20151026, 14:35  #1 
"Mike"
Aug 2002
8,167 Posts 
"A First Course in Number Theory" discussion group
Mr. Silverman has recommended this book for us to read to learn the basics of number theory.
http://www.amazon.com/FirstCourseN.../dp/0534085148 We have ordered a copy. It looks like you can get one for around $15 shipped easily. The idea we propose is that maybe some of you all will get the same book and then as a forum we can (slowly!) work through the book. (Buy your book now before the demand drives the prices up!) It would be awesome if people who are already proficient in this field would be available to help. What do you all think of this idea? We picture this as a longterm project, similar to one of the forum's chess games. If this idea takes off we can make a separate subforum for it, or whatever you all want to do. Thoughts and suggestions are appreciated! 
20151026, 18:35  #2  
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
9577_{10} Posts 
Quote:
What other math courses should one have taken (or learned) as a prerequisite for this? 

20151026, 18:43  #3 
Nov 2003
1D24_{16} Posts 

20151026, 19:35  #4  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·7^{2}·109 Posts 
Quote:
Much valuable mathematics has been inspired without rigorous proofs being produced. The Riemann hypothesis is a notorious example, as is Fermat's last theorem. Many results in computational number theory are conditional on unproven conjectures. 

20151026, 19:44  #5 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·7^{2}·109 Posts 
On a more constructive note than my previous comment  the ability to perform background reading, including knowing how to search for background information and how to ask questions should it prove necessary afterwards. In summary: to understand the difference between training and education.

20151026, 21:16  #6  
Nov 2003
2^{2}·5·373 Posts 
Quote:
e.g. as a start, derive the Fundamental Theorem of Arithmetic. Show that it is true. Do people need a hint? Start by Proving: If p is prime and p  ab then pa or pb. Note that this is NOT true if p isn't prime, e.g. 6  (4*3) but 6 divides neither 4 nor 3. Unfortunately, it is too easy for people to cheat (and they cheat themselves in the process) by looking such things up on Wiki. 

20151026, 21:32  #7 
If I May
"Chris Halsall"
Sep 2002
Barbados
2568_{16} Posts 

20151026, 21:33  #8  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
29BA_{16} Posts 
Quote:
I'm trying to draw a distinction between proving the FTA and, say, proving that the NFS runs in L(1/3) time. 

20151026, 21:52  #9  
"Gang aft agley"
Sep 2002
2×1,877 Posts 
Quote:
A common path among acquaintances with the benevolence of slight mutual mentoring sounds nice. 

20151026, 22:23  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
linear algebra, modern algebra, and number theory. Do you know what it means for a group to act on a set by conjugation? no? Then you are not ready for this book. 

20151026, 22:31  #11  
Nov 2003
16444_{8} Posts 
Quote:
Or is this just a taunt? As with all homework (not just math!) one learns by doing. Do you know what the theorem says? Look it up. Now ask: What do I need to show in order to establish that the result is true? This is one of the most basic and fundamental results in number theory. If the theorem as a whole is too hard, can you prove the following, If p,q are primes, then p*q != r*s, where r,s are not equal to either p or q. 

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