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Mathematics for the Adventurous Self-Learner

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Re: Mathematics for the Adventurous Self-Learner

#41

Post by mnyary »

injb wrote: post #30
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 won't repeat the good suggestions already made, but I'll add this: find a set of the Open University MST124 text books. The OU publishes their own maths books, which are specially written for self-study (since that's your only option with the OU) and their courses generally assume very little or no previous knowledge. There's an even more basic course (MST123 I think) if that one is too advanced. These are serious…

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

Re: Mathematics for the Adventurous Self-Learner

#42

Post by l_t »

daxfohl wrote: post #22

This is so difficult. I've been doing it off and on for twenty years and not made much of a dent in things. The hardest part I think is understanding and measuring your progress. In school you've got exams and classmates to compare against, profs to talk to. Alone it's much harder. "Do I understand this well enough?" "Did I do the problems right?" (Especially with proof problems, how do you know you're right?). "I ca…

I've tried a few things recently that help with that:

1. Don't do exercises unless you want to. Completionism is a trap.

2. Take notes. Rewrite things in your own words. Imagine you're writing a guide for your past self.

3. Ask questions. Anytime you write something down, pause and ask yourself. Why is this true? How can we be sure? What does it imply? How could this idea be useful?

4. Cross-reference. Don't read linearly. Instead, have multiple textbooks, and "dig deep" into concepts. If you learn about something new (say, linear combinations) -- look them up in two textbooks. Watch a video about them. Read the Wikipedia page. _Then_ write down in your notes what a linear combination is.

Anyway, everyone's different of course, but these practices have been helping me get re-invigorated with self-learning math. Hope they help someone else out there. I welcome any feedback!

(edit: formatting)

Re: Mathematics for the Adventurous Self-Learner

#43

Post by integerclub »

For all the adventurous self-learners out here, we would like to invite you to our self-study group named Integer Club.

IRC: https://webchat.freenode.net/#integerclub

Slack: https://bit.ly/integerclubslackinvite

Mailing list: https://groups.google.com/d/forum/integerclub

We pick up old concepts from popular textbooks and literature as well as new stuff from new literature in both mathematics and computer science. We plan to have online meetings periodically to share what we learn, work through popular literature, and have a few talks on interesting topics.

It is a tiny community right now that hangs out at Freenode IRC but the Slack channel is there too if you are more comfortable with that.

Re: Mathematics for the Adventurous Self-Learner

#44

Post by daniel_reetz »

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 had the same problem. There is a series of books for folks like us -"Pre-Algebra Demystified", "Algebra Demystified" etc. I used them to catch up for a graduate level statistics course. One hour every morning for three months took me from pre-algebra through trig, and I did very well in class. I loved these simple books. They contain exactly zero owl-drawing.

Re: Mathematics for the Adventurous Self-Learner

#45

Post by throwlaplace »

l_t wrote: post #42
daxfohl wrote: post #22

This is so difficult. I've been doing it off and on for twenty years and not made much of a dent in things. The hardest part I think is understanding and measuring your progress. In school you've got exams and classmates to compare against, profs to talk to. Alone it's much harder. "Do I understand this well enough?" "Did I do the problems right?" (Especially with proof problems, how do you know you're right?). "I ca…

I've tried a few things recently that help with that: 1. Don't do exercises unless you want to. Completionism is a trap. 2. Take notes . Rewrite things in your own words. Imagine you're writing a guide for your past self. 3. Ask questions . Anytime you write something down, pause and ask yourself. Why is this true? How can we be sure? What does it imply? How could this idea be useful? 4. Cross-reference . Don't read…

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 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. a lot of exercises are a hazing ritual or imagined by the author to be a dose of bitter medicine (i'm looking at you electrodynamics by jd jackson) since they mistakenly believe all readers are formal students.

the most important exercise is to mull over and consider what you're reading/learning. naturally dovetails in to asking question: what happens if i remove a hypothesis from a theorem, what happens if i add one, is there an analogy to another object/group/measure/etc, etc.

also read multiple books (http://libgen.is/ is your very very good friend and generous friend). a lot of math authors (no matter how esteemed they are) are terrible writers or make mistakes (look up errata for previous editions of your favorite book).

the only thing i'd add is to learn to use LaTeX to take notes - it is much easier and faster and neater.

Re: Mathematics for the Adventurous Self-Learner

#46

Post by integerclub »

dorchadas wrote: post #34
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…

Ha - I actually suggested the exact same thing before seeing your post. It's definitely much better to have a group. Since I've found this group I'm currently in, I've also been much more motivated, but also able to get feedback from more advanced people, and pare the problem numbers down to only the ones that are useful and will help me build concepts, limiting how many "calculation" problems I have to repeat.

Made a group announcement on the same topic on this thread: https://news.ycombinator.com/item?id=22401750

See the user profile of my account for more details.

Re: Mathematics for the Adventurous Self-Learner

#48

Post by p1esk »

laichzeit0 wrote: post #36

I pretty much followed the same route as OP re-studying mathematics seriously after 10 years in industry after initially doing a CS degree and doing mostly software engineering but transitioning into Data Science the last 3 years. When I saw Book of Proof then Spivak then Apostol on his list I chuckled because that’s exactly the route I ended up following as well. Studying from 04:30 to 06:30 in the week and about 8…

So, you've made all that effort, how does it help you in your new role as a data scientist? Is there anything you do now that requires "mathematical maturity"? Or is it something that can be learned much quicker on as needed basis?

Re: Mathematics for the Adventurous Self-Learner

#49

Post by dentalperson »

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…

It's not super clear to me how this actually works in practice. I've seen there is one public math meetup in SF, but the topic is usually different from the one I want to study.

I'm glad to see there are online options for groups like Stack Exchange or tighter group's like the one integerclub mentions, but I still seem to run into the same problem. For example, I'm not sure how to get a group of people that are interested in reading book X when I want to start it. If anyone has advice on that, please share.

Re: Mathematics for the Adventurous Self-Learner

#50

Post by peterhj »

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 first learned about calculus from, I think, this book, "Calculus the Easy Way" [1] (or, at least the first chapter or two). It does make use of some algebra, but you're not necessarily limited to the strict progression of pre-algebra -> algebra -> calculus.

[1] (amazon: https://www.amazon.com/Calculus-Easy-Way-Douglas-Downing/dp/...)

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