Undergraduate Level Number Theory Text

In summary, the book "An Introduction to the Theory of Numbers" by G.H. Hardy does not include any practice problems, and may not be suitable for use in a modern number theory course. "A Course of Pure Mathematics" by Hardy is a good book to have, but is not as up-to-date as some of the other texts available.
  • #1
GreenMathlete
6
0
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.
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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!
 
Last edited:
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
Last edited:

1. What is number theory and why is it important?

Number theory is a branch of mathematics that deals with the properties and relationships of numbers. It is important because it has many applications in fields such as cryptography, computer science, and physics. It also helps us understand the fundamental structure of numbers and their patterns.

2. What topics are typically covered in an undergraduate level number theory text?

An undergraduate level number theory text typically covers topics such as prime numbers, divisibility, modular arithmetic, congruences, Diophantine equations, and quadratic residues. It may also touch on more advanced topics such as continued fractions, cryptography, and the Riemann Hypothesis.

3. Is a strong background in mathematics necessary to study number theory?

A strong background in mathematics is helpful, but not necessarily required, to study number theory at an undergraduate level. Basic knowledge of algebra, geometry, and calculus is usually sufficient. However, a strong foundation in logical reasoning and problem-solving skills is important for understanding and applying the concepts in number theory.

4. How can studying number theory benefit me in my future career?

Studying number theory can benefit you in a variety of ways, depending on your career path. If you are interested in pursuing a career in mathematics, computer science, or cryptography, a strong understanding of number theory is essential. It can also improve your critical thinking and problem-solving skills, which are valuable in any field.

5. Are there any real-world applications of number theory?

Yes, number theory has many real-world applications. For example, it is used in cryptography to secure communication and protect sensitive information. It is also used in computer science for data encryption and error detection. In addition, number theory has applications in fields such as physics, engineering, and economics.

Similar threads

  • Science and Math Textbooks
Replies
3
Views
806
  • Science and Math Textbooks
Replies
2
Views
1K
  • Science and Math Textbooks
Replies
9
Views
4K
  • Science and Math Textbooks
Replies
19
Views
2K
  • Science and Math Textbooks
Replies
3
Views
2K
  • Science and Math Textbooks
Replies
8
Views
2K
  • Science and Math Textbooks
Replies
2
Views
1K
  • Science and Math Textbooks
Replies
5
Views
3K
  • Science and Math Textbooks
Replies
5
Views
1K
  • Science and Math Textbooks
Replies
13
Views
3K
Back
Top