I’d encourage you to just apply to some good programs, don’t get psyched out by your perceptions of the competition.
Grades, papers, recommendations are all important, but they’re not everything. There’s a certain randomness to the graduate admissions process - different departments have differing values and priorities, and often the graduate admissions committee is different year to year. Many departments just use grades and such as a heuristic to help narrow the pool.
A demonstrated ability to write well (put time and care into your statements) and think independently count for a whole lot.
I'm more or less going this route. My current plan, if I do strike out completely, is to enroll non-degree near my hometown and build some credentials & relationships in the local department while working. It's a top 50 Mathematics program, so it should still provide what I'm looking for.
Grades, papers, recommendations are all important, but they’re not everything. There’s a certain randomness to the graduate admissions process - different departments have differing values and priorities, and often the graduate admissions committee is different year to year. Many departments just use grades and such as a heuristic to help narrow the pool.
A demonstrated ability to write well (put time and care into your statements) and think independently count for a whole lot.