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Mathematics for the Adventurous Self-Learner

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Re: Mathematics for the Adventurous Self-Learner

#141

Post by throwlaplace »

ColinWright wrote: post #132
throwlaplace wrote: post #130

Earlier quoted context omitted.

>Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it. Isn't that literally exactly what I said? > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them

The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said: > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it…

> you won't actually be able to do the math

but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books).

>And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

no i didn't. that's precisely why i used the word "exposed".

>violent agreement

we don't agree but i'm not being violent. but my responses are short and yours are long.

i do not see the exercises as essential for anyone other than practicing mathematicians. i have read a great many serious math books (i just recently finished Tu's Manifolds book and am now reading Oksendal's SDEs). i read them without doing absolutely any exercises but following the rest of the guidelines in the post i responded to. the experience is gratifying because i learn about new objects and new ways of thinking about objects i've already learned about. that's absolutely the only thing that matters to me.

but let me ask you something

>That, to me, implies learning to do, not learning about.

here's a fantastic explanation of the topological proof of Abel-Ruffini

https://www.youtube.com/watch?v=zeRXVL6qPk4

would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?

Re: Mathematics for the Adventurous Self-Learner

#142

Post by DecayingOrganic »

gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

I'd highly recommend OpenStax math textbooks, they are completely free, openly licensed, peer reviewed, and by Rice University. They also start from Pre-algebra.

https://openstax.org/subjects/math

Re: Mathematics for the Adventurous Self-Learner

#143

Post by pbhjpbhj »

gfxgirl wrote: post #88
mnyary wrote: post #41

Earlier quoted context omitted.

It seems that the more basic course is Discovering mathematics (MU123). http://mathschoices.open.ac.uk/mu123

https://students.open.ac.uk/openmark/mct.level3/ > Question 1: Sara wants to buy a desk before she starts her Open University course. She has chosen a suitable place for it but needs to measure the space before going to buy it. > Which of these units is the most suitable for measuring the width of the desk? (a) millimetres, (b) metres, (c) centimetres, (d) kilometres. Seems pretty arbitrary to me. Okay (d) is arguabl…

The reason for the question, IMO, is not to get the given answer.

The reason is to learn why there is an answer, at which point you can give an opinion as to whether cm/mm are better. You've missed the primary step, and almost certainly are - as others point out - over qualified for this question (which is a precursor to discussions of decimal precision).

Often when helping the kids with homework I find myself answering "well this is the answer they want ... but the real answer is ...".

tl;dr the question is there to make you think, not because there's only one answer.

Re: Mathematics for the Adventurous Self-Learner

#144

Post by ZeroCool2u »

angry_octet wrote: post #80
polyphonicist wrote: post #24

I am going to suggest something that might go against this idea of self-studying math. Do not do it alone. I mean, it is okay to self-learn mathematics as much as possible but don't let that be the only way to learn. Find a self-study group where you can discuss what you are learning with others. I think the social-effect can be profound in learning. I realized this when I used to learn calculus on my own. My progres…

Agree. And if one is a well paid software engineer, one can definitely afford to pay a maths grad student for an hour week, preferably a bit more than whatever pittance the local univeristy pays them for being a tutor. You will progress far quicker and with fewer wrong turns. It is also far cheaper than enrolling at a university. A personal trainer for the brain.

I actually did this as an undergrad, despite barely being able to afford school. I left school for a bit, so I could figure out how to actually pay for it. After getting that worked out, I came back and realized I'd forgotten way more math than I had anticipated. Between my CS courses and math I was getting overwhelmed with the sheer breadth of information I needed to be have mastered to comfortably follow along. I took a one semester long remedial class that served as a refresher to all high school level math.

After that I worked through my classes with a tutors help. Everything up to and including linear algebra and numerical analysis with the help of a extremely kind PhD student named Adnan. He had the patience of a saint and ended up becoming a very good friend.

The most valuable part of having someone like this available for an hour or two every week is that it increases your knowledge or understanding/minute rate dramatically. It's like having Google or Khan academy on steroids. Someone that did everything already and knows exactly what page of a text book to look lat to help you understand, but they don't even need the textbook, because they know how to explain the concept you're having trouble with.

To this day I work as one of many data lscientists on a team where we all have fairly diverse backgrounds. In fact I'm the only person that is only CS and does not have a graduate degree. I have a teammate that did her undergrad and Masters in mathematics and if I'm having a hard time with something math heavy after some googling, the first thing I do is ask her for a quick explainer. She does the same with me for CS or programming issues as well and I help her with informal code reviews.

I know this will seem like basic teamwork to a lot of folks, but far too often I see people in our industry exert huge amounts of effort to understand a difficult concept that likely someone they're sitting a few feet away from has a very good understanding of and would be happy to help them with, so they're not banging their head against the wall for hours. I had to have a similar conversation with my intern a couple years ago. She was spending hours doing pen on paper math to understand Kalman filters. Things went much more quickly after I talked to her about my process of working with my colleagues and asking for help when I didn't understand something.

TL;DR Ask for help sooner rather than later. We all stand on the shoulders of giants.

Re: Mathematics for the Adventurous Self-Learner

#145

Post by ColinWright »

throwlaplace wrote: post #141
ColinWright wrote: post #132

Earlier quoted context omitted.

The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said: > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it…

> you won't actually be able to do the math but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books). >And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises. no i didn't. that's precisely why i used the word "exposed". >violent agreement we don't agree but i'm not b…

We agree that if you want actually to be able to do the math then you need to do the exercises.

Do we agree that if you don't do the exercises then you probably won't actually be able to do the math?

You are discussing learning about the math, and not eventually being able to do it, because you say that you don't care about becoming a mathematician, therefore you don't need to do the math. Fair enough.

But my reading is that that's not what this thread is about. This thread, and the original submission, is about learning how to do the math.

> i do not see the exercises as essential for anyone other than practicing mathematicians.

I think you're wrong. Knowing how to actually do the math has proven useful to many people for whom it is a tool in their craft/job/employment. Learning Linear Algebra properly, being able to actually do it rather than just talk about it, can be enormously useful in Machine Learning.

>> That, to me, implies learning to do, not learning about.

> here's a fantastic explanation of the topological proof of Abel-Ruffini ... would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?

Understanding a single proof implies very little about one's ability to actually do the math. I've met many people who are math enthusiasts and who have watched hundreds of math videos. They say they understand all of what they've seen, and yet they are unable to do the simplest proofs, or the most elementary calculations.

My experience of people's abilities is that if they haven't done the exercises, they usually can't actually do the math.

But you complain about the length of my replies, so I'll stop. I think I've made my position clear, and I think I understand what you're saying, even if I don't agree with it.

Re: Mathematics for the Adventurous Self-Learner

#146

Post by dwrodri »

I recently had the experience of taking my first graduate-level probability course. It assumed quite a strong familiarity with real/complex analysis, and I suffered quite heavily. Something of note was that once I finally managed to "peel back" the analysis, the underlying intuition made a lot of sense for the simplest cases in probability (e.g. hypothesis testing between two normal distributions is a matter of figuring out whose mean you are "closer" to).

I am of the opinion that notation is a very powerful tool for thought, but the terseness of mathematical notation often hides the intuition which is more effectively captured through good visualizations. I would really like to take self-driven "swing" at signal processing, this time approaching it through the lens of solving problem on time-series data, since as a programmer I believe that would be quite useful and relevant.

Re: Mathematics for the Adventurous Self-Learner

#147

Post by pbhjpbhj »

rustybolt wrote: post #70
puritanicdev wrote: post #67

Earlier quoted context omitted.

I'm in the same shoes, and as ridiculous as it sounds but I've been in programming (self-taught) for 10 years now without an especially good knowledge of math. I've been slacking in HS on math classes, despite the fact that I loved math and was really good once I sat to listen, practice and understand the material. Also, I'm painfully aware of the fact that my math is really bad and that I'm missing on utilizing it i…

What is an example where you missed mathematical knowledge to do your job? Honestly curious, I never needed any math during programming for my job.

Now I'm curious. IANAProgrammer, what programs have you made that don't have any maths in them?

Can you share example code? I can't see how that works.

Re: Mathematics for the Adventurous Self-Learner

#148

Post by throwlaplace »

ColinWright wrote: post #145
throwlaplace wrote: post #141

Earlier quoted context omitted.

> you won't actually be able to do the math but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books). >And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises. no i didn't. that's precisely why i used the word "exposed". >violent agreement we don't agree but i'm not b…

We agree that if you want actually to be able to do the math then you need to do the exercises. Do we agree that if you don't do the exercises then you probably won't actually be able to do the math? You are discussing learning about the math, and not eventually being able to do it, because you say that you don't care about becoming a mathematician, therefore you don't need to do the math. Fair enough. But my reading…

>You are discussing learning about the math

You keep repeating this but you're evading the question about abel-ruffini and the question about whether reading a history book is "learning about history" as opposed to learning history.

You're making a weird distinction. People learn in different ways. Some by doing exercises and some by just playing with the objects. I wonder how you think actual research mathematicians learn new math from papers that don't include exercises lol.

You edited your response.

>I've met many people who are math enthusiasts and who have watched hundreds of math videos

There's a difference between watching numberphile or whatever and essentially watching a lecture on a proof. Very few people are watching/consuming rigorous expositions. I think that's the difference not the lack of exercise.

Re: Mathematics for the Adventurous Self-Learner

#149

Post by injb »

angry_octet wrote: post #77

The most key piece of advice is to take walks. Walking is essentials for mathematics. Many times when walking with my father he would turn for home and start walking faster, and by that sign I knew that he wanted to get home and write down a lemma.

I'm glad you posted this, because I use walks this way too. And because it reminds me of William Rowan Hamilton and the quaterions!

Re: Mathematics for the Adventurous Self-Learner

#150

Post by fizixer »

gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

Simmons - Precalculus Mathematics in a Nutshell [0] (128 page booklet)

[0] https://books.google.com/books?id=dN1KAwAAQBAJ

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