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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.
Author(s): Victor Shoup
NA Pages 
Theory of Computation by Jim Hefferon
This PDF covers the following topics related to Theory of Computation : Mechanical Computation, Background, Languages and graphs, Automata, Computational Complexity.
Author(s): Jim Hefferon
439 Pages
Models of Computation by John E. Savage
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.
Author(s): John E. Savage, Brown University
698 Pages
Introduction to Theory of Computation Lecture Notes
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.
Author(s): Mahesh Viswanathan
NA Pages
Advanced Theory in Computation
This note covers the following topics: Analysis of Algorithms, String Matching, Amortized Analysis, Knuth-Morris-Pratt Algorithm, Pattern-Matching Machine, Boyer-Moore Algorithm, Horspool Algorithm, Suffix Trees, Dictionary Techniques, Ziv-Lempel Coding, Randomized Algorithms, Reservation-Price-Policy, Portfolio Selection, Statistical Adversaries.
Author(s): Seoul National University
NA Pages
Theory of Computation Tutorials
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
NA Pages
Theory of Computation Lectures
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.
Author(s): UNSW Sydne
NA Pages
Theory of Computation Lecture Notes
This note covers the following topics: Mathematical Perliminaries, Automata Theory, Combinatorics and Graph Theory, DFAs to Regular Expressions- Brzozowski’s Algebraic Method, Myhill-Nerode and DFA Minimization, Group Theory, Turing Machines and Computability Theory, Complexity Theory.
Author(s): Michael Levet
114 Pages
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.
Author(s): Konrad Slind
231 Pages
Introduction to Theory of Computation
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.
Author(s): Anil Maheshwari and ichiel Smid
246 Pages
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.
Author(s): Victor Shoup
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