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 pdf begins with an overview of resources, organization and
motivation and preview of CS theory covering the Limits of Computation, the
Undecidability of the Halting Problem.The Automata and Machines including
Deterministic and Nondeterministic Finite-state Automata, Pushdown Automata, and
Turing Machines and Language Classes. Finally focus shifts to Computational
Complexity, discussing NP-Completeness, Approximation Algorithms, and the
Hardness of Approximation.
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: Languages, Finite Automata,
Regular Languages and Sets, Context-Free Grammars, Pushdown Automata and
Context-Free Languages, Turing Machines, The Chomsky Hierarchy, P and NP.
This
note explains the following topics: Discrete mathematics, Deterministic Finite
Automata, Nondeterministic Finite Automata, Equivalence of DFA and NFA,
Nondeterministic Finite Auotmata, egular expressions and finite automata,
Non-regular languages and Pumping Lemma, Myhill-Nerode Theorem, Context-free
languages and Ambiguity, Closure Properties, Pumping Lemma and non-CFLs,
Closure Properties and non-CFL Languages, Decidable and Recognizable
Languages.
This note
explains the theoretical computer science areas of formal languages and
automata, computability and complexity. Topics covered include: regular and
context-free languages, finite automata and pushdown automata, Turing
machines, Church's thesis, computability - halting problem, solvable and
unsolvable problems, space and time complexity, classes P, NP and PSPACE, NP-Completenes.
Author(s): The Australian National University, Canberra
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 course is an introduction to
the Theory of Computation. Topics covered includes: Background Mathematics,
Models of Computation, Context-Free Grammars, Automata, The Chomsky
Hierarchy.
This book covers the
following topics: The RAM Model, The Primitive Recursive Functions, The
Partial Recursive Functions, Coding and Godelization, The Hierarchy of
Primitive Recursive Functions, Universality and Parametrisation, The type-free
lambda calculus.
This note covers the following topics: A brief history of
computing, Fundamentals, Formal languages and machine models, Computability
and undecidability, NP-completeness, Generalized number systems and
Cryptography mental poker.
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