A Computational Number Theory & Algebra by Victor Shoup
A Computational Number Theory & Algebra - Table of Contents
1. Basic Properties of the Integers
2. Congruences
3. Computing with Large Integers
4. Euclid's Algorithm
5. The Distribution of Primes
6. Abelian Groups
7. Rings
8. Finite and Discrete Probability Distributions
9. Probabilistic Algorithms
10. Probabilistic Primality Testing
11. Finding Generators and Discrete Logarithms in Zp
12. Quadratic Reciprocity and Computing Modular Square Roots
13. Modules and Vector Spaces
14. Matrices
15. Subexponential Time Discrete Logarithms and Factoring
16. More Rings
17. Polynomial Arithmetic and Applications
18. Linearly Generated Sequences and Applications
19. Finite Fields
20. Algorithms for Finite Fields
21. Deterministic Primality Testing
What You Will Learn in A Computational Number Theory & Algebra
"A Computational Introduction to Number Theory and Algebra" by "Victor Shoup" introduces number theory and algebra with a focus on computational methods and real-world applications, particularly in cryptography and coding theory. Designed for students in computer science or mathematics, the book requires minimal mathematical prerequisites i.e only basic calculus and some experience with proofs. It covers topics such as modular arithmetic, primality testing, finite fields, and error-correcting codes, interspersing theoretical concepts with practical algorithms. It includes numerous exercises and examples to reinforce learning, making it suitable for both self-study and classroom use.
This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. It covers the basics of number theory, abstract algebra and discrete probability theory.
This book covered includes the basics of number theory (including unique factorization, congurences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory.
Book Details & Specifications
Title:
A Computational Number Theory & Algebra by Victor Shoup
Publisher:
Cambridge University Press
Year:
2010
Pages:
743
Type:
PDF
Language:
English
ISBN-10 #:
0521516447
ISBN-13 #:
978-0521516440
License:
CC BY-NC-ND 3.0
Amazon:
Amazon
About the Author: Victor Shoup
The author Victor Shoup
is an American computer scientist and mathematician known for his significant contributions to cryptography and computational number theory. He earned his Ph.D. in computer science from the University of Wisconsin–Madison in 1989. Currently, he serves as a professor at the Courant Institute of Mathematical Sciences at New York University (NYU) and is a Principal Research Scientist at Offchain Labs.
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