Hello HN,
I work as a software engineer in the business and web application world. I love programming and am quite successful at it, but I'd love to transition into scientific programming and data science. I have an undergraduate degree in the humanities, so my quantitative background is honestly a bit lacking. I've considered a second undergraduate degree in, say, math and physics or electrical engineering to fill the gaps. In an ideal world I pursue my studies independently, but my day job doesn't leave me with much free time, and frankly I'm not sure how seriously I would be taken without a proper degree.
Advice from science and data hackers is much appreciated.
1. _Stats: Data and Models_ by De Veaux, Velleman & Bock
2. _Fifty Challenging Problems in Probability with Solutions_ by Mosteller
3. http://yudkowsky.net/rational/bayes
Basic data analysis:
1. _Python for Data Analysis_ by Wes McKinney
2. http://camdavidsonpilon.github.io/Probabilistic-Programming-...
3. _Exploratory Data Analysis_ by Tukey
4. _The Visual Display of Quantitative Information_ by Tufte
Tools:
- R & ggplot2 & (Sweave | knitR)
- Python & numpy & pandas
- UNIX tools (https://news.ycombinator.com/item?id=6046682, https://news.ycombinator.com/item?id=6412190)
- basic SQL (https://schemaverse.com/tutorial/tutorial.php)
- data visualization: (R & ggplot2) | (Python & matplotlib) | d3.js
- OPTIONAL: C/C++/Java for hardcore Bayesian stuff, Julia for being cool, Fortran for specific academic domains
On getting people to take you seriously: If you knew the stuff up there, I would take you very seriously, even without the STEM degree. You can pick this stuff up outside the classroom (in fact it might be hard to find uni classes that cover this stuff). So if you did self-study, and blogged about it or something, people would take you seriously (esp. if you got good at something "hot" like d3.js or Bayesian). In fact, given your background in web / software / business, you could be considered even more valuable (by web / software / business people).
What are you interested in specifically? Where do you want to end up?