Introductions to number theory

In summary, the individual is seeking an accessible introduction to the field of number theory, specifically focusing on primes and the proofs of infinite primes by Euler and Goldbach. They mention their knowledge of calculus1-3 and request any necessary clarifications. They have found helpful resources through a Google search and are now specifying their request for an introduction to primes in number theory.
  • #1
moriheru
273
17
Greetings,
I am looking for a accesable introduction to the field of number theory that leads up to primes eulers proof of infinite primes, goldbach proof of inifinite primes and their deriviations(the deriviations are the most important and should be clear if possible) and so on. I have a knowledge of caculus1-3(integrals,differentials,sums and convergency tests...), so if I am lacking essential knowledge please mention this.

Thanks for any clarifications.
 
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  • #2
moriheru said:
Greetings,
I am looking for a accesable introduction to the field of number theory that leads up to primes eulers proof of infinite primes, goldbach proof of inifinite primes and their deriviations(the deriviations are the most important and should be clear if possible) and so on. I have a knowledge of caculus1-3(integrals,differentials,sums and convergency tests...), so if I am lacking essential knowledge please mention this.

Thanks for any clarifications.
If you google "number theory pdf" you'll find more texts introducing you to number theory than you could imagine. I can't vouch for any of them, but they will generally assume only a basic mathematical knowledge and will be very much from the ground up.
 
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  • #3
PeroK said:
If you google "number theory pdf" you'll find more texts introducing you to number theory than you could imagine. I can't vouch for any of them, but they will generally assume only a basic mathematical knowledge and will be very much from the ground up.

Thanks PeroK the saylor PDF was helpfull.

I think I should specify. A introduction on primes in numbertheory would be more acurate. Thanks for any helpfull suggestions.
 

Related to Introductions to number theory

1. What is number theory?

Number theory is a branch of mathematics that studies the properties and relationships of integers. It involves topics such as prime numbers, divisibility, and modular arithmetic.

2. Why is number theory important?

Number theory has many practical applications, such as cryptography, coding theory, and number theory-based algorithms used in computer science. It also helps us understand the fundamental properties of numbers and their patterns.

3. What are prime numbers?

Prime numbers are positive integers that are only divisible by 1 and themselves. Examples include 2, 3, 5, 7, and 11. They play a crucial role in number theory and have many interesting properties.

4. What is modular arithmetic?

Modular arithmetic is a system of arithmetic where numbers wrap around after reaching a certain value, known as the modulus. It is often used in cryptography and has applications in computer science and engineering.

5. How is number theory related to other branches of mathematics?

Number theory has connections to many other branches of mathematics, such as algebra, geometry, and calculus. It also has applications in fields such as physics, engineering, and computer science.

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