companies now days (this is the easier route). Just prepare the same way as you would prepare for interviews at any software engineering role at a tech company.