71–80 of 281 posts
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…
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…
I am always so disappointed when I hear people express this. Being able to place an effort in a broader context is so helpful in being able to approach the work well. A few teachers in the Literature department in high school had the same attitude and it was incredibly demoralizing and left me kinda directionless in their classes. I wish things like https://youtube.com/watch?v=suf0Jdt2Hpo had existed back then to give me some idea of what useful and interesting literary analysis looked like and could do.
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…
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…
http://www.cs.cmu.edu/~tom/mlbook.html
Where other textbooks tended to jump two or three steps ahead with a comment about the steps being "obvious" or "trivial", Mitchell would just include each little step.
Yes, you could argue it was my responsibility to remember all of my calculus and linear algebra. But it is kind to the reader to spell out the little steps, for those of us who maybe forgot some of our calculus tricks, or maybe don't even have all of the expected pre-requisites but are trying to press on anyway. Or actually know how to perform the steps but have to stop and puzzle through which particular combination of steps you are describing as "obvious" in this particular instance.
I just remember how nice it was to have those extra steps spelled out, and how much more pleasant it made reading Tom's book.
So thanks, Dr. Mitchell!
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.
Earlier quoted context omitted.
> (the one exception is that I always found proving things difficult) Proofs are at the heart of math. Everything else is something different.
V.I. Arnold: “Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of characters.”
Arts -> Social Sciences -> Life Sciences -> Physical Sciences -> Mathematics -> Arts
Mathematics was/is a very creative process for me.
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.
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…
> type theory Not sure if related to your username, but I have a book on it (that was recommended to me here, in fact) on this topic, which I was curious about due to its implications in the programming field
Earlier quoted context omitted.
> (the one exception is that I always found proving things difficult) Proofs are at the heart of math. Everything else is something different.
V.I. Arnold: “Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of characters.”
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…
I don't know... I'm taking a theory of computability class right now and I'm sure glad that the pumping lemma for regular languages is called "the pumping lemma for regular languages"
The intuition for the person who discovered this lemma, clearly envisioned the underlying process as a device pumping out new strings belonging to the language.