11 ms·

Physics and Mathematics Self-Study Project

364 points by JoeDaDude 4y ago

melling 4y ago
I've been studying MIT's OCW for Probability with a partner. It's a great course. https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-an... We're 4 months in and on Lecture 15. These do take a while. I feel like I'm not getting everything and will need another round. I've been binge watching Stat 110 too: https://projects.iq.harvard.edu/stat110 https://projects.iq.harvard.edu/stat110 "All probabilities are conditional"
- sy7ar 4y ago
  Very nice. Where do you find a study partner?
frognumber 4y ago
Context would be nice here. Who is this? Is this am unemployed autistic kid with nothing else to do? A brilliantly gifted high school student? A software engineer? A college student at a school without relevant courses? An independently wealthy semi-retired rich kid? Why? To be macho? As an alternative to college? To level up his skills? Quick web search answers a few of those, but not all of those. If OP is the creator, look at the web site from the perspective of a visitor, and give some answers. As a footnote, there really ought to be a way to give college credit for this sort of thing.
- password11 4y ago
  > Who is this? Brilliantly gifted high school student it turns out. > https://www.scotthyoung.com/blog/2023/02/21/diego-vera-mit-challenge-math-physics/ https://www.scotthyoung.com/blog/2023/02/21/diego-vera-mit-c... > Interviewer: Tell me a bit about your life situation at the time. Were you working on the project full-time? What did you do for funds? > Diego: The year COVID hit was the most transformative year of my life. I was 15 at the time. A combination of both personal circumstances along with isolation gave me so much clarity—I transformed 180 degrees. During this time, I really got into self-improvement and started working out, meditating, reading, taking cold showers etc. Personally, I did some of what he did when I was his age, but not to the same extent and I mostly decided to chill out and enjoy college. At that age it's really risky to do. Really hard to go to college and sit in classes for 4 years if you already know everything. I guess you could go straight to grad school or industry, but you miss out on a lot of the social maturity and friendships you develop in college. Learning all this is almost a curse; he will always, in some sense, be alone in his newfound abilities. (Sorry for the edits. Done editing before any child comments.)
  - btheshoe 4y ago
    nah, i have plenty of similarly smart friends who are doing just fine. he'll fit right in in some college environments, and he can take the time he's not wasting doing class and pursue real things that matter, like research.
  - dopu 4y ago
    I disagree, I think it will provide him with a great foundation for college. As great as online learning is, I don’t think it’s the same as taking a class that you go to multiple times a week and get in person feedback on. It also takes multiple passes at a given subject to properly understand it. I’m sure he’d learn many new things he didn’t quite get from his self study if he enrolled in an actual analysis course or w/e.
    - onetimeusename 4y ago
      this makes sense to me. I skimmed what he took and it says he learned real analysis, a pretty challenging course. It's one thing to listen to the lectures and solve some problems and it's another to be given a difficult homework on a very tight deadline and perform well, same for exams. I think it's extremely cool though and really a great idea but I am cautious about saying he has the equivalent of those undergraduate degrees.
      - hgsgm 4y ago
        > it's another to be given a difficult homework on a very tight deadline and perform well, same for exams. This is the stupid, broken part of school, that only exists as a cost-cutting measure. Real learning and creativity doesn't have this nonsense. It's like saying that living in a nice house is bad because you don't get to smell your poop while you eat. No one needs that. Diego is getting a better education because it isn't being arbitrarily cut short and of track before the going gets good.
        deleted 4y ago
        [deleted]
- mfragin 4y ago
  As a former teacher of math and comp sci at a pretty low socio-economic school in (US) Colorado's front range, I can attest that kids like this are out there. Before I gave up on teaching as a career, it was kids like this that kept me going.
  - sethhovestol 4y ago
    Mr. G! I was just looking back at Robby the Robot stuff from my time at skyline! You should email me so we can catch up! Pick nearly anything at my lastname dot com to reach out!
mjfl 4y ago
People love self-study materials, but do you really have the time to absorb it? Yeah you could do this stuff every day after work, but then you may not go to the gym, go on that date, etc... Not enough time in the world to go through even a single learning resource people promote.
- susam 4y ago
  In 2021, a bunch of us, software engineers, did a small book club to learn analytic number theory from a book written by Apostol. We met for 40 minutes a day and read every line of the book and every page of the book in great detail. We did it for the joy of learning. It took us 79 hours spread across 120 days to complete reading the book and gain a good understanding of analytic number theory along with the analytic proof of the prime number theorem. Meetup log: https://susam.net/maze/meet/iant/log.html https://susam.net/maze/meet/iant/log.html A few blog posts about it: https://susam.net/maze/tag/iant.html https://susam.net/maze/tag/iant.html
  - wheelinsupial 4y ago
    I skimmed your blog posts and logs, so apologies if I missed it. How many problems or exercises did you work through in the book? Did people put in any additional time individually between sessions?
    - susam 4y ago
      I can't speak for all participants of these meetings and I haven't kept an exact count of the problems I solved but I believe I must have solved somewhere between 160 to 200 problems from the exercises in the book. See also https://news.ycombinator.com/item?id=34908191 https://news.ycombinator.com/item?id=34908191 for more details on this topic.
  - FiberBundle 4y ago
    Sorry, but you don't properly learn any math topic in 80 hours. I've spent more than 10 hours on some problem sets in difficult courses. Solving hard problems takes a lot of time and is absolutely essential to learn math. When you read a book or a script you feel as if you have grasped the content, but most of the time you really haven't. It's only when you attack problems from different angles that you really build intuition for the concepts taught in that book.
trollerator23 4y ago
Holy shit that's ballsy. In 2 years? There are quite a few of tough courses there. Respect.
Ralo 4y ago
I would love to learn a much deeper level of mathematics but where do people find the time for that? If it's not related to work, or future work I couldn't find the large amount of time required. And self study doesn't get recognized on resumes very well. Perhaps spread out over the course of many many years on your own personal time.
- d4rkp4ttern 4y ago
  Indeed, “work” prevents learning. One of the reasons I like freelancing is that I can intentionally set aside 15 hours a week to catch up on areas I’m very interested in. Yes I don’t get paid for this “learning” time but I see this as an investment.
- nohaydeprobleme 4y ago
  > "Perhaps spread out over the course of many many years on your own personal time." That is a very workable approach, so long as you consistently study. For motivation, if you'd like to get better at mathematics just as a life goal, that should be valid enough to spend time on the hobby. If you're studying primarily for personal enjoyment and fulfilment (and especially if you find joy in the process of learning), the slower pace doesn't matter as there are no expectations to learn quickly. If you're studying mathematics or a technical subject for work, I believe it's better to earn a graduate degree from an accredited program for the resume (as a record of passing proctored exams is seen by hiring managers as strong evidence of learning), plus it's nice to be able to learn from your fellow students and ask the professor questions. For myself, I've found it much easier to find motivation to consistently self-study mathematics outside of accredited coursework by practicing out of personal interest, as it eases up a lot of pressure about learning a certain concept by a certain time. I won't expect to learn as quickly as the person's reported progress in the submitted article, but this also makes the practice more enjoyable and easier to keep up in the long term for myself.
- paulpauper 4y ago
  I would love to learn a much deeper level of mathematics but where do people find the time for that? Setting aside 1-2 hours a day should be enough. I think this is not unreasonable for most people. But why? Unless you need it for a resume or degree, I don't think it matters that much. So you can make a blog post about it?
hnthrowaway0315 4y ago
I'm thinking about a historical approach. For example what exactly is Ptolomy system? What's the math involved? Why did the phases of Venus rebutes the model? How did Tycho make his observations? Can we repeat it for say a few months? How did Newton come up his ideas? What are Einstein's thought experiments. Basically I want to put myself in the shoes of great minds, learn what math tools were available at the time, do their observations, know how their thought processes work. edit Would appreciate if someone could recommend a textbook that follows such approach.
- nohaydeprobleme 4y ago
  Though I lack personal experience with a historical approach to studying mathematics, a starting point could be the reading list by St. John's College as part of the materials the faculty uses to teach mathematics to their undergraduates: https://www.sjc.edu/academic-programs/undergraduate/subjects/mathematics https://www.sjc.edu/academic-programs/undergraduate/subjects... Readings include Archimedes's "On the Equilibrium of Planes" and "On Floating Bodies" and Nicomachus's "Arithmetic." However, I've heard of some mixed reviews on the effectiveness of learning math [1] [2] via reading historical texts at St. John's, versus more traditional approaches today in good mathematics programs. A bit separately but as a related idea, I've spoken to a couple people who said they preferred older mathematics books from the 1900s to the 1960s for their studies over modern books. I personally prefer modern books with recent editions that are well-recommended, as they usually have good visualizations of ideas and shouldn't frequently have errors (due to their reputation). If you're studying as a hobby, though, the most effective mathematics book, assuming it's reasonably reputable and heard-of, is the one that interests you enough to stick with it for consistent study in the long-term. [1] https://old.reddit.com/r/stjohnscollege/comments/ehcem3/how_are_the_math_courses_at_stjohns/ https://old.reddit.com/r/stjohnscollege/comments/ehcem3/how_... [2] https://old.reddit.com/r/stjohnscollege/comments/ngpu0i/math_at_st_johns/ https://old.reddit.com/r/stjohnscollege/comments/ngpu0i/math...
  - password11 4y ago
    If you go through for the "great books" approach, just be aware that it's not the same curriculum as a major in mathematics: > Mathematics is one of the many subjects studied in the college’s interdisciplinary great books curriculum. There are no majors at St. John’s. It may be fulfilling from a humanistic/personal development perspective, but you won't really have the tools to do anything useful like cryptography, algorithms, physics, statistical inference, data analysis, etc., which, in my mind are the really cool things you can understand by learning math.
paulpauper 4y ago
Pre-calc to quantum field theory in 2 years? nuts
- Koshkin 4y ago
  Unless you do it by working through the Demystified series, of course!
- whatshisface 4y ago
  It sounds reasonable to me, a four-year degree at most universities is about half non-major classes.
  - paulpauper 4y ago
    It's not really a time issue. It's more of a learning issue. I tutored math one-on-one and even of the smartest kids in my cohort found it hard to get calculus; there was a major learning curve for sure. No amount of time will help if the concepts do not click. Feynman-level of physics means you need to understand stuff like variationals, etc which is well above your typical calc course. Shows how truly exceptional this person is.
    - whatshisface 4y ago
      I don't think variational methods are that big a step beyond integration by parts.
      - Koshkin 4y ago
        The Lazy Universe by Coopersmith may provide some intuition as well.
raydiatian 4y ago
I wonder if you could build a service that ingests self taught students’ notes, uses ML to investigate their displayed level of mastery, and upon decision associates with a university that will give them credit for a course, or even a full on degree.
admsmz 4y ago
If people want to replicate the same feats as this kid you should check out http://mathacademy.com http://mathacademy.com People are constantly talking about chatGPT and reinforcement learning but mathacademy is using AI to teach humans. And from my experience very effectively.
- boyter 4y ago
  Can also recommend https://mathacademy.com https://mathacademy.com Very impressed with what I have seen of it so far, and the founder's of it have an impressive amount of passion and drive to deliver. You can read more about it here as covered by the washington post https://www.washingtonpost.com/education/2022/10/16/math-academy-accelerated-math/ https://www.washingtonpost.com/education/2022/10/16/math-aca...
- rychco 4y ago
  The testimonials on the homepage are aggressively positive, what has your existence been like? I’m interested in revisiting the various University topics, particularly DiffEQ/stats/LinAlg, and have been looking for an excuse/resource to study.
  - admsmz 4y ago
    My experience has been that I never fail to make progress whenever I encounter something I didn’t know or was weak in. The system offers you plenty of practice problems, at just the right level, to make sure you master the material before moving on to material that builds on the previous lesson. Aggressively positive? Maybe. I have been a paying customer since october and very happy with the results.
    - rychco 4y ago
      Thanks for responding. I may give it a try!
- nsajko 4y ago
  Math Academy seems like it could be a game-changer for learning, it's a paid service and in beta-testing. They only cover math, though, at least right now. In addition to presenting the topics and providing exercises, MA automates some tasks that are usually left to the learner, like spaced-repetition and tracking down prerequisite topics. They have a detailed DAG of math topics connected with dependency relations that enables this. Basically automation of a lot of what a tutor would provide.
ecshafer 4y ago
Maybe this isn't the exact right place to bring it up, but is related. But there is a lot of self-paced learning things coming up between schools and alternative to schools. But an issue I have is that this self paced learning is really limited in scope. Why can I take classes so easily for an MS in computer science or IT, or get an MBA or take data analysis courses, but I can't easily get a degree / certificate for say a bachelors in Mathematics? Or literature? There seems to be a big split where so much is focused on job training but very little is being done on education.
- deleted 4y ago
  [deleted]
- l33t233372 4y ago
  The oft cited refrain is that colleges/universities serve several purposes aside from education: 1.) Verification, standardization, and authentication of work being done and of knowledge being gained. 2.) Networking opportunities and social/professional development and maturation in a a limited-stakes playground surrounded by others in the same social and economic class, and 3.) A sort of IQ test laundering service.
- ouid 4y ago
  The answer is that mathematics is a thing that you can actually assert that someone is doing incorrectly, but for which it will not be obvious to non-mathematicians. If a programmer writes a bad program, the user can tell. If a mathematician writes a bad proof, basically it takes a mathematician to tell. It doesn't take an incredible mathematician, but it does take one. If you want to say that you learned mathematics, you have to do more than this student did. you may have chosen to give him the benefit of the doubt, but I did not. I checked his work, and its mostly wrong. The reason that it is mostly wrong is because the practice of mathematics requires some training to get to the point where you can be relied upon to know if you are lying, and the author of this blog did not reach that point.
  - rtodea 4y ago
    > I checked his work, and its mostly wrong Can you show some examples that make you draw this conclusion? Thanks!
loveparade 4y ago
Hats off, I think it takes some real dedication to stick with it. > One of the things I found useful here was to get immediate practice once I knew just enough. I think this is one of the reasons project-based learning can be so powerful: you have a problem and research your way into it versus researching your way into it and then seeing what to apply. This. Perhaps it varies from person to person, but this is also how I learn best. I want to start with a problem, struggle to solve it, and then learn how to actually solve it. That way the material immediately clicks and sticks with me longer. Why don't schools teach this way?
- flandish 4y ago
  This is how I take to learning new programming languages. Project Euler. ( https://projecteuler.net/ https://projecteuler.net/ ) Bite sized “specs” calling for an answer to be solved in your new language. Each getting harder and dealing with important concepts to grok and hurdles to overcome.
- photochemsyn 4y ago
  It's indeed the best way to learn, but schools are charged with issuing grades to students and there are just too many problems with take-home projects (i.e. paying someone else to do it, etc.), and with group collaboration on such projects (one person doing 80% of the work, etc.), that it generally doesn't ever happen except in a few small-sized high-level undergrad or perhaps graduate courses, where the students are more motivated about learning the material then they are about gettting a good grade, or just passing the class. Hands-on lab courses are something of an exception, as you simply have to do the project yourself in class, but these tend to be long classes (three hour sessions etc.) and again are limited to relatively small groups of students. Building computer simulations in real-time of physics problems might be a way to do it, but the students would need to have good programming skills beforehand. Basically a physics hackathon using a standardized set of programming tools, that would be fun and educational.
- nextos 4y ago
  Some universities teach this way. In Europe, there are a few institutions that shifted to problem and project-based learning during the reforms of the 1960s. A few notable cases are cited here: https://www.pblfuture.aau.dk/about https://www.pblfuture.aau.dk/about. As far as I know, some American institutions use the same approach, e.g. Olin College. IMHO, when done well, i.e. having an equally strong focus on theory, this leads to excellent learning outcomes. However, at undergrad level, schools are reluctant to teach this way because it requires a lot of supervision.
ouid 4y ago
I looked through his topology problems and notes, and he could really use the guidance of a professor, or at least someone to give him feedback. It's not practical to teach yourself mathematics to start before you can really check your own work. There are quite a few mistakes and misquoted/misunderstood definitions that have no way of ever getting corrected.
- whatshisface 4y ago
  If you never see something a second time, maybe you didn't need to learn it.
  - ouid 4y ago
    What? You don't need to learn anything. Dogs don't know any math, and they do fine.
    - whatshisface 4y ago
      If he was learning physics and that stuff about topology came up, he'd notice his definitions weren't adding up and fix it. If he never saw it again then the maybe didn't need to learn it to accomplish his goal.
      - ouid 4y ago
        This is very optimistic. I watch people fail to learn things all the time without noticing, especially if they do not have the tools to be honest with themselves, which is a thing that is almost exclusively learned through formal training. Sure, not everyone arrives at that state, but they are much more likely to with guidance.
        whatshisface 4y ago
        I'm inclined to be very optimistic, because the guy is fifteen years old and the opportunity cost is League of Legends. :-) But more to the point you're addressing, physics tends to be easier to grade than math because there is a big focus on calculation, and there you can have answers in the back with no subtle questions about things like whether a student's proof skipped a step because they thought it was obvious or because they didn't know it was necessary. That is not to say physics doesn't have those questions, just that a lot of times the answer is clearer-cut. If the whole thing had been about topology it'd be different.
jdkee 4y ago
I would add axiomatic set theory and discrete mathematics to his list.
- Koshkin 4y ago
  Wolfram has gone nuts trying to make these the foundation of the “new” physics.
stonlyb 4y ago
This is inspiring. I'm a student in the Arizona State University online Physics BA degree (soon to transition to BSc). And by student I mean adult learner with a full plate of other commitments doing this for fun and I dont know when I'll finish.
- admsmz 4y ago
  Maybe a long shot but is there a course on “Geometric Algebra” offered by ASU by any chance? The founder of GA, David Hestenes is a former professor there (emeritus).
dabiged 4y ago
A lot of my favorite physics classes were Applied Physics. These were great as you used the building blocks from 1st/2nd year level to show complex phenomena in the universe. It is a shame this list has none of these. Things like: * Stellar Nucleosynthesis - S-process, R-process, stellar evolution * Fluid mechanics - Navier Stokes equations * Physical Oceanogrpahy - Ocean currents, tides, Pressure and Salinity effects * Plasma Physics - MHD equations, Alfven waves * Medical Physics - CAT, PET, MRI scanners. Radiation treatments. * Planetary Science - Plate tectonics, Gas giant phenomena. * Geophysics - EM, seismic, anisotropy * Electron Microscopy - SEM, TEM, AFM etc.
- JoeDaDude 4y ago
  Great list. Did you manage to take these courses online? If so, where?
hyperthesis 4y ago
Can you 2 sigma yourself? (https://wikipedia.org/wiki/Bloom%27s_2_sigma_problem https://wikipedia.org/wiki/Bloom%27s_2_sigma_problem) Can you identify gaps - and worse, misconceptions - that you don't know you have? I think you can "debug" yourself, to some extent, starting with what you do know: you have trouble with that something . Start with the symptom, and diagnose. Narrow down where the problem occurs, by attempting sub-parts of the problem, simpler versions, and prerequisites. If you can't identify it, it's a sign that the problem is not where you think itis. i.e. you have a misconception about something you think you know. Then, there are many resources available to try to remedy it: textbooks, courses, subreddits, stackexchanges. Of course... so much easier to have a perceptive coach who can instantly see where and why you stumble.
- hyperthesis 4y ago
  One thing about the 2 sigma effect of tutoring is that it doesn't generalize; it doesn't make you smarter, just better at what you were taught. A different mechanism, but similar effect is learning the "trick" of solving a puzzle/problem - you just look smarter (and, well, know that specific trick). In other words, tutoring is spoon-feeding. This is still great, if you need that skill for something, such as for a specific technical job, or in order to learn something subsequent at which you are talented.
  - Nevermark 4y ago
    Yet, tutoring seldom makes someone dumber. And a good tutor doesn't spoon feed. At a meta-level, an intelligent person wants to solve problems, or increase their ability to solve problems. So an intelligent motivated person would appreciate anyone more familiar with a subject strategically removing some of the friction. Even if it didn't make them innately smarter. Time, after all, is finite for us all. And nothing is worse for learning, than an unnecessary stall. — Nevermark
ezconnect 4y ago
I am still struggling to find the motivation to learn a new language(Japanese)
- JoeDaDude 4y ago
  Action creates motivation, rather than the reverse. Just take the first few steps. Goals? Nice to have, but you don't need them either (from a fellow Nihingo student). https://www.youtube.com/watch?v=AO0GTMgqPI8 https://www.youtube.com/watch?v=AO0GTMgqPI8
  - ezconnect 4y ago
    I started on numbers since I need that when buying stuff and when the locals says the numbers it still hard to understand. Seems like I need hundred of hours exposure to it before it becomes easy.

364 points by JoeDaDude 4y ago

I've been studying MIT's OCW for Probability with a partner. It's a great course. https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-an... We're 4 months in and on Lecture 15. These do take a while. I feel like I'm not getting everything and will need another round. I've been binge watching Stat 110 too: https://projects.iq.harvard.edu/stat110 https://projects.iq.harvard.edu/stat110 "All probabilities are conditional"

sy7ar 4y ago
Very nice. Where do you find a study partner?

frognumber 4y ago

Context would be nice here. Who is this? Is this am unemployed autistic kid with nothing else to do? A brilliantly gifted high school student? A software engineer? A college student at a school without relevant courses? An independently wealthy semi-retired rich kid? Why? To be macho? As an alternative to college? To level up his skills? Quick web search answers a few of those, but not all of those. If OP is the creator, look at the web site from the perspective of a visitor, and give some answers. As a footnote, there really ought to be a way to give college credit for this sort of thing.

password11 4y ago
> Who is this? Brilliantly gifted high school student it turns out. > https://www.scotthyoung.com/blog/2023/02/21/diego-vera-mit-challenge-math-physics/ https://www.scotthyoung.com/blog/2023/02/21/diego-vera-mit-c... > Interviewer: Tell me a bit about your life situation at the time. Were you working on the project full-time? What did you do for funds? > Diego: The year COVID hit was the most transformative year of my life. I was 15 at the time. A combination of both personal circumstances along with isolation gave me so much clarity—I transformed 180 degrees. During this time, I really got into self-improvement and started working out, meditating, reading, taking cold showers etc. Personally, I did some of what he did when I was his age, but not to the same extent and I mostly decided to chill out and enjoy college. At that age it's really risky to do. Really hard to go to college and sit in classes for 4 years if you already know everything. I guess you could go straight to grad school or industry, but you miss out on a lot of the social maturity and friendships you develop in college. Learning all this is almost a curse; he will always, in some sense, be alone in his newfound abilities. (Sorry for the edits. Done editing before any child comments.)
- btheshoe 4y ago
  nah, i have plenty of similarly smart friends who are doing just fine. he'll fit right in in some college environments, and he can take the time he's not wasting doing class and pursue real things that matter, like research.
- dopu 4y ago
  I disagree, I think it will provide him with a great foundation for college. As great as online learning is, I don’t think it’s the same as taking a class that you go to multiple times a week and get in person feedback on. It also takes multiple passes at a given subject to properly understand it. I’m sure he’d learn many new things he didn’t quite get from his self study if he enrolled in an actual analysis course or w/e.
  - onetimeusename 4y ago
    this makes sense to me. I skimmed what he took and it says he learned real analysis, a pretty challenging course. It's one thing to listen to the lectures and solve some problems and it's another to be given a difficult homework on a very tight deadline and perform well, same for exams. I think it's extremely cool though and really a great idea but I am cautious about saying he has the equivalent of those undergraduate degrees.
    - hgsgm 4y ago
      > it's another to be given a difficult homework on a very tight deadline and perform well, same for exams. This is the stupid, broken part of school, that only exists as a cost-cutting measure. Real learning and creativity doesn't have this nonsense. It's like saying that living in a nice house is bad because you don't get to smell your poop while you eat. No one needs that. Diego is getting a better education because it isn't being arbitrarily cut short and of track before the going gets good.
      - deleted 4y ago
        [deleted]
mfragin 4y ago
As a former teacher of math and comp sci at a pretty low socio-economic school in (US) Colorado's front range, I can attest that kids like this are out there. Before I gave up on teaching as a career, it was kids like this that kept me going.
- sethhovestol 4y ago
  Mr. G! I was just looking back at Robby the Robot stuff from my time at skyline! You should email me so we can catch up! Pick nearly anything at my lastname dot com to reach out!

mjfl 4y ago

People love self-study materials, but do you really have the time to absorb it? Yeah you could do this stuff every day after work, but then you may not go to the gym, go on that date, etc... Not enough time in the world to go through even a single learning resource people promote.

susam 4y ago
In 2021, a bunch of us, software engineers, did a small book club to learn analytic number theory from a book written by Apostol. We met for 40 minutes a day and read every line of the book and every page of the book in great detail. We did it for the joy of learning. It took us 79 hours spread across 120 days to complete reading the book and gain a good understanding of analytic number theory along with the analytic proof of the prime number theorem. Meetup log: https://susam.net/maze/meet/iant/log.html https://susam.net/maze/meet/iant/log.html A few blog posts about it: https://susam.net/maze/tag/iant.html https://susam.net/maze/tag/iant.html
- wheelinsupial 4y ago
  I skimmed your blog posts and logs, so apologies if I missed it. How many problems or exercises did you work through in the book? Did people put in any additional time individually between sessions?
  - susam 4y ago
    I can't speak for all participants of these meetings and I haven't kept an exact count of the problems I solved but I believe I must have solved somewhere between 160 to 200 problems from the exercises in the book. See also https://news.ycombinator.com/item?id=34908191 https://news.ycombinator.com/item?id=34908191 for more details on this topic.
- FiberBundle 4y ago
  Sorry, but you don't properly learn any math topic in 80 hours. I've spent more than 10 hours on some problem sets in difficult courses. Solving hard problems takes a lot of time and is absolutely essential to learn math. When you read a book or a script you feel as if you have grasped the content, but most of the time you really haven't. It's only when you attack problems from different angles that you really build intuition for the concepts taught in that book.

trollerator23 4y ago

Holy shit that's ballsy. In 2 years? There are quite a few of tough courses there. Respect.

Ralo 4y ago

I would love to learn a much deeper level of mathematics but where do people find the time for that? If it's not related to work, or future work I couldn't find the large amount of time required. And self study doesn't get recognized on resumes very well. Perhaps spread out over the course of many many years on your own personal time.

d4rkp4ttern 4y ago
Indeed, “work” prevents learning. One of the reasons I like freelancing is that I can intentionally set aside 15 hours a week to catch up on areas I’m very interested in. Yes I don’t get paid for this “learning” time but I see this as an investment.
nohaydeprobleme 4y ago
> "Perhaps spread out over the course of many many years on your own personal time." That is a very workable approach, so long as you consistently study. For motivation, if you'd like to get better at mathematics just as a life goal, that should be valid enough to spend time on the hobby. If you're studying primarily for personal enjoyment and fulfilment (and especially if you find joy in the process of learning), the slower pace doesn't matter as there are no expectations to learn quickly. If you're studying mathematics or a technical subject for work, I believe it's better to earn a graduate degree from an accredited program for the resume (as a record of passing proctored exams is seen by hiring managers as strong evidence of learning), plus it's nice to be able to learn from your fellow students and ask the professor questions. For myself, I've found it much easier to find motivation to consistently self-study mathematics outside of accredited coursework by practicing out of personal interest, as it eases up a lot of pressure about learning a certain concept by a certain time. I won't expect to learn as quickly as the person's reported progress in the submitted article, but this also makes the practice more enjoyable and easier to keep up in the long term for myself.
paulpauper 4y ago
I would love to learn a much deeper level of mathematics but where do people find the time for that? Setting aside 1-2 hours a day should be enough. I think this is not unreasonable for most people. But why? Unless you need it for a resume or degree, I don't think it matters that much. So you can make a blog post about it?

hnthrowaway0315 4y ago

I'm thinking about a historical approach. For example what exactly is Ptolomy system? What's the math involved? Why did the phases of Venus rebutes the model? How did Tycho make his observations? Can we repeat it for say a few months? How did Newton come up his ideas? What are Einstein's thought experiments. Basically I want to put myself in the shoes of great minds, learn what math tools were available at the time, do their observations, know how their thought processes work. edit Would appreciate if someone could recommend a textbook that follows such approach.

nohaydeprobleme 4y ago
Though I lack personal experience with a historical approach to studying mathematics, a starting point could be the reading list by St. John's College as part of the materials the faculty uses to teach mathematics to their undergraduates: https://www.sjc.edu/academic-programs/undergraduate/subjects/mathematics https://www.sjc.edu/academic-programs/undergraduate/subjects... Readings include Archimedes's "On the Equilibrium of Planes" and "On Floating Bodies" and Nicomachus's "Arithmetic." However, I've heard of some mixed reviews on the effectiveness of learning math [1] [2] via reading historical texts at St. John's, versus more traditional approaches today in good mathematics programs. A bit separately but as a related idea, I've spoken to a couple people who said they preferred older mathematics books from the 1900s to the 1960s for their studies over modern books. I personally prefer modern books with recent editions that are well-recommended, as they usually have good visualizations of ideas and shouldn't frequently have errors (due to their reputation). If you're studying as a hobby, though, the most effective mathematics book, assuming it's reasonably reputable and heard-of, is the one that interests you enough to stick with it for consistent study in the long-term. [1] https://old.reddit.com/r/stjohnscollege/comments/ehcem3/how_are_the_math_courses_at_stjohns/ https://old.reddit.com/r/stjohnscollege/comments/ehcem3/how_... [2] https://old.reddit.com/r/stjohnscollege/comments/ngpu0i/math_at_st_johns/ https://old.reddit.com/r/stjohnscollege/comments/ngpu0i/math...
- password11 4y ago
  If you go through for the "great books" approach, just be aware that it's not the same curriculum as a major in mathematics: > Mathematics is one of the many subjects studied in the college’s interdisciplinary great books curriculum. There are no majors at St. John’s. It may be fulfilling from a humanistic/personal development perspective, but you won't really have the tools to do anything useful like cryptography, algorithms, physics, statistical inference, data analysis, etc., which, in my mind are the really cool things you can understand by learning math.

paulpauper 4y ago

Pre-calc to quantum field theory in 2 years? nuts

Koshkin 4y ago
Unless you do it by working through the Demystified series, of course!
whatshisface 4y ago
It sounds reasonable to me, a four-year degree at most universities is about half non-major classes.
- paulpauper 4y ago
  It's not really a time issue. It's more of a learning issue. I tutored math one-on-one and even of the smartest kids in my cohort found it hard to get calculus; there was a major learning curve for sure. No amount of time will help if the concepts do not click. Feynman-level of physics means you need to understand stuff like variationals, etc which is well above your typical calc course. Shows how truly exceptional this person is.
  - whatshisface 4y ago
    I don't think variational methods are that big a step beyond integration by parts.
    - Koshkin 4y ago
      The Lazy Universe by Coopersmith may provide some intuition as well.

raydiatian 4y ago

I wonder if you could build a service that ingests self taught students’ notes, uses ML to investigate their displayed level of mastery, and upon decision associates with a university that will give them credit for a course, or even a full on degree.

admsmz 4y ago

If people want to replicate the same feats as this kid you should check out http://mathacademy.com http://mathacademy.com People are constantly talking about chatGPT and reinforcement learning but mathacademy is using AI to teach humans. And from my experience very effectively.

boyter 4y ago
Can also recommend https://mathacademy.com https://mathacademy.com Very impressed with what I have seen of it so far, and the founder's of it have an impressive amount of passion and drive to deliver. You can read more about it here as covered by the washington post https://www.washingtonpost.com/education/2022/10/16/math-academy-accelerated-math/ https://www.washingtonpost.com/education/2022/10/16/math-aca...
rychco 4y ago
The testimonials on the homepage are aggressively positive, what has your existence been like? I’m interested in revisiting the various University topics, particularly DiffEQ/stats/LinAlg, and have been looking for an excuse/resource to study.
- admsmz 4y ago
  My experience has been that I never fail to make progress whenever I encounter something I didn’t know or was weak in. The system offers you plenty of practice problems, at just the right level, to make sure you master the material before moving on to material that builds on the previous lesson. Aggressively positive? Maybe. I have been a paying customer since october and very happy with the results.
  - rychco 4y ago
    Thanks for responding. I may give it a try!
nsajko 4y ago
Math Academy seems like it could be a game-changer for learning, it's a paid service and in beta-testing. They only cover math, though, at least right now. In addition to presenting the topics and providing exercises, MA automates some tasks that are usually left to the learner, like spaced-repetition and tracking down prerequisite topics. They have a detailed DAG of math topics connected with dependency relations that enables this. Basically automation of a lot of what a tutor would provide.

ecshafer 4y ago

Maybe this isn't the exact right place to bring it up, but is related. But there is a lot of self-paced learning things coming up between schools and alternative to schools. But an issue I have is that this self paced learning is really limited in scope. Why can I take classes so easily for an MS in computer science or IT, or get an MBA or take data analysis courses, but I can't easily get a degree / certificate for say a bachelors in Mathematics? Or literature? There seems to be a big split where so much is focused on job training but very little is being done on education.

deleted 4y ago
[deleted]
l33t233372 4y ago
The oft cited refrain is that colleges/universities serve several purposes aside from education: 1.) Verification, standardization, and authentication of work being done and of knowledge being gained. 2.) Networking opportunities and social/professional development and maturation in a a limited-stakes playground surrounded by others in the same social and economic class, and 3.) A sort of IQ test laundering service.
ouid 4y ago
The answer is that mathematics is a thing that you can actually assert that someone is doing incorrectly, but for which it will not be obvious to non-mathematicians. If a programmer writes a bad program, the user can tell. If a mathematician writes a bad proof, basically it takes a mathematician to tell. It doesn't take an incredible mathematician, but it does take one. If you want to say that you learned mathematics, you have to do more than this student did. you may have chosen to give him the benefit of the doubt, but I did not. I checked his work, and its mostly wrong. The reason that it is mostly wrong is because the practice of mathematics requires some training to get to the point where you can be relied upon to know if you are lying, and the author of this blog did not reach that point.
- rtodea 4y ago
  > I checked his work, and its mostly wrong Can you show some examples that make you draw this conclusion? Thanks!

loveparade 4y ago

Hats off, I think it takes some real dedication to stick with it. > One of the things I found useful here was to get immediate practice once I knew just enough. I think this is one of the reasons project-based learning can be so powerful: you have a problem and research your way into it versus researching your way into it and then seeing what to apply. This. Perhaps it varies from person to person, but this is also how I learn best. I want to start with a problem, struggle to solve it, and then learn how to actually solve it. That way the material immediately clicks and sticks with me longer. Why don't schools teach this way?

flandish 4y ago
This is how I take to learning new programming languages. Project Euler. ( https://projecteuler.net/ https://projecteuler.net/ ) Bite sized “specs” calling for an answer to be solved in your new language. Each getting harder and dealing with important concepts to grok and hurdles to overcome.
photochemsyn 4y ago
It's indeed the best way to learn, but schools are charged with issuing grades to students and there are just too many problems with take-home projects (i.e. paying someone else to do it, etc.), and with group collaboration on such projects (one person doing 80% of the work, etc.), that it generally doesn't ever happen except in a few small-sized high-level undergrad or perhaps graduate courses, where the students are more motivated about learning the material then they are about gettting a good grade, or just passing the class. Hands-on lab courses are something of an exception, as you simply have to do the project yourself in class, but these tend to be long classes (three hour sessions etc.) and again are limited to relatively small groups of students. Building computer simulations in real-time of physics problems might be a way to do it, but the students would need to have good programming skills beforehand. Basically a physics hackathon using a standardized set of programming tools, that would be fun and educational.
nextos 4y ago
Some universities teach this way. In Europe, there are a few institutions that shifted to problem and project-based learning during the reforms of the 1960s. A few notable cases are cited here: https://www.pblfuture.aau.dk/about https://www.pblfuture.aau.dk/about. As far as I know, some American institutions use the same approach, e.g. Olin College. IMHO, when done well, i.e. having an equally strong focus on theory, this leads to excellent learning outcomes. However, at undergrad level, schools are reluctant to teach this way because it requires a lot of supervision.

ouid 4y ago

I looked through his topology problems and notes, and he could really use the guidance of a professor, or at least someone to give him feedback. It's not practical to teach yourself mathematics to start before you can really check your own work. There are quite a few mistakes and misquoted/misunderstood definitions that have no way of ever getting corrected.

whatshisface 4y ago
If you never see something a second time, maybe you didn't need to learn it.
- ouid 4y ago
  What? You don't need to learn anything. Dogs don't know any math, and they do fine.
  - whatshisface 4y ago
    If he was learning physics and that stuff about topology came up, he'd notice his definitions weren't adding up and fix it. If he never saw it again then the maybe didn't need to learn it to accomplish his goal.
    - ouid 4y ago
      This is very optimistic. I watch people fail to learn things all the time without noticing, especially if they do not have the tools to be honest with themselves, which is a thing that is almost exclusively learned through formal training. Sure, not everyone arrives at that state, but they are much more likely to with guidance.
      - whatshisface 4y ago
        I'm inclined to be very optimistic, because the guy is fifteen years old and the opportunity cost is League of Legends. :-) But more to the point you're addressing, physics tends to be easier to grade than math because there is a big focus on calculation, and there you can have answers in the back with no subtle questions about things like whether a student's proof skipped a step because they thought it was obvious or because they didn't know it was necessary. That is not to say physics doesn't have those questions, just that a lot of times the answer is clearer-cut. If the whole thing had been about topology it'd be different.

jdkee 4y ago

I would add axiomatic set theory and discrete mathematics to his list.

Koshkin 4y ago
Wolfram has gone nuts trying to make these the foundation of the “new” physics.

stonlyb 4y ago

This is inspiring. I'm a student in the Arizona State University online Physics BA degree (soon to transition to BSc). And by student I mean adult learner with a full plate of other commitments doing this for fun and I dont know when I'll finish.

admsmz 4y ago
Maybe a long shot but is there a course on “Geometric Algebra” offered by ASU by any chance? The founder of GA, David Hestenes is a former professor there (emeritus).

dabiged 4y ago

A lot of my favorite physics classes were Applied Physics. These were great as you used the building blocks from 1st/2nd year level to show complex phenomena in the universe. It is a shame this list has none of these. Things like: * Stellar Nucleosynthesis - S-process, R-process, stellar evolution * Fluid mechanics - Navier Stokes equations * Physical Oceanogrpahy - Ocean currents, tides, Pressure and Salinity effects * Plasma Physics - MHD equations, Alfven waves * Medical Physics - CAT, PET, MRI scanners. Radiation treatments. * Planetary Science - Plate tectonics, Gas giant phenomena. * Geophysics - EM, seismic, anisotropy * Electron Microscopy - SEM, TEM, AFM etc.

JoeDaDude 4y ago
Great list. Did you manage to take these courses online? If so, where?

hyperthesis 4y ago

Can you 2 sigma yourself? (https://wikipedia.org/wiki/Bloom%27s_2_sigma_problem https://wikipedia.org/wiki/Bloom%27s_2_sigma_problem) Can you identify gaps - and worse, misconceptions - that you don't know you have? I think you can "debug" yourself, to some extent, starting with what you do know: you have trouble with that something . Start with the symptom, and diagnose. Narrow down where the problem occurs, by attempting sub-parts of the problem, simpler versions, and prerequisites. If you can't identify it, it's a sign that the problem is not where you think itis. i.e. you have a misconception about something you think you know. Then, there are many resources available to try to remedy it: textbooks, courses, subreddits, stackexchanges. Of course... so much easier to have a perceptive coach who can instantly see where and why you stumble.

hyperthesis 4y ago
One thing about the 2 sigma effect of tutoring is that it doesn't generalize; it doesn't make you smarter, just better at what you were taught. A different mechanism, but similar effect is learning the "trick" of solving a puzzle/problem - you just look smarter (and, well, know that specific trick). In other words, tutoring is spoon-feeding. This is still great, if you need that skill for something, such as for a specific technical job, or in order to learn something subsequent at which you are talented.
- Nevermark 4y ago
  Yet, tutoring seldom makes someone dumber. And a good tutor doesn't spoon feed. At a meta-level, an intelligent person wants to solve problems, or increase their ability to solve problems. So an intelligent motivated person would appreciate anyone more familiar with a subject strategically removing some of the friction. Even if it didn't make them innately smarter. Time, after all, is finite for us all. And nothing is worse for learning, than an unnecessary stall. — Nevermark

ezconnect 4y ago

I am still struggling to find the motivation to learn a new language(Japanese)

JoeDaDude 4y ago
Action creates motivation, rather than the reverse. Just take the first few steps. Goals? Nice to have, but you don't need them either (from a fellow Nihingo student). https://www.youtube.com/watch?v=AO0GTMgqPI8 https://www.youtube.com/watch?v=AO0GTMgqPI8
- ezconnect 4y ago
  I started on numbers since I need that when buying stuff and when the locals says the numbers it still hard to understand. Seems like I need hundred of hours exposure to it before it becomes easy.