7

I know that Scott Young tried this for computer science by utilizing resources on OCW. I am more interested in mathematics (pure and applied). I wondered how feasible to do the same thing for mathematics.

As for my background, I was in a much worse situation than Scott's. I received no formal education (primarily for financial reasons) since I was 19. English is not my native language. And I am 28 now and know very little mathematics (or at least according to my own standards). All I have is interest and determination. I worked as a computer programmer for the past years. Although MOOC was declared failure as revolution since it is criticized to be preaching to the converted, but it does benefit people like me a lot. I plan to apply to AMSS, a top mathematics graduate school in my country. The only good thing about the system in my country is that the entrance of a school is only determined by the entrance exam and interview. This means my lack of college education will have relatively little negative impact on me. The only thing I worry about is my age. I feel I am just too old to do anything great. Look at those wunderkinds who always achieve great things at young ages. However, five years ago, I audited for half a semester at Fudan university (a school famous for its mathematics program). I didn't find the average math students there are impressive. I was doing very well for that half semester and students there actually asked me for clarifying some concepts. Therefore, I do believe I have an aptitude for math. My goal is really humble and I just want to make a living by doing things I love.

  • 17
    If it was feasible to learn all of undergraduate math in one year, why would everyone spend 3-4 years doing it? – Dan Romik Dec 5 '20 at 6:48
  • 1
    To continue with @Dan Romik's comment, even those "wunderkinds" didn't learn all of undergraduate math in one year, at least not the vast majority of them. (However, I did know one person who did this in 18 months -- beginning calculus through standard upper level undergraduate material. He was from China, attended Indiana University's graduate program afterwards for one year 1982-83, then managed to get into the graduate program at MIT.) – Dave L Renfro Dec 5 '20 at 7:01
  • 1
    What course did you attend at Fudan university? Who were your classmates? Math students or students from other departments? AMSS is one of the best math academy in China. You must be super good to get into. Did you consider other places? – scaaahu Dec 5 '20 at 7:17
  • 3
    I believe it could be learned in one year, but I also believe there is no reason to try to do it. – Anonymous Physicist Dec 5 '20 at 8:24
  • 2
    Age is no barrier to further study. You'll be 29 next year regardless of whether you study maths or not. – astronat Dec 5 '20 at 9:51
21

I see that this question is being voted down for being interesting, so let me blacken my own reputation by addressing it.

Mathematics undergraduates do not study mathematics. They study studying, they study structuring their time, they study the work-life balance, they study manipulating their teachers, they study the opposite sex,… and in their spare time they also study mathematics.

As an adult you therefore have a considerable advantage over the children because you have studied all those other subjects and graduated in some of them. That means that unlike them, you can devote 100% of your time to mathematics.

On the other hand, there is a natural pace at which one can learn. Learning is not a conscious process but an unconscious one, and we have very little control over how fast the unconscious mind decides to process things.

Moreover, in mathematics 90% of one’s learning time is completely wasted - the remaining 10# then more than makes up for it. When you are learning from people and with people, this process adjusts itself naturally. When learning in isolation, it is not clear that it will. You do need someone to guide you. The guidance is not actual tuition (as it would be if you were an 18-year-old child) - more, it is mentoring. Your guide will tell you things like “yes, that concept is difficult” or “this book’s approach does not suit you: try that one instead”.

So think hard about who might be able to guide you. It doesn’t necessarily have to be someone senior. I don’t know enough about your situation and environment to be able to advise.

BUT I have read your question a few times and I cannot understand why you are specifically talking about one year. There may be good reasons for it - but without those reasons, it sounds unnecessarily restrictive. You will certainly be able to learn some one-semester subjects in a couple of weeks. But there will be others that will take far longer than you expect.

Overall though: the signs are good and don’t worry about being too old!

  • 3
    +1 for the second paragraph. There is much more to studying as an 18-year old than the subject. It's also often the first time you have to earn your own living (and, even as a mathematics college instructor, I have to say, the non-mathematical skills/friends/sexual experience/hobbies often help you more in life than the mathematical do. I pity every young person who does (and often, has to do) devote their whole life to studying.) – user111388 Dec 5 '20 at 10:20
  • 1
    One year schedule is just tentative. I'll see how things goes and don't mind extending it to two years. If longer than two years, I will declare myself not a good fit for math and just go back to the computing industry. One reason for one year is age and another is the fact of being without any income during the time. You could call both of them status anxiety (old, not working and not formally matriculated, essentially a NEET). – Lei Zhao Dec 5 '20 at 11:14
  • As for mentor, would you kindly mentor me? Currently, I almost finish 6.431x on edX. I plan to do quick review of calculus with 18.014 and 18.024, and then start the proper analysis series (18.100C, 18.101). As for algebra, I plan to do 18.700, 18.701, and 18.702. If time permitted, I wish to finish Stein's four books on analysis, Zorich's two books, and Godement's four books. My primary interest for graduate study is mathematical logic and set theory and I want to study with Qi Feng at AMSS. – Lei Zhao Dec 5 '20 at 11:36
  • 6
    ...you must have gone to a different university compared to me as I was busy with my maths degree... Though maybe because I was focused on the university degree I would have liked more content... Content density will also depend by country and university. – DetlevCM Dec 5 '20 at 17:32
  • 1
    One thing I would like to expand on as it comes to time spent to learn something is that there are varying depths to which you can know something. If you read through a calculus book as fast as possible you could learn all of the definition, notation, and big results pretty quickly, but you might not be as good at using the ideas to solve problems or prove new theorems as a student who studied the subject for months. And that's okay! You don't need to know everything in-depth, but there will always be more to learn even in subjects you think you already know! – NaturalLogZ Dec 6 '20 at 2:08

Not the answer you're looking for? Browse other questions tagged or ask your own question.