A Computational Introduction to Number Theory and Algebra (V. Shoup)
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A Computational Introduction to Number Theory and Algebra (V. Shoup)
A Computational Introduction to Number Theory and Algebra (V. Shoup)
This book introduces the basic concepts from computational number theory
and algebra, including all the necessary mathematical background. Covered topics
are: Basic properties of the integers, Congruences, Computing with large
integers, Euclid’s algorithm, The distribution of primes, Abelian groups, Rings,
Finite and discrete probability distributions, Probabilistic algorithms,
Probabilistic primality testing, Finding generators and discrete logarithms in
Zp, Quadratic reciprocity and computing modular square roots, Modules and vector
spaces, Matrices, Subexponential-time discrete logarithms and factoring,
Polynomial arithmetic and applications.
This note exlains the following topics: foundational concepts
like strings and DFAs, then progresses to regular expressions, nondeterministic
automata, and formal language theory, Advanced topics include Turing machines,
decidability, and language-related problems it offers a comprehensive look at
formal languages, automata, and computability.
This pdf includes overview and
mathematical foundations, Regular operations and regular expressions, Proving
languages to be nonregular, Further discussion of regular languages, Parse
trees, ambiguity, and Chomsky normal form, Pushdown automata, Turing machines,
Variants of Turing machines, Stack machines, Universal Turing machines and
undecidable languages, Further discussion of computability.
This PDF covers the
following topics related to Theory of Computation : Mechanical Computation,
Background, Languages and graphs, Automata, Computational Complexity.
This note covers the following topics: Sets,
functions and other preliminaries, Formal Languages, Finite Automata ,
Regular Expressions, Turing Machines, Context-Free Languages, Rice's Theorem,
Time complexity, NP-Completeness, Space Complexity , Log Space, Oracle
machines and Turing Reducibility, Probabilistic Complexity, Approximation and
Optimisation, Complexity Hierarchy Theorems.
This lecture note covers the
following topics: Theory Of Computation, Introduction To Automata, Finite
Automata, Regular Expressions And Languages, Properties Of Regular Language,
Context-free Grammars And Languages, Applications Of Context-free Grammars,
Pushdown Automata, Properties of Context-Free Languages.
Author(s): Prof. D. Chandrasekhar Rao, Prof.
Kishore Kumar Sahu and Prof. Pradipta Kumar Das
This is a free textbook for an undergraduate course
on the Theory of Computation, which have been teaching at Carleton University
since 2002.Topics covered includes: Finite Automata and Regular Languages,
Context-Free Languages, Turing Machines and the Church-Turing Thesis,
Decidable and Undecidable Languages and Complexity Theory.
This course note provides a challenging introduction to some of the
central ideas of theoretical computer science. It attempts to present a vision
of computer science beyond computers: that is, CS as a set of mathematical
tools for understanding complex systems such as universes and minds.
This note covers the following
topics: introduction to theoretical computer science, language, regular
language, finite automata, language accepted by dfa, nondeterministic finite
automata, equivalence of nfa, regular language and fa, application of fa,
nonregular languages, context free languages, turing machines, computability
and complexity.
Author(s): Pavan
Kumar Anumula, Andrea Di Fabio and Jia Zhu