Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mathematics for the Adventurous Self-Learner

neilwithdata.com

Post reply on HN
Print view View original

171–180 of 216 posts

Re: Mathematics for the Adventurous Self-Learner

#171

Post by l_t »

ColinWright wrote: post #97
throwlaplace wrote: post #45

Earlier quoted context omitted.

this is excellent execellt advice. seriously anyone interested in learning math, chancing on this comment, should write it down. i wish i could upvote many more times. i have a bachelors in pure math and am 10 years out. i have time and again revisited things and didn't make good substantive progress until i came to these same exact conclusions. especially the part about skipping the exercises. if you're not trying t…

> this is excellent execellt advice ... especially the part about skipping the exercises. 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 I think this is deeply mistaken. In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your unders…

> In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your understanding.

This is a great point and example of the problem with a one-size-fits-all strategy. For some books, exercises are an essential part of comprehension. For others, not so much.

> Math is not a spectator sport. Reading about math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that.

My experience is that by taking excellent notes and asking why, you engage with the material to a similar degree, if not a greater degree, than by doing exercises. (Once again, depending on the book, as you mentioned.)

> Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.

I would argue that's the point. Usually self-taught math is about self-growth. Getting new ideas, being exposed to new concepts, recognizing patterns. Being able to actually "do it" on-the-spot is beside the point (and is the quickest level of skill to evaporate once you stop focusing on that material, anyway.)

Re: Mathematics for the Adventurous Self-Learner

#172

Post by bemmu »

greymalik wrote: post #128
bemmu wrote: post #98

Earlier quoted context omitted.

I solved this by just buying all the high school math textbooks and going through those on my own. I preferred this way, because it lets you have the same background as everyone else. In attempt #1 I was jumping ahead to read the interesting stuff (calculus), and while I could make some progress, it was needlessly difficult because I didn't start from the basics. It attempt #2 I started from the very beginning (cours…

Can you clarify how step 3 was different for you from step 2? (I’ve had similar unsuccessful steps 1 and 2, wondering what they keys were for you to turn the corner)

In step 2 I was just making progress when I felt like studying, so many days might pass between reading about some new concept and then needing to apply it. By that time I might have already forgotten some, and progress felt so slow that it wasn't very motivating to come back to it.

Doing it every day on the other hand, I would quickly need the thing I just learned, both reinforcing the learning and making it easier to apply it. Then as progress was much faster, it was more motivating as I could see myself making gradual progress each day, such that completing each course seemed like a doable undertaking.

Re: Mathematics for the Adventurous Self-Learner

#173

Post by ColinWright »

throwlaplace wrote: post #155
ColinWright wrote: post #151

Earlier quoted context omitted.

Learning about history is not the same as then being able to do research in history, nor being able to apply the principles learned from it in context. So no, reading a history book is learning about history, not necessarily being able to "do history". > You're making a weird distinction. As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry,…

>As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math Me too so now what? I don't think your credentials give you any real authority but just make you look like you're gatekeeping. >Doing the exercises is playing with the objects to try to answer specific questions. Great so then we're in agreement: playing with the object is doi…

> I don't think your credentials give you any real authority ...

It wasn't intended to, it was to provide a context for my opinion.

So let me state my opinion as clearly as I can, and then I'll leave it.

* Math is a "contact sport" ... you have to engage with it;

* Reading books is not, of itself, engaging with the math;

* Watching math videos is not, of itself, engaging with the math;

* Well designed exercises are a valuable resource;

* If you can easily do an exercise, skip ahead;

* If you can't do an exercise, persist (for a time);

* Ignoring the exercises is ignoring a resource;

* For the vast majority of people, doing the exercises is an efficient way to engage with the material;

* To say "ignore the exercises" is, for the vast majority of people, an invitation to not bother engaging with the subject;

* Doing all the exercises is probably a waste. Doing none of them is an invitation to end up with a superficial overview of the subject, and no real understanding.

Re: Mathematics for the Adventurous Self-Learner

#175

Post by khanacademygrad »

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…

Khanacademy

Re: Mathematics for the Adventurous Self-Learner

#176

Post by jcurbo »

This is a solid read, with good book recommendations. After several years of tinkering with self-learning I bit the bullet and applied to a MSc in Applied Math program. (via ep.jhu.edu) I've had to take some pre-reqs to get started since it's been almost 20 years since I have been in a college math class, but it's been an enlightening journey re-learning calculus and now dipping my toes into differential equations. I don't think I could have gotten this far with self-learning, but I realize YMMV.

I will say I don't feel like single-variable real number calculus tells the whole story. I had taken that and linear algebra in undergrad but never any further, and now that I've taken single and multiple variable calculus, with real and complex numbers, plus integration of linear algebra ideas, the mathematical model feels a lot more like a cohesive whole to me, highlighting fundamental ideas that only barely peek through in a typical Calculus I class. I would encourage anyone talking to calculus to at least do the typical Calc II class, if not Calc III/multivariate. There is a beauty and structure to building up from calc I through III that I was missing before.

Re: Mathematics for the Adventurous Self-Learner

#177

Post by User23 »

jhart99 wrote: post #164
dhimes wrote: post #125

Earlier quoted context omitted.

I hope I'm not too late here, but if you are in the US I would highly, highly recommend signing up for developmental classes at your local community college. You are exactly whom those classes are for. If you've tried on your own before and struggled to stay motivated, doing it in a structured way, in 15 week "sprints", may be just the kickstart to your self-study program you need. Disclaimer: I was a full-time commu…

I'd also like to chime in with support for community college math classes. I was pretty good at math to the point that it was becoming a problem for my JR High, so they sent me to the community college to take the math series starting from the bottom up. Went all the way through Differential Equations at community college. Maybe an even better way to start would be with trying to take a math class during the summer s…

I'd like to further recommend this course of action. Community colleges are a wonderful resource and at the one I attended the Math Department stood out as being particularly good. The student body tends to be extremely diverse too, from high school kids to retirees and everything in between. Oh and it's extremely affordable.

Re: Mathematics for the Adventurous Self-Learner

#178

Post by manu_ss »

leto_ii wrote: post #152
manu_ss wrote: post #139

Earlier quoted context omitted.

Seems to have some intro to logic and math language, if you have never read an math books as the ones referred in this post, that book should be a nice way to ease into it.

I see, thanks. I do have some experience with proofs and maths in general, but I never went through a text dedicated explicitly to developing proving techniques. I might give it a go anyway, but do you know of a more advanced version of this book as well?

Not really. I'm a math major, what you usually do is have an intro to logic course and then just jump into those books.

Re: Mathematics for the Adventurous Self-Learner

#179

Post by leto_ii »

manu_ss wrote: post #178
leto_ii wrote: post #152

Earlier quoted context omitted.

I see, thanks. I do have some experience with proofs and maths in general, but I never went through a text dedicated explicitly to developing proving techniques. I might give it a go anyway, but do you know of a more advanced version of this book as well?

Not really. I'm a math major, what you usually do is have an intro to logic course and then just jump into those books.

Thanks!

Re: Mathematics for the Adventurous Self-Learner

#180

Post by kevstev »

Do any of you all have some tips for understanding mathematical notation? I feel this is often poorly explained, and it feels like a language all its own that just does not speak to me. I did pretty well in calculus, but I still don't really understand what the dx was supposed to represent and in reality I was just really good at pattern matching when it wasn't supposed to be there anymore.

I try to read papers now and again with a math orientation, and I quickly get lost when trying to translate the concepts into cryptic formulas, and often when they make the "obvious" transition from step 3 to step 4 I just have no idea how they got there.

I feel this is by far my biggest barrier to understanding most mathematics, and I have thus far found no way to overcome it.

Post reply on HN