Recommendation for textbook on number theory

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Discussion Overview

The discussion revolves around recommendations for textbooks on number theory, particularly for a course that currently lacks an assigned textbook. Participants share their experiences and suggest resources to aid in preparation for an upcoming test.

Discussion Character

  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses the need for a textbook to supplement their number theory course, which does not use a specific text.
  • Another participant requests clarification on the topics covered in the course to provide more tailored recommendations.
  • Topics covered in the course include divisions, GCD, modular arithmetic, Fermat's Little Theorem, Fermat and Mersenne primes, Euler's phi function, and orders.
  • One suggestion is "Elementary Number Theory" by Jones & Jones as a potential resource.
  • Another participant mentions "Elementary Number Theory" by Rosen and Ireland, noting it is considered a classic text.
  • Concerns are raised about the difficulty level of the Rosen and Ireland text, with one participant describing it as a "graduate text."
  • A participant mentions that the Rosen and Ireland book is recommended on their university's course website for an undergraduate course, suggesting it may depend on the reader's mathematical maturity.
  • Another participant acknowledges the difficulty of Rosen & Ireland but suggests it could be beneficial for those who can follow it, while recommending a more accessible book instead.
  • One participant recommends "Elements of the Theory of Numbers" by Dence as an accessible introduction that covers the listed topics and more advanced subjects.
  • A suggestion is made to search online for number theory ebooks or torrents to find additional resources.

Areas of Agreement / Disagreement

Participants express a range of opinions on the suitability and accessibility of different textbooks, indicating that there is no consensus on a single recommended text. Some participants advocate for more accessible options, while others reference more advanced texts.

Contextual Notes

Participants have not reached a consensus on which textbook is the best fit for the course, and there are varying opinions on the difficulty and appropriateness of the suggested texts based on individual mathematical backgrounds.

dpackard
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So I'm in a number theory course this semester but we aren't using a textbook (the professor gave the explanation that they'd never found a textbook that does exactly what they wanted or something, but it seems from my investigations that our course follows a pretty standard introduction).

Anyway, I have a test coming up this week, and I think I'd like to find a good textbook to help me prepare. This is the second test, and after not performing as well on the first test as I would have liked, I believe reading something else would help. My notes are too disorganized to be of real use besides helping me remember concepts, and I obviously cannot write down detailed explanations of the "whys", only copy down the "hows." So if you know of a good book for this purpose, I would really appreciate any recommendations.
 
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It would help if you listed the topics your course is covering!
 
sorry! we've covered divisions, GCD, modular arithmetic, fermat's little theorem, fermat and mersenne primes, euler's phi function, and orders so far.
 
Try Elementary Number Theory by Jones & Jones.
 
well, if I'm not mistaken the classic is by rosen and ireland.
 
The rosen and ireland one seems to be a "graduate text," would you still recommend it?
 
I hate it when therer is no textbook, especially when there exists a million out there for number theory.
 
dpackard said:
The rosen and ireland one seems to be a "graduate text," would you still recommend it?
well it's recommended in my univ's course website here:
http://www.math.tau.ac.il/~rudnick/courses/int_numth.html
and it's an undergraduate course, so I guess it depends on your mathematical maturity.
 
Rosen & Ireland is hard. If you can follow it, you'll be well-prepared... but you might be better served by a more accessible book. I keep mine on a shelf and consult it when needed.
 
  • #10
I would strongly recommend Elements of the Theory of Numbers by Dence. It is a very accessible and up to date introduction to the subject, covering all of the subjects you listed in addition to more advanced subjects suitable for a second course in number theory. Or, you could just search for "number theory ebook" or "number theory torrent" on google and download a plethora of books from which you have your choice.
 

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