Undergraduate Level Number Theory Text

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Discussion Overview

The discussion revolves around recommendations for undergraduate-level textbooks on number theory. Participants share their experiences with various texts, express preferences, and discuss the suitability of these books for self-study or coursework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for undergraduate-level number theory textbooks, indicating a solid math background but no prior exposure to the topic.
  • Another participant mentions "Elementary Number Theory" as an accessible and rigorous introduction, noting its affordability and ease of reading.
  • Several participants reference "Introduction to the Theory of Numbers" and "A Classical Introduction to Modern Number Theory" as commonly used texts in courses.
  • A participant expresses interest in the second book due to its basis in abstract algebra but admits to lacking motivation to engage with it fully.
  • One participant points out that the edition of "Introduction to the Theory of Numbers" used at Princeton is the sixth edition, which includes contributions from Andrew Wiles, but questions the relevance of the main text's updates since Hardy's death.
  • Another participant, after receiving the sixth edition of Hardy's book, notes the absence of practice problems and expresses concern about its suitability for coursework.
  • There is a suggestion to research books thoroughly before purchasing, especially if they have not been previewed.

Areas of Agreement / Disagreement

Participants express varying opinions on the suitability of different textbooks for undergraduate study, with some favoring certain texts while others raise concerns about their content and structure. No consensus is reached regarding the best choice for a primary textbook.

Contextual Notes

Some participants highlight the importance of practice problems in textbooks, indicating that the lack of such problems in certain recommended texts may limit their effectiveness for self-study.

GreenMathlete
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Hey guys. Does anyone know of a good undergraduate level textbook on number theory? I have a pretty solid undergraduate level math background but have never had the chance to take a course on this particular topic. If anyone could recommend a textbook that he/she likes, or is widely used at the undergrad level, I'd appreciate it. Thanks in advance.
 
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It is far less likely that someone will find and answer my question in this section of the forum than they would in the number theory section of the forum.
 
I never got around to studying number theory, either. I recently started reading this book:

Elementary Number Theory

It's very easy and pleasant to read, but it doesn't lack rigor. With a decent math background, you should be able to read it from start to finish in just a few days, yet it's quite interesting and doesn't feel brain-dead. (The exercises are mostly too easy, though.) And it's a Dover book so you can't beat the price: $8.79 on Amazon at the moment.

Most of the people I know who took a number theory course used one of these two books:

Introduction to the Theory of Numbers

A Classical Introduction to Modern Number Theory

The second one interests me more, because it's firmly based in abstract algebra, but every time I've looked into it, I lacked the motivation to get very far with it. Thus the decision to try reading a short elementary introduction first.
 
Thanks for the advice. I found out that the one called "Introduction to the Theory of Number" for which you posted the link, is the one they use at Princeton. There is another one of the same title but with different authors, which includes Andrew Wiles as an editor. It was 6th edition rather than 5th. I think I'm going to start with that one.
 
GreenMathlete said:
There is another one of the same title but with different authors, which includes Andrew Wiles as an editor. It was 6th edition rather than 5th. I think I'm going to start with that one.

I just checked on Amazon - that's the famous book by Hardy and Wright. Don't let the edition numbering fool you; it probably has an essay or foreword by Wiles, but the main text is unlikely to have been updated since the 1940s, as Hardy died in 1947. It's certainly a classic but I recommend taking a look at it before deciding its suitability as a standard undergraduate textbook nowadays.

I haven't read that book, but I have Hardy's "A Course of Pure Mathematics", which is of a similar vintage, and quite old-fashioned compared to today's analysis texts. It's fun and insightful to read, but I wouldn't recommend it as a primary textbook in 2012.

[edit] I see under the book description: "Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory."

So this may indeed be worth a look!
 
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Well, I finally got the sixth edition of the G.H. Hardy book in the mail today. At first glance it looks to have a lot of good information. However, it appears that there are no practice problems. Maybe this text isn't used in actual number theory courses? I am happy with the range of the material covered, but it's unfortunate that there are no practice problems and I may have to look for something to supplement this text. Not sure how I could have known in advance that there weren't going to be practice problems. Ugh.
 
GreenMathlete said:
Not sure how I could have known in advance that there weren't going to be practice problems. Ugh.

If you google "Hardy Wright Number Theory" the first results page has a thread on math.stackexchange noting that there are no problems in the book and asking for good companion texts with problems included. If you are going to buy a book that you have not glanced through before, then it is a good idea to research it thoroughly before buying it online.
 
jgens said:
If you are going to buy a book that you have not glanced through before, then it is a good idea to research it thoroughly before buying it online.

Yes, it is a good idea. I'm happy with my purchase.
 
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