Pleas, suggest a advanced+serious Number Theory book

In summary, The conversation is about book recommendations for advanced and serious number theory and set theory. Some suggested authors for set theory are Kunen, Jech, and Hrbaceck. For number theory, Ireland and Rosen's book is recommended for those with knowledge of abstract algebra and Burton's book for beginners. Other recommended books include Trygve Nagell's book, Hardy & Wright's highly-rated text, and Apostol's or Landau's book on number theory.
  • #1
whitehead k
1
0
Hi guys,

I want to know about some information of books,
I recently finished a Number Theory course by Pommersheim and you know it was pretty easy, and it took for 3 days.

Please suggest advanced and serious Number Theory book.
+ set theory.


Thank you in advanced.
 
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  • #2
For set theory you can check the textbooks by the authors:
Kunen, Jech and Hrbaceck.

for number theory, if you know a little bit of abstract algebra then there's a textbook by Ireland and Rosen, if you still want an easy going textbook then there's Burton's book.
 
  • #3
trygve nagell's book is impressive.
 
  • #4
Hardy & Wright is a highly-rated text, not too trivial, not too obscure, covers a wide range of topics.
 
  • #5
Try Apostol's or Landau's book on number theory.
 
  • #6
Eynstone said:
Try Apostol's or Landau's book on number theory.

If anyone is mystified by this comment - that's the OTHER Landau.

But Hardy/Wright is better simply because it's bigger than these two put together (620 pages vs. 350+250).
 

FAQ: Pleas, suggest a advanced+serious Number Theory book

1. What is Number Theory and why is it important?

Number Theory is a branch of mathematics that studies the properties and relationships of integers. It has applications in cryptography, computer science, and other fields. It also helps us understand patterns and structures in numbers, which can lead to important discoveries and advancements in various industries.

2. What makes a Number Theory book "advanced" and "serious"?

An advanced and serious Number Theory book would typically cover topics beyond the basics, such as advanced theorems, proofs, and applications. It would also require a strong foundation in mathematics and a deep understanding of abstract concepts. These books are usually intended for students pursuing higher education in mathematics or professionals in related fields.

3. Can you recommend a specific advanced and serious Number Theory book?

There are many great advanced and serious Number Theory books available, and the best one for you will depend on your level of understanding and your specific interests. Some popular options include "Introduction to Analytic Number Theory" by Tom M. Apostol, "Algebraic Number Theory" by J. W. S. Cassels and A. Fröhlich, and "An Introduction to the Theory of Numbers" by G. H. Hardy and E. M. Wright.

4. How can I use an advanced and serious Number Theory book to improve my understanding of mathematics?

Studying Number Theory can help improve your critical thinking skills, problem-solving abilities, and overall understanding of mathematics. By working through challenging proofs and problems in an advanced and serious Number Theory book, you can deepen your understanding of abstract concepts and strengthen your mathematical reasoning skills.

5. Are there any online resources or courses I can use to supplement my learning from an advanced and serious Number Theory book?

Yes, there are many online resources and courses available to supplement your learning from an advanced and serious Number Theory book. Some options include online lectures and courses from reputable universities, online forums and communities for discussing and solving problems, and interactive websites with practice problems and simulations. It is always beneficial to supplement your learning with a variety of resources to gain a well-rounded understanding of the subject.

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