Discover the Best Basic Books on Number Theory

In summary, number theory is a branch of mathematics that studies integers and their properties. Some important topics in number theory include prime numbers, divisibility, modular arithmetic, Diophantine equations, and the distribution of prime numbers. It has many real-world applications in areas like cryptography, coding theory, finance, physics, and engineering. To improve understanding, one can study textbooks, attend lectures and seminars, and solve practice problems. There are also famous unsolved problems in number theory, such as the Goldbach Conjecture, Twin Prime Conjecture, and Riemann Hypothesis.
  • #1
kurt.physics
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Is there any good "basic" books on number theory?
 
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  • #2
If by "basic" you mean elementary, try Courant's "What is mathematics".

Its a classic text and its cheap to buy. Its got very good stuff on our number system, from natural numbers, primes, rationals, and irrationals. Its one of the best books I have ever read. Its not a book exclusivley on number theory though, rather it has chapters on a bunch of interesting math bits. More of a "intro to abstraction" type of book. Check it out, its a damn good read.
 

What is number theory?

Number theory is a branch of mathematics that deals with the study of integers and their properties, patterns, and relationships.

What are some important topics in number theory?

Some important topics in number theory include prime numbers, divisibility, modular arithmetic, Diophantine equations, and the distribution of prime numbers.

What are some real-world applications of number theory?

Number theory has many practical applications, such as in cryptography, coding theory, and computer science. It is also used in areas like finance, physics, and engineering.

How can I improve my understanding of number theory?

To improve your understanding of number theory, it is recommended to study algebra and number theory textbooks, attend lectures and seminars, and solve practice problems and exercises.

Are there any famous unsolved problems in number theory?

Yes, there are several famous unsolved problems in number theory, such as the Goldbach Conjecture, the Twin Prime Conjecture, and the Riemann Hypothesis. These problems have puzzled mathematicians for centuries and continue to be important areas of research.

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