Number Theory Books: Find the Right Book for You!

In summary, the conversation is about finding a good number theory book that incorporates algebra, specifically group theory and ring theory. The book should be accessible for someone with a background in undergraduate abstract algebra. The recommended book is "Elementary Number Theory: An Algebraic Approach" by Bolker, which is affordable at $10.
  • #1
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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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  • #3
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.
 

1. What is number theory?

Number theory is a branch of mathematics that deals with the study of integers and their properties, such as divisibility, prime numbers, and arithmetic operations.

2. Why should I read a book on number theory?

Reading a book on number theory can help you develop critical thinking skills, improve your problem-solving abilities, and gain a deeper understanding of mathematical concepts. It can also help you prepare for advanced mathematical studies or research.

3. What are the key topics covered in a number theory book?

The key topics covered in a number theory book include prime numbers, divisibility, congruences, Diophantine equations, and number systems. Some books may also cover more advanced topics such as cryptography and computational number theory.

4. Are there any prerequisites for reading a number theory book?

While a basic understanding of algebra and arithmetic is helpful, most number theory books are designed for readers with a strong foundation in mathematics. Some books may also assume knowledge of topics such as calculus or abstract algebra.

5. How do I choose the right number theory book for me?

The right number theory book for you will depend on your level of mathematical knowledge, your specific interests, and your learning style. It's important to read reviews and preview the content of the book before making a decision. You may also consider consulting with a math teacher or expert for recommendations.

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