more/better number theory than AoPS?

[AEC]

Hello!

 

  DD12 enjoys math -in particular number theory.  She's been through AoPS Intro Alg. I've got the AoPS NT book and we'll start on that soon in parallel w/ Geometry.  I wonder if anyone has suggestions for better or more thorough programs that she could handle w/o a ton more background.  It's such a big and interesting subject, but the AoPS book doesn't seem to really cover much.  I was motivated to find something better by

 

http://www.cnn.com/2016/07/17/asia/china-migrant-worker-good-will-hunting/ and it's reference to Carmichael numbers...

[Mike in SA]

There are quite a few texts which run deeper, but I don't know of many as accessible.  Many are written for college students, with the assumption that they have had some formal pure math.  Intro to Algebra doesn't quite get there, to say the least (their precalculus text probably does, though only just).

 

We have a book called "Theory of Arithmetic" which goes into other number systems used historically, and then dives into number theory, but it is long out of print and hard to get.  I'm sure there are others like it - I just couldn't suggest one.  You will probably find supplemental problem solving books pretty easily.  The Art of Problem Solving (the originals) might be an option...

 

 

[lewelma]

The intermediate number theory class through AoPS is a huge leap forward, but it does not have a textbook.

 

Ruth in NZ

[quark]

You might have to pick and sort through selections.

 

Number Theory: A Lively Introduction

 

Beiler's Recreations in the Theory of Numbers

 

When DS was interested in abstract algebra and a few other things, we had luck just googling 'introductory' + 'name of the topic' and attaching a 'pdf' at the end of the search term. You might be able to find pdf texts online in the same way. Then see if they are accessible to her level.

 

If she likes number trivia, Prime Curios and Number Freak are fun.

 

I agree with Mike about the AoPS Vol 1 and 2 books.

 

ETA: She might like N is a Number, a documentary about Paul Erdos.

 

Edited July 19, 2016 by quark

[AEC]

thanks for the suggestions - I'll check those out.

 

And we'll go through the AoPS book as well, and I'm sure it'll be useful.  She's loved all their books so far <shrug>.

Just from looking through the ToC it seems a bit underwhelming.

[quark]

thanks for the suggestions - I'll check those out.

 

And we'll go through the AoPS book as well, and I'm sure it'll be useful.  She's loved all their books so far <shrug>.

Just from looking through the ToC it seems a bit underwhelming.

 

In that case, just borrow a copy of Vol 2 and don't buy the books yet. DS found Vol 2 more interesting than Vol 1. But he's not a 100% AoPS books all the time kind of kid.

 

DS has however, become a 90%-ish-of-his-time on Crowd Math kind of kid...has your DD taken a look at that section of the AoPS website? She might really enjoy it.