A Computational Introduction to Number Theory and Algebra (V. Shoup)
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 covers the
following topics related to Theory of Computation : Mechanical Computation,
Background, Languages and graphs, Automata, Computational Complexity.
This PDF Models of Computation by John E. Savage covers the following
topics related to Computation Theory : The Role of Theory in Computer Science,
General Computational Models, Logic Circuits, Machines with Memory, Finite-State
Machines and Pushdown Automata, Computability, Algebraic and Combinatorial
Circuits, Parallel Computation, Computational Complexity, Complexity Classes,
Circuit Complexity, Space–Time Tradeoffs, Memory-Hierarchy Tradeoffs, VLSI
Models of Computation.
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 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 note provides
an introduction to the theory of computational complexity. Topics covered
includes: Models of computation, Time and space complexity classes,
Nonterminism and NP, Diagonalization, Oracles and relativization, Alternation,
Space complexity, Natural proofs, Randomized classes, Counting classes,
Descriptive complexity and Interactive proofs.
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 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.
The aim of this course note
is to introduce several apparently different formalisations of the informal
notion of algorithm; to show that they are equivalent; and to use them to
demonstrate that there are incomputable functions and algorithmically
undecidable problems.