I no longer understand my PhD dissertation • Hacker News Board

Re: I no longer understand my PhD dissertation

#81

Post by YeGoblynQueenne » Mon, Feb 15, 2016, 2:10 AM UTC

jholman wrote: post #12

All of these arguments are arguments for replacing the mathematics curriculum with video gaming. Games require generalized problem solving (arguably better-generalized than math, and arguably better-transferrable to other domains). Games build character: grit and tenacity, cautious optimism, etc blah blah etc. And games are fun (for many more people than find math fun). Guess math teachers should start learning to pl…

Don't laugh it off. Personally, I learned to code by building Magic: the Gathering decks and playing at tournaments at high school. I learned things about resource management, reducing solutions, integrating disparate components into a functional system and so on, and even a bit of probabilities along the way. Not to mention what it did for my ability to concentrate and analyse an adversarial situation.

If you think about it, a lot of education is really a kind of game and games themselves are often educational, usually by accident.

Frex, I think a lot of people would recognise the value of teaching kids to play chess in order to improve their concentration and problem-solving skills. Well, why not more modern board games?

Re: I no longer understand my PhD dissertation

#82

Post by vlunkr » Mon, Feb 15, 2016, 2:10 AM UTC

brachi wrote: post #64

rjzzleep wrote: post #56

Earlier quoted context omitted.

In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went o…

> Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based univers…

High school math was awful at this in the US. I went through a year of calculus and never knew what the heck it was for.

Re: I no longer understand my PhD dissertation

#83

Post by ivansavz » Mon, Feb 15, 2016, 2:12 AM UTC

rjzzleep wrote: post #56

gjulianm wrote: post #42

Earlier quoted context omitted.

> I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition. If it only happened on mathematical papers... It is all over the place, in books, classes, etc. Few professors tell you what are they doing and why; they just throw formulas, theorems and symbols at you. Intuition is not given its necessary importance, first because it's hard to grasp some con…

In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went o…

> Why can't we just provide a simple real life example first and then go on explaining the details?

That's a very good approach, which I try to follow in all my writings. Basically, I imagine a reader that is generally uninterested in the material, so the first thing to do is to "pitch" the mathematical concept using a simple example, or just say why the concept is useful. In the remainder of the lesson, I assume the reader might lose interest and stop reading at any point, so this is why I put the most valuable content first (definitions and formulas), followed by explanations, and finally a general discussion about how the material relates to other concepts.

Re: I no longer understand my PhD dissertation

#84

Post by jimbokun » Mon, Feb 15, 2016, 2:15 AM UTC

vinceguidry wrote: post #65

cname wrote: post #63

Earlier quoted context omitted.

> I don't see comments helping me... I don't know why people say this type of thing, as if there's some choice you have to make between good names and comments. You can have both, and there are absolutely times when comments are necessary . Too many comments may be a "smell", but code that doesn't require any comments at all is very unlikely.

> there are absolutely times when comments are necessary . I'll have to take your word for it, because I've yet to run into that situation.

I find one place where comments are absolutely critical is in external facing APIs. Summary of the purpose of the API, purpose of each method, valid arguments and possible return values. Think how often you need to read the comments for whatever libraries and APIs you use in your work.

Re: I no longer understand my PhD dissertation

#85

Post by seanp2k2 » Mon, Feb 15, 2016, 2:16 AM UTC

brachi wrote: post #64

rjzzleep wrote: post #56

Earlier quoted context omitted.

In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went o…

> Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based univers…

Yeah, teaching the basics of an abstract concept without first explaining how it fits into the bigger picture is IMO not the best way to motivate some people. I'm also a person who wants to understand why it's important instead of just trusting someone that it'll be useful "later".

It'd be cool if, once you start your major, there was basically an overview class explaining why each of your courses is important and what concepts (at a high level) you should be grokking with each course and semester; basically some context to frame your learnings.

Re: I no longer understand my PhD dissertation

#86

Post by ghthor » Mon, Feb 15, 2016, 2:17 AM UTC

vinceguidry wrote: post #65

cname wrote: post #63

Earlier quoted context omitted.

> I don't see comments helping me... I don't know why people say this type of thing, as if there's some choice you have to make between good names and comments. You can have both, and there are absolutely times when comments are necessary . Too many comments may be a "smell", but code that doesn't require any comments at all is very unlikely.

> there are absolutely times when comments are necessary . I'll have to take your word for it, because I've yet to run into that situation.

Comments are incredibly useful for that bit of code that you spent hours trying to make it work and you couldn't figure out a way to name things well or to improve it. That's where a comment is priceless.

Re: I no longer understand my PhD dissertation

#87

Post by jimbokun » Mon, Feb 15, 2016, 2:21 AM UTC

closure wrote: post #73

layble wrote: post #70

Earlier quoted context omitted.

I can totally relate and to this day I describe one of my greatest failures as a manager as analogous to how "easy" math was to me. Until Calc II I really found nothing about math challenging at all. The result of this was that everyone wanted me to tutor them in math. The problem was that I didn't solve math problems like other people did, in fact I had no idea how I did what I did. I just did it. As a result when I…

This is why I have always found proofs difficult. I just don't know what steps people think are important to spell out but.

Then spell out all of them, and have someone else tell you when it's become too tedious.

Re: I no longer understand my PhD dissertation

#88

Post by brachi » Mon, Feb 15, 2016, 2:27 AM UTC

crackpotbaker wrote: post #25

closure wrote: post #11

This does not surprise me in the least. Math was always extremely easy for me growing up. Up through my first differential equations class I found almost everything trivial to learn (the one exception is that I always found proving things difficult). I made the mistake of minoring in math and that slowly killed my enjoyment of it. Once I got to differential geometry and advanced matrix theory it all just became too a…

General skill of problem solving seems to stick with you forever. It's probably because most of your problem solving knowledge is your own invention. Whereas math and programming is your own invention if you solve all the problems by yourself, if you code everything from the start. This gives you the understanding of the problems, and the reasoning/tools to solve it. I've been dropping in and out of problem solving f…

Reminds me of the quote "What I cannot create, I do not understand." by Feynman.

Re: I no longer understand my PhD dissertation

#89

Post by aldanor » Mon, Feb 15, 2016, 2:29 AM UTC

As someone who left academia after a PhD in math (been working as a quant in HFT for the last few years, which mostly involves coding in one form or another), I can totally relate! Back then, all those stochastic integrals and measures made much more sense. However, it doesn't seem totally alien -- I'm pretty sure I could go to hacking math if required, but it would require at least several months to get into the flow.

Re: I no longer understand my PhD dissertation

#90

Post by vinceguidry » Mon, Feb 15, 2016, 2:30 AM UTC

ghthor wrote: post #86

vinceguidry wrote: post #65

Earlier quoted context omitted.

> there are absolutely times when comments are necessary . I'll have to take your word for it, because I've yet to run into that situation.

Comments are incredibly useful for that bit of code that you spent hours trying to make it work and you couldn't figure out a way to name things well or to improve it. That's where a comment is priceless.

Maybe it's because I write in Ruby, and so never have to do any tricky optimizing, but if solving a particular problem starts to run over a half hour, I look to re-architect the project, either by reaching for a gem or telling my boss that X is too hard and we should do Y instead. My patience for going down rabbit holes has mostly gone over the last year.

Also, again perhaps because I use Ruby, it never takes me more than a few seconds to name something. If it does, then it's a code smell and I go looking for the missing class.