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Learning Math

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Re: Learning Math

#41

Post by sgoraya »

I really found the following blog helpful for various math topics

http://betterexplained.com/articles/how-to-develop-a-mindset...

In addition, I have found myself reviewing 'Discrete Mathematics w/ Applications' by Epp on numerous occasions;

My .02 - review logic / discrete math & move from there - The fundamentals of math logic and reasoning have been very important for me - I always felt this type of course should have been taught before a lot of the other subjects like Calc / Diff Equations etc.

Good learning!

Re: Learning Math

#42

Post by asdflkj »

vitaminj wrote: post #39
asdflkj wrote: post #30

Start with mathematical logic, set theory, abstract algebra and number theory, in that order. Do not follow the usual course of calculus, differential equations, linear algebra and so on. That is, do learn those things, but later on. The problem with math education is that "the basics" (things that I recommend you start with) are neither easy to understand nor obviously useful in "the real world". Or at least the lat…

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 school? That's already set theory.

Re: Learning Math

#43

Post by curi »

curi wrote: post #36
curi wrote: post #18

You don't have to say "thanks" 6 times.

Wow. <3

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

Re: Learning Math

#44

Post by iamwil »

curi wrote: post #43
curi wrote: post #36

Earlier quoted context omitted.

Wow. <3

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

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 to the topic at hand, it usually gets downmodded. Exceptions seem to be if they're wise-ass or snarky comments.

Re: Learning Math

#45

Post by larryfreeman »

Hi,

I had the same feeling as you (when I was 38) and I started a blog: http://fermatslasttheorem.blogspot.com

I started with a sketch of the historical approach to Fermat's Last Theorem (Diophantus, Euler, Gauss, etc.) and I tried to resolve all proofs down to postulates.

I would recommend finding an area that you are interested in and then finding a famous problem. My favorite books are:

* Euler: Master of us all

* Euclid's Elements

* Hardy and Wright: Introduction to a Theory of Numbers

* Jonathan Stillwell: Yearning for the Impossible

* Ash and Gross: Fearless Symmetry

* Jean-Pierre Tignol: Galois' Theory of Algebraic Equations

* Edwards: Fermat's Last Theorem/Galois Theory

I've been doing it now for almost three years and it's really worked out well for me and surprisingly, I am getting around 11,000 unique visitors to my site every month.

Glad to see all the responses to your comment. :-)

-Larry

Re: Learning Math

#46

Post by curi »

iamwil wrote: post #44
curi wrote: post #43

Earlier quoted context omitted.

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

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 refuting it.

Re: Learning Math

#47

Post by bayareaguy »

larryfreeman wrote: post #45

Hi, I had the same feeling as you (when I was 38) and I started a blog: http://fermatslasttheorem.blogspot.com I started with a sketch of the historical approach to Fermat's Last Theorem (Diophantus, Euler, Gauss, etc.) and I tried to resolve all proofs down to postulates. I would recommend finding an area that you are interested in and then finding a famous problem. My favorite books are: * Euler: Master of us all *…

I love your blog. I used to follow it a few months ago (but then I got busy). Keep up the good work.

Re: Learning Math

#48

Post by Trep »

I remember when our math teacher stood in front of us in High School and told us math was important because of all the ways we'd use it...

She lied. I think I used the Pythagorean Theorem once, for a cool bookshelf, five years ago.

Now, I'm learning it all over again. One thing I've found is that if I can teach something, I understand it better. In that spirit, I'm volunteering with the local Alternative School, tutoring math. It works out great. I keep myself about two chapters ahead, the kids are bright and unafraid, and I find myself motivated ever time I plow into my own book.The best thing is, I spend less time tutoring the kids than the rest of my morbidly unmotivated 'catch up' math class spends practicing problem sets. I'm saving time, having fun, and understanding.

I highly recommend it.

Re: Learning Math

#49

Post by wallflower »

Trep wrote: post #48

I remember when our math teacher stood in front of us in High School and told us math was important because of all the ways we'd use it... She lied. I think I used the Pythagorean Theorem once, for a cool bookshelf, five years ago. Now, I'm learning it all over again. One thing I've found is that if I can teach something, I understand it better. In that spirit, I'm volunteering with the local Alternative School, tuto…

I've found that we don't know how much we don't know until we try teaching it to someone. Congratulations for choosing to tutor math. Long live SOHCAHTOA.

Re: Learning Math

#50

Post by foonamefoo »

iamwil wrote: post #44
curi wrote: post #43

Earlier quoted context omitted.

This is interesting. No one gives any reason I'm wrong about what I said. I don't quite see the purpose of downmodding a post that's already on the bottom and greyed out. But I guess no one is going to explain their reasons.

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…

So by this logic you (and I) should be downmodded.
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