What Are the Best Number Theory Books for Various Levels of Expertise?

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SUMMARY

The forum discussion centers on recommended number theory books suitable for various levels of expertise. Key titles mentioned include "Prime Numbers: A Computational Perspective" by Carl Pomerance, "Number Theory for Computing" by Yan, "A Computational Introduction to Number Theory and Algebra" by Shoup, and "Number Theory with Computer Applications" by Kumanduri. Additionally, "Algorithmische Zahlentheorie" by Forster is noted as a valuable resource, although it is less accessible due to its German language. These texts cater to individuals with a foundational understanding of elementary number theory and algebra.

PREREQUISITES
  • Elementary number theory knowledge
  • Basic algebra background
  • Familiarity with computational methods in mathematics
  • Understanding of algorithmic concepts
NEXT STEPS
  • Research "Prime Numbers: A Computational Perspective" by Carl Pomerance
  • Explore "Number Theory for Computing" by Yan for practical applications
  • Study "A Computational Introduction to Number Theory and Algebra" by Shoup for foundational concepts
  • Investigate "Algorithmische Zahlentheorie" by Forster for advanced German-language resources
USEFUL FOR

Students, educators, and researchers in mathematics, particularly those interested in number theory and its computational applications.

modnarandom
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Does anyone have suggestions for number theory references? I'm already familiar with elementary number theory and have some algebra background, but I'm not sure what kind of number theory I'm interested in yet. Thanks!
 
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Prime Numbers a Computational Perspective
by Carl Pomerance

is one of the best.
 
Yan: Number Theory for Computing
Shoup: A Computational Introduction to Number Theory and Algebra
Kumanduri: Number Theory with Computer Applications
Hard to find an written in German:
Forster: Algorithmische Zahlentheorie
 

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