Concise Introduction Book to Number Theory?

In summary, the person is seeking recommendations for introductory books on number theory before delving into analytic number theory for their research project. They mention that their advisers are not familiar with general introductions to number theory. One recommendation given is "A Classical Introduction to Modern Number Theory" by K.Ireland and M.Rosen, but the person mentions it does not fit their needs. Another suggestion is "Elementary Number Theory and Its Applications" by Kenneth Rosen, which is a concise and simple treatment of the basics of number theory and can be found used for a low price.
  • #1
Dear Physics Forum advisers,

Could you recommend me some brief, introductory books on the number theory I can read for few weeks before jumping into the analytic number theory? Big part of my near-future research project will involve a lot of the analytic number theory, so it is needed to read books like Iwaniec and Davenport. Unfortunately, I am not quite familiar with the basic number theory, so I thought it would be wise to seek your recommendation. Unfortunately, my advisers learned the NT from algebraic and analytic aspects, so they are not familiar with the general introduction.
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  • #2
"A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics)", by K.Ireland , M.Rosen.
  • #3
Ssnow said:
"A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics)", by K.Ireland , M.Rosen.

I just took a brief look at that book, and it does not fit with my need. I just need a concise introduction to the basics of NT before reading the analytic NT>
  • #4
If you want something really basic, you could try Elementary Number Theory and Its Application by Kenneth Rosen. The 4th edition can be had used for very little.

It's a very simple treatment, but I do still find it useful as a reference for some topics.

1. What is Number Theory?

Number Theory is a branch of mathematics that deals with the properties and relationships of numbers, particularly integers. It involves studying patterns and structures in numbers and their interactions with other mathematical concepts.

2. Why is Number Theory important?

Number Theory has many practical applications, such as in cryptography, coding theory, and computer science. It also helps us understand the fundamental properties of numbers and their behavior, which can lead to new discoveries and advancements in mathematics and other fields.

3. Who can benefit from learning Number Theory?

Anyone interested in mathematics can benefit from learning Number Theory. It is particularly useful for students pursuing degrees in mathematics, computer science, and engineering. It can also be beneficial for individuals in fields that involve problem-solving and critical thinking skills.

4. Is a background in advanced mathematics necessary to understand Number Theory?

A basic understanding of algebra and geometry is helpful, but it is not necessary to have a background in advanced mathematics to understand the concepts in Number Theory. This introductory book is designed to be accessible to readers with a range of mathematical backgrounds.

5. What topics are covered in this Concise Introduction Book to Number Theory?

This book covers a wide range of topics in Number Theory, including prime numbers, divisibility, factorization, congruences, and Diophantine equations. It also includes real-world applications and examples to help readers understand the relevance of Number Theory in various fields.

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