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 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.
This
note covers the following topics: Mathematical Modeling, Euler’s Method, Taylor
Series, Taylor Polynomials, Floating-Point Numbers, Normalized Floating-Point
Numbers , MATLAB.
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