Number Theory Books: Find the Right Book for You!

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SUMMARY

The discussion centers on finding suitable number theory books that incorporate underlying algebra concepts, particularly for undergraduate students. The recommended title is "Elementary Number Theory: An Algebraic Approach" by Bolker, which is noted for its accessibility and affordability. The existing book by Everest and Ward is acknowledged but criticized for its brevity and lack of depth in algebraic explanations. Participants emphasize the importance of integrating group theory and ring theory in understanding key theorems like Fermat's Little Theorem and the Chinese Remainder Theorem.

PREREQUISITES
  • Understanding of abstract algebra concepts, including group theory and ring theory.
  • Familiarity with Fermat's Little Theorem and the Chinese Remainder Theorem.
  • Basic knowledge of number theory principles.
  • Experience with undergraduate-level mathematics coursework.
NEXT STEPS
  • Research "Elementary Number Theory: An Algebraic Approach" by Bolker for its algebraic insights.
  • Explore additional resources on group theory applications in number theory.
  • Investigate other number theory textbooks that emphasize algebraic methods.
  • Review the content of "Number Theory" by Everest and Ward for comparative analysis.
USEFUL FOR

Undergraduate mathematics students, educators in number theory, and anyone seeking to deepen their understanding of algebraic approaches in number theory.

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I'm looking for a good number theory book which doesn't hesitate to talk about the underlying algebra of some of the subject (e.g. using group theory to prove Fermat's Little Theorem and using ring theory to explain the ideas behind the Chinese Remainder Theorem). I'm still an undergraduate, so the book should be accessible to someone who has been through (or is going through, maybe) the standard undergrad abstract algebra coursework.

The book closest to my description is one by Everest and Ward, which I own already. The problem is that it's a little short and they shove aside some of the algebra in the earlier chapters as well...

Any suggestions?
 
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Try Elementary Number Theory: An Algebraic Approach by Bolker. I haven't read much of it, but it seems to be just what you're looking for. It's a little $10 Dover book, so you can't really go wrong.
 

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