A learning strategy that has served me well is to look at syllabus and recommended texts for an academic program closely aligned to my interest. Going through recommended texts in these programs on my own has helped me gain more structured knowledge on the topic of interest. Each successive module builds on previous modules.
In your case, you want to check out academic programs related to financial engineering and computational finance such as at Baruch, Carnegie-Mellon, UW etc. Here is a link to UW Computational Finance and Risk Management curriculum: http://depts.washington.edu/compfin/content/ms-degree/curric.... The link to course description shows the recommended textbooks. Going through these books will prepare your well to be a Quant.
In case you want to see recommended readings from other programs, check out list of financial engineering program at https://www.quantnet.com/mfe-programs-rankings/. I am sure some of them have detailed syllabus and recommended readings available on Interest.
A few other resources for recommended readings:
Quant net Forum Book section https://www.quantnet.com/forum/books.37/
Quant net Master Reading List https://www.quantnet.com/threads/master-reading-list-for-qua...
