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Mathematics and Computation
This lecture note covers the following topics, Prelude, computation, undecidability and the limits of mathematical knowledge, Computational complexity 101, the basics, Problems and classes inside N P, Lower bounds, Boolean Circuits, and attacks on P vs. NP, Proof complexity, Randomness in computation, Abstract pseudorandomness, Weak random sources and randomness extractors, Randomness in proof, Randomness in proofs, Arithmetic complexity, Interlude, Concrete interactions between Math and Computational Complexity.
Author(s): Avi Wigderson
372 Pages 
Computational Mathematics An Introduction by I Liang Chern
This note explains the following topics, solving equations of one variable, Basic numerical linear algebra, Approximation theory, Numerical integration, Numerical ordinary differential equations.
Author(s): I Liang Chern, National Taiwan University
160 Pages
Computing Mathematics Lecture Notes by Dr Jon Shiach
This note covers mathematical fundamentals, Logic circuits, Algorithms and graph theory.
Author(s): Dr Jon Shiach
110 Pages
Computational Mathematics by Oxford
This PDF book covers the following topics related to Computational Mathematics, Introduction to MATLAB, Algebraic equations and calculus, Differential equations, sums, matrices and vectors, Loops, conditionals and functions, A simple matrix function.
Author(s): Prof. Nick Trefethen
56 Pages
Computational Mathematics by Jose Augusto Ferreira
This lecture note explains the following topics, This Numerical Methods for ODEs, Discretizations for ODEs, The RungeKutta Methods, Linear Multistep Methods, Numerical Methods for PDEs, Tools of Functional Analysis, The RitzGalerkin Method, FDM for TimeDependent PDES, Finite Difference Methods for Elliptic Equations, Computational Projects.
Author(s): Augusto Ferreira
177 Pages