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Learning Math

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Re: Learning Math

#51

Post by davidw »

curi wrote: post #46
iamwil wrote: post #44

Earlier quoted context omitted.

Generally, people that pervade hacker news are pretty sensitive to cultivate a high signal to noise ratio, probably because a lot of us have the 'slippery slope' mentality, and seen what can happen if you give and inch, if Reddit and Digg are any indication. In the guidelines: "Resist complaining about being downmodded. It never does any good, and it makes boring reading. " If your comments don't add any information…

How come people who want a high signal to noise ratio, downmod a short, helpful comment which lets someone know not write "thanks" 6 times? In other words, I was asking someone to improve the signal to noise ratio. As far as getting downmodded for my additional comments, I expected that and don't mind. I have read the rules. BTW, I do think people here are far too inclined to downmod stuff they dislike without refuti…

Or, if you don't like it, let it stay at 0 or -1. No need to keep going beyond that for anything but blatant trolls.

Re: Learning Math

#52

Post by rms »

curi wrote: post #46
iamwil wrote: post #44

Earlier quoted context omitted.

Generally, people that pervade hacker news are pretty sensitive to cultivate a high signal to noise ratio, probably because a lot of us have the 'slippery slope' mentality, and seen what can happen if you give and inch, if Reddit and Digg are any indication. In the guidelines: "Resist complaining about being downmodded. It never does any good, and it makes boring reading. " If your comments don't add any information…

How come people who want a high signal to noise ratio, downmod a short, helpful comment which lets someone know not write "thanks" 6 times? In other words, I was asking someone to improve the signal to noise ratio. As far as getting downmodded for my additional comments, I expected that and don't mind. I have read the rules. BTW, I do think people here are far too inclined to downmod stuff they dislike without refuti…

I upmodded every post in your comments history.

<3 downmodders.

Re: Learning Math

#53

Post by curi »

rms wrote: post #52
curi wrote: post #46

Earlier quoted context omitted.

How come people who want a high signal to noise ratio, downmod a short, helpful comment which lets someone know not write "thanks" 6 times? In other words, I was asking someone to improve the signal to noise ratio. As far as getting downmodded for my additional comments, I expected that and don't mind. I have read the rules. BTW, I do think people here are far too inclined to downmod stuff they dislike without refuti…

I upmodded every post in your comments history. <3 downmodders.

lol. did you read them?

Re: Learning Math

#54

Post by vitaminj »

asdflkj wrote: post #42
vitaminj wrote: post #39

Earlier quoted context omitted.

I certainly agree that logic, set theory, etc are the formal bases of mathematics, but I wouldn't say they are the basics. It'd be like learning the syntactic rules of grammar before learning words and constructing simple sentences by rote. Sometimes it's better to have an appreciation of the goals (which are easier to learn) before embarking on the fundamentals (which are rigorous but abstract). When I first started…

I agree about the zig-zag path, but I don't think it necessarily means you should study calculus before set theory (for example). Only that you shouldn't delve too deep on your fist pass over set theory. Obviously, AOC independence proof would not be suitable for high school students. But it doesn't take much effort to understand what a function is in terms of sets. And don't they teach Venn diagrams to kids in grade…

Yeah fair enough

Re: Learning Math

#55

Post by kashif »

At your level, you may want to go through the video lectures - "Joy of Mathematics" Google for it.

PS: There is some excellent advice here and I intend to make good use of it. Thanks everyone.

Re: Learning Math

#56

Post by Prrometheus »

projectileboy wrote: post #40

Funny you should ask... I took a lot of math classes all through college, but at every step I was reaching beyond my grasp, so I never had great understanding. And then after a few years, I forgot it all. So in my early thirties, I started over. Much more important than which text you use is your attitude, and a willingness to really walk through and understand the proof of a theorem, and a willingness to work throug…

Number theory is cool because it works with items that everybody understands, namely numbers. The only prerequisites you need are basic concepts like squares, even and odd numbers, and similar items. Instead of building up some giant edifice of weird symbols and concepts, like one does in calculus, you're just solving puzzles.

It will also answer 90% of the "hard" problems on the GRE, if anybody cares.

Also, I second not jumping into calculus too quick. It can be frustrating and isn't terribly useful for problems outside of Physics.

Re: Learning Math

#57

Post by Kaizyn »

There's an author Morris Kline who wrote a number of fairly useful books on mathematics. Particularly worth mentioning are Mathematics for the Nonmathematician and Calculus: An Intuitive and Physical Approach. The former traces through the history of mathematics and places each of the math discoveries in their proper context. The latter covers most of the topics covered in the first couple calculus classes. What makes Kline's approach valuable is how he grounds the abstract math topics in practical examples and in ways making them more accessible than your typical textbooks.

Re: Learning Math

#58

Post by giardini »

Before digging into the various books others have suggested, you would do well to read "Where Mathematics Comes From" by George Lakoff and Rafael Nunez: http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring...

That book explains the origins and understanding of the basic items of mathematical analysis: infinity, sets, classes, limits, the epsilon-delta of calculus and alternatives, infinitesimals, etc. The explanation is from the viewpoint of psychological understanding. It details how we build up a scaffolding of tools (starting with basic counting) sufficient to slay the dragons of modern physics and mathematics.

Re: Learning Math

#59

Post by cwurld »

projectileboy wrote: post #40

Funny you should ask... I took a lot of math classes all through college, but at every step I was reaching beyond my grasp, so I never had great understanding. And then after a few years, I forgot it all. So in my early thirties, I started over. Much more important than which text you use is your attitude, and a willingness to really walk through and understand the proof of a theorem, and a willingness to work throug…

Nice list. I have been kind of doing the same thing - only over many years. One book that was incredible and disturbing was a small paperback - giving a layman's guide to Godel's Proof (maybe by Nagel&Newman?). The topic is too abstract to ever apply to a real world problem. But it is so profound that it is hard to imagine going through life not knowing it.

Re: Learning Math

#60

Post by timmmccoy »

projectileboy wrote: post #40

Funny you should ask... I took a lot of math classes all through college, but at every step I was reaching beyond my grasp, so I never had great understanding. And then after a few years, I forgot it all. So in my early thirties, I started over. Much more important than which text you use is your attitude, and a willingness to really walk through and understand the proof of a theorem, and a willingness to work throug…

very interesting.

network and graph theory are definitely interesting topics. but what you've covered is most definitely a lot of interesting math. im an engineering (just a freshman), so all i get to see is integral calc. but theres definitely a lot of interesting math out there. combinatorics is also pretty nifty.

a very nice structured list. i might have to go pick up some books...

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