A Computational Introduction to Number Theory and Algebra by Victor Shoup
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About this book :-
This textbook that 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 Detail :-
This book has following details information.
Title:
A Computational Introduction to Number Theory and Algebra by Victor Shoup by NA
Publisher:
Cambridge University Press
Series:
FreeCompBooks, eBooksDirectory
Year:
2010
Pages:
743
Type:
PDF
Language:
English
ISBN-10 #:
0521516447
ISBN-13 #:
978-0521516440
Country:
Pakistan
License:
CC BY-NC-ND 3.0
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
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
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