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 pseudo-randomness, Weak random sources and
randomness extractors, Randomness in proof, Randomness in proofs, Arithmetic
complexity, Interlude: Concrete interactions between Math and Computational
Complexity.
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.
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 pseudo-randomness, Weak random sources and
randomness extractors, Randomness in proof, Randomness in proofs, Arithmetic
complexity, Interlude: Concrete interactions between Math and Computational
Complexity.
This lecture
note explains the following topics: This Numerical Methods for ODEs,
Discretizations for ODEs, The Runge-Kutta Methods, Linear Multistep Methods,
Numerical Methods for PDEs, Tools of Functional Analysis, The Ritz-Galerkin
Method, FDM for Time-Dependent PDES, Finite Difference Methods for Elliptic
Equations, Computational Projects.
The goal of computational
mathematics, put simply, is to find or develop algorithms that solve
mathematical problems computationally. Topics covered includes: Errors and Error
Propagation, Root Finding, Interpolation, Integration, Discrete Fourier Methods
and Numerical Linear Algebra.
Author(s): H. De Sterck, P. Ullrich, Department of
Applied Mathematics, University of Waterloo