Kindly note that we have put a lot of effort into researching the best books on Computational Number Theory subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Computational Number Theory" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “Computational Number Theory (Discrete Mathematics and Its Applications)” by Abhijit Das
“Computational Number Theory (Discrete Mathematics and Its Applications) 1st Edition” Book Review: This book is designed for advanced undergraduate and beginning graduate students in engineering. It is also helpful for researchers new to the field. Practitioners of cryptography in industry can also benefit from this book. The book provides a complete coverage of numbertheoretic algorithms. Coverage of all important applications in the area of engineering along with explaining all computational aspects has been done. Elliptic curves, primality testing etc are also discussed. Theoretic tools are used in cryptography and cryptanalysis are explored. Examples and exercises are also provided.


2. “Computational Number Theory and Modern Cryptography (Information Security)” by Song Y Yan  
3. “Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics)” by William Stein
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“Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) 2009th Edition” Book Review: This book is designed for undergraduate students. It aims to bring readers closer to active research that can resolve the congruent number problem. Deeper understanding of prime numbers is also provided. The book contains problems solved using Sage mathematical software. Exercises and examples are present throughout the text. The book assumes basic knowledge regarding reading and writing mathematical proofs.


4. “Computational Algebra and Number Theory (Mathematics and Its Applications)” by Wieb Bosma and Alf van der Poorten
“Computational Algebra and Number Theory (Mathematics and Its Applications (325)” Book Review: This book highlights the interaction between computers and maths. It explores the depth of the combination of these two fields. Examples from the field are drawn for better understanding. Different theories like theory, graphs etc have been explained in detail. The main emphasis of the book is on emphasising on the basic principles and commonly used methods.
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5. “C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs” by Ulrich Kulisch and Matthias Hocks
“C++ Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Programs” Book Review: This book provides a number of C++ programmes for solving numeric problems. Results are also verified using these programs. The text uses the CXSC library. The boom does not assume a great amount of knowledge about C++ programming.


6. “Cryptography and Computational Number Theory (Progress in Computer Science and Applied Logic)” by Kwok Y Lam and Igor Shparlinski  
7. “Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics)” by Henri Cohen
“Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics (193)” Book Review: This book can be used by those doing a sixmonth or yearlong course in computational number theory. It explores different topics in computational number theories. Chapters move from the basics to complex topics.
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8. “Numerical Methods for Scientists and Engineers (Dover Books on Mathematics)” by Richard W Hamming
“Numerical Methods for Scientists and Engineers (Dover Books on Mathematics)” Book Review: This book is designed for undergraduate and graduate students of mathematics, science and engineering. It can also be used by professionals and researchers. would be of interest to mathematicians and computer scientists. Numerical methods and its importance in computers are explained. Five important concepts that aim at producing meaningful numbers are also highlighted.
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9. “The Mathematical Theory of Communication” by Claude E Shannon and Warren Weaver  
10. “The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics)” by Susanne Brenner and Ridgway Scott
“The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics Book 15) 3rd Edition” Book Review: This book is designed for mathematicians as well as engineers and physical scientists. The book explores the basic mathematical theories of finite methods. The book highlights the most common tools used by researchers in this field. The book provides basic knowledge about theories, functional & numeral analysis and approximation. Additional exercises are provided with all chapters for better practice.


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