I'm a 20-year-old Singaporean who got rejected by the local university as my high school grades were terrible. However, I have self-studied a good amount of math in my free time, including the standard undergraduate fare and some graduate-level topics (e.g., measure theory and graduate real analysis from Tao, computational complexity from Arora–Barak, etc. — as evidence, I have written detailed solutions on my website [0]). As additional proof of my geekiness, I also have 0x$5d.60 in Don Knuth's Bank of San Serriffe [1] for finding bugs in his books, making me the 14th richest person there.<p>But I have little to show for all of this — no fancy grades or awards, and no publications either. I'm not sure what to do at this point, since it'll be another year before I can apply to any universities.<p>I'm quite lost. Should I just find a job? Should I push myself towards publishing something? Should I sharpen my programming skills and try to get hired? I'd love to just be alone and study my own math, but it seems that it is finally time for me to face the real world.<p>What should I do? Thank you.
(I will do my best to answer any questions you may have!)<p>[0]: https://boonsuan.github.io/misc/
[1]: https://www-cs-faculty.stanford.edu/~knuth/boss.html
You should look at it from their perspective. You are a smart person who is capable of the work, yet still had bad grades. You don't need to show them you are smart and capable of doing math - it is not about that. It is about whether you can do those things in a structured school environment. Stop trying to prove you can do math and start trying to prove that you can work within their system.<p>I don't know the school system in Singapore, but in the US, we have community colleges that accept everyone. Most people in your situation take a few classes at a community college to prove that they can succeed in that environment, and then try again with the university. If there are similar option in Singapore, I'd go that route.
A math major will require you to take a bunch of courses that you don't need. For example, imagine spending an entire semester just to learn induction and some very basic proofs. Even if you think you understand the material, these courses won't be easy. There will be a high volume of arbitrary homework and passing exams often requires drilling rote computations.
Research the math faculty at various universities.<p>Reach out to <i>a few</i> individuals to explain your situation.<p>Maybe you can get in through a side door.<p>Or consider emigration to a place with more open higher education...in the US community colleges are open to pretty much anyone.<p>Good luck.<p>Edit: Write to Donald Knuth and ask for a letter of recommendation.