7 ms·

> This is NOT a course for absolute beginners I disagree with that, as long as you have some mathematics background (calculus, a bit of linear algebra), and an

> This is NOT a course for absolute beginners I disagree with that, as long as you have some mathematics background (calculus, a bit of linear algebra), and an understanding of probability theory (which can be taken from the prerequisite course https://www.edx.org/course/probability-the-science-of-uncertainty-and-data https://www.edx.org/course/probability-the-science-of-uncert...), this course is self-sufficient and does not need prior knowledge of the subject. I was a complete beginner in the subject and I am able to follow the course without too much difficulties.

wenc 6y ago
I took a look at the material (the slides on Method of Moments, in particular) and my feeling is that it is a particularly mathematically-heavy treatment of statistics. As it states in its goals, it aims to introduce the mathematical theory of statistics. On the course's main page, it is listed as a senior undergraduate/graduate course. The style tends toward being expository rather pedagogical -- it's a very French/European approach to teaching mathematics. It does seem to require mathematical maturity beyond the basics, and in my opinion this is likely not accessible to most beginners without some advanced mathematical training. If you find it accessible as a beginner then I congratulate you on your mathematical prowess.
- int3 6y ago
  "Basic" is ill-defined, but I think sloonz is right about it only requiring calc + linalg, which most CS / Eng majors will have taken.
  - wenc 6y ago
    So I've taught undergrad courses, and my sense is, the average US college engineering sophomore with linalg and say Calculus II (but no Real Analysis) might struggle with this material somewhat. They may know the material for linalg and calculus (and may have gotten As), but my feeling is that many would not have reached the mathematical maturity to truly internalize concepts. I would place this course maybe at the senior level (with graduate level cross-registration)...400-500 level elective. What is your sense? -- Side note: it's interesting in that in other countries, e.g. say France, the math curriculum is so darned advanced. In undergrad Year 1 at École Polytechnique, real analysis and variational methods are already covered in common courses. https://programmes.polytechnique.edu/en/ingenieur-polytechnicien-program/program-details/year-1-of-the-ingenieur-polytechnicien-program https://programmes.polytechnique.edu/en/ingenieur-polytechni... Functional analysis in Year 2. https://programmes.polytechnique.edu/en/ingenieur-polytechnicien-program/program-details/year-2-of-the-ingenieur-polytechnicien-program https://programmes.polytechnique.edu/en/ingenieur-polytechni... Then again the top French schools filter out non-math folks via classes prépas and exams.
    - nightski 6y ago
      I'm in the demographic you describe, yet I've had a hard time finding resources to develop that "mathematical maturity" short of going back to graduate school. Which I'd love to do, but am at a point in my career where that would be devastatingly expensive to my future since these are the prime earning and wealth building years. I wish there was more of a self directed way to achieve this.
      - wenc 6y ago
        Just curious, the topic above aside: what would you say is the main reason behind why you'd like to strive for "mathematical maturity"? (from what you wrote, I gather it's not for reasons of vocation?)
      - ghufran_syed 6y ago
        I just finished an MS in math and statistics a long time after doing a non-mathematical undergrad degree. I feel a lot of what is called mathematical maturity is actually getting comfortable doing proofs, which I think is hard to learn while also learning more advanced math. I would recommend working through "Mathematical proofs" by Polimeni/Chartrand/Zhang. Unlike math at an earlier level, you can't just check your answers against the official ones to see if you made a mistake - writing proofs is more like writing essays, the grammar is the easy bit, it's the process of putting the arguments together in the right detail and the right order that's important and hard to do without feedback. So you also need to get feedback from mathematicians on your proofs if possible. The best way to do that if you don't have a buddy who happens to be a mathematician is to learn to use LaTeX and ask questions on math.stackexchange.com. An alternative is to do the proof and abstract algebra courses via (asymmetric) distance learning at https://westcottcourses.com/courses.html https://westcottcourses.com/courses.html I know someone who took these courses and felt like they got good feedback on their homeworks from the profs running the course. Feel free to get in touch if you want to chat, I spent a long time trying to self-learn this stuff before starting my math MS, so happy to help in any way I can!
        marai2 6y ago
whymauri 6y ago
For those who might speed through 18.650, the natural next step is [0] 18.655 (Mathematical Statistics) followed by the new course [1] 9.521 (Non-Asymptotic Perspectives in Statistics). [0] https://ocw.mit.edu/courses/mathematics/18-655-mathematical-statistics-spring-2016/ https://ocw.mit.edu/courses/mathematics/18-655-mathematical-... [1] http://www-math.mit.edu/~rigollet/IDS160/notes.html http://www-math.mit.edu/~rigollet/IDS160/notes.html
norcon4 6y ago
I actually agree with your point on prerequisites. I think by absolute beginner I meant to say no experience with probability theory either. With the prerequisites you outlined, I think a determined person could do well with the material. Mainly posting this follow-up to correct myself so people curious on whether they'd be able to follow the course are better-informed.
xenihn 6y ago
What would you recommend for someone who doesn't have the calculus and linear algebra?
- int3 6y ago
  Gilbert Strang's linalg lectures on MIT OCW are amazing.
jackallis 6y ago
"I disagree with that, as long as you have some mathematics background (calculus, a bit of linear algebra), and an understanding of probability theory" right, so it's not for beginners.

wenc 6y ago

I took a look at the material (the slides on Method of Moments, in particular) and my feeling is that it is a particularly mathematically-heavy treatment of statistics. As it states in its goals, it aims to introduce the mathematical theory of statistics. On the course's main page, it is listed as a senior undergraduate/graduate course. The style tends toward being expository rather pedagogical -- it's a very French/European approach to teaching mathematics. It does seem to require mathematical maturity beyond the basics, and in my opinion this is likely not accessible to most beginners without some advanced mathematical training. If you find it accessible as a beginner then I congratulate you on your mathematical prowess.

int3 6y ago
"Basic" is ill-defined, but I think sloonz is right about it only requiring calc + linalg, which most CS / Eng majors will have taken.
- wenc 6y ago
  So I've taught undergrad courses, and my sense is, the average US college engineering sophomore with linalg and say Calculus II (but no Real Analysis) might struggle with this material somewhat. They may know the material for linalg and calculus (and may have gotten As), but my feeling is that many would not have reached the mathematical maturity to truly internalize concepts. I would place this course maybe at the senior level (with graduate level cross-registration)...400-500 level elective. What is your sense? -- Side note: it's interesting in that in other countries, e.g. say France, the math curriculum is so darned advanced. In undergrad Year 1 at École Polytechnique, real analysis and variational methods are already covered in common courses. https://programmes.polytechnique.edu/en/ingenieur-polytechnicien-program/program-details/year-1-of-the-ingenieur-polytechnicien-program https://programmes.polytechnique.edu/en/ingenieur-polytechni... Functional analysis in Year 2. https://programmes.polytechnique.edu/en/ingenieur-polytechnicien-program/program-details/year-2-of-the-ingenieur-polytechnicien-program https://programmes.polytechnique.edu/en/ingenieur-polytechni... Then again the top French schools filter out non-math folks via classes prépas and exams.
  - nightski 6y ago
    I'm in the demographic you describe, yet I've had a hard time finding resources to develop that "mathematical maturity" short of going back to graduate school. Which I'd love to do, but am at a point in my career where that would be devastatingly expensive to my future since these are the prime earning and wealth building years. I wish there was more of a self directed way to achieve this.
    - wenc 6y ago
      Just curious, the topic above aside: what would you say is the main reason behind why you'd like to strive for "mathematical maturity"? (from what you wrote, I gather it's not for reasons of vocation?)
    - ghufran_syed 6y ago
      I just finished an MS in math and statistics a long time after doing a non-mathematical undergrad degree. I feel a lot of what is called mathematical maturity is actually getting comfortable doing proofs, which I think is hard to learn while also learning more advanced math. I would recommend working through "Mathematical proofs" by Polimeni/Chartrand/Zhang. Unlike math at an earlier level, you can't just check your answers against the official ones to see if you made a mistake - writing proofs is more like writing essays, the grammar is the easy bit, it's the process of putting the arguments together in the right detail and the right order that's important and hard to do without feedback. So you also need to get feedback from mathematicians on your proofs if possible. The best way to do that if you don't have a buddy who happens to be a mathematician is to learn to use LaTeX and ask questions on math.stackexchange.com. An alternative is to do the proof and abstract algebra courses via (asymmetric) distance learning at https://westcottcourses.com/courses.html https://westcottcourses.com/courses.html I know someone who took these courses and felt like they got good feedback on their homeworks from the profs running the course. Feel free to get in touch if you want to chat, I spent a long time trying to self-learn this stuff before starting my math MS, so happy to help in any way I can!
      - marai2 6y ago

whymauri 6y ago

For those who might speed through 18.650, the natural next step is [0] 18.655 (Mathematical Statistics) followed by the new course [1] 9.521 (Non-Asymptotic Perspectives in Statistics). [0] https://ocw.mit.edu/courses/mathematics/18-655-mathematical-statistics-spring-2016/ https://ocw.mit.edu/courses/mathematics/18-655-mathematical-... [1] http://www-math.mit.edu/~rigollet/IDS160/notes.html http://www-math.mit.edu/~rigollet/IDS160/notes.html

norcon4 6y ago

I actually agree with your point on prerequisites. I think by absolute beginner I meant to say no experience with probability theory either. With the prerequisites you outlined, I think a determined person could do well with the material. Mainly posting this follow-up to correct myself so people curious on whether they'd be able to follow the course are better-informed.

xenihn 6y ago

What would you recommend for someone who doesn't have the calculus and linear algebra?

int3 6y ago
Gilbert Strang's linalg lectures on MIT OCW are amazing.

jackallis 6y ago

"I disagree with that, as long as you have some mathematics background (calculus, a bit of linear algebra), and an understanding of probability theory" right, so it's not for beginners.