Math Is Fun Forum

bossk171

Member

Registered: 2007-07-16

Posts: 305

Which book should I read first?

I have two books, both on subjects I'm fascinated by, both subjects way over my head.

The first is the four color theorem,  the second on Abel's proof that the quintic is unsolvable.

Which would be more approachable for someone who's education only includes High school up to and including Calculus? Which is more interesting to you guys? Which am I going to get halfway through, realize it's much harder than thought and give up in a fit of rage?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

precious

Member

Registered: 2007-01-05

Posts: 1

Re: Which book should I read first?

i think u should read the proof 1 first

hopped i helped:D:);):P

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Which book should I read first?

Four color theorem ... an interesting aspect is involving computer programs in a proof.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Which book should I read first?

Thanks, Anyone else?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Which book should I read first?

Well, Abel's proof is a bit out-of-the-way and abstract. The four color theorem has lots of applications and is a good exercise using counting arguments. It's totally up to you, of course, but I'd probably go for the four color theorem.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Which book should I read first?

When you say "out-of-the-way" What do you mean?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Which book should I read first?

Well, from what I've heard, it uses group theory, which is some pretty complicated abstract maths, and it likely doesn't have many applications. After all, it's just a proof.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Which book should I read first?

That makes more sense, thanks.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Which book should I read first?

It probably uses some form of Galois theory, which builds off of group theory.  I remember trying to learn Galois theory after an introduction to group theory, but I couldn't even get the least bit into it.  I would certainly recommend something else, for the time being.  But Galois theory has been called one of the most beautiful of all the mathematics, so it's certainly something to come back to when you're ready.

However, the four color theorem isn't every simple either.  You say you have only had up to high school calculus, then I wouldn't imagine you would have a lot (or any, really) combinatorics.

One book I would recommend is the construction of the number systems.  From Numbers To Analysis, by Rana is a book I have.  The construction of the integers from the naturals and rationals from the integers would be something quite doable for anyone who has a good understanding of algebra.  The construction of the reals and natural numbers on the other hand might be a bit much.

However I do recommend trying to bite off more than you can chew.  Just remember not to get frustrated when doing so.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Which book should I read first?

By now I have tried reading about 5 different books about number theory, and although I've done some exercises, everything I've learnt seems to slowly be slipping away. After all, I'm not going to encounter number theory again until university, and that's still 2 years away.

treehugger96

Member

Registered: 2007-12-24

Posts: 10

Re: Which book should I read first?

four colours therom

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........"To my mind having care and concern for others is the highest of human qualities"
.........Fred Hollows