A Computational Introduction to Number Theory and Algebra
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications;...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
[2009]
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| Series: | Open textbook library.
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| Subjects: | |
| Online Access: | Access online version |
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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 Z∗p
- 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 Finite Fields
- 19 Linearly generated sequences and applications
- 20 Algorithms for finite fields
- 21 Deterministic primality testing