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# Computational & Applied Mathematics

CAAM 335: MATRIX ANALYSIS

Hong Kong UST

Math 2121: Linear Algebra

This will be a first course in linear algebra, from an applied perspective. The main topics covered will include solving linear systems of equations, vector spaces, matrices, linear mappings and matrix forms, inner products, orthogonality, eigenvalues and eigenvectors, and symmetric matrices. No prior knowledge of matrix algebra is assumed.

Syllabus

CAAM 335: MATRIX ANALYSIS

Nanyang Technological University

CV2019: Matrix Algebra and Computational Methods

Introduction to matrix algebra; Linear system of equations; Gauss elimination and solution types for Ax=b; Linear independence; Rank of matrix and solution type; Matrix inverse; Gauss-Jordan elimination; Determinant of matrix; Cramer’s rule; Inverse of matrix; Matrix norm and Matrix conditioning; Eigenvalues and Eigenvectors; Mathematical Modelling and Numerical Methods; Roots of Equations; Numerical Interpolation; Numerical Integration and Differentiation; Numerical Solution of Ordinary Differential Equations.

Syllabus

CAAM 353: COMPUTATIONAL NUMERIC ANALYSIS

The University of Manchester

MATH20602: Numerical Analysis 1

Numerical analysis is concerned with finding numerical solutions to problems for which analytical solutions either do not exist or are not readily or cheaply obtainable. This course provides an introduction to the subject, focusing on the three core topics of iteration, interpolation and quadrature.

The module starts with 'interpolation schemes', methods for approximating functions by polynomials, and 'quadrature schemes', numerical methods for approximating integrals, will then be explored in turn. The second half of the module looks at solving systems of linear and nonlinear equations via iterative techniques. In the case of linear systems, examples will be drawn from the numerical solution of differential equations.

Students will learn about practical and theoretical aspects of all the algorithms. Insight into the algorithms will be given through MATLAB illustrations, but the course does not require any programming.

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CAAM 378: INTRO TO O.R. AND OPTIMIZATION

London School of Economics & Political Science

MA231: Operational Research Methods

An introduction to all the main theoretical techniques of Operational Research. Linear optimisation: from the most basic introduction to sufficient conditions for optimality; duality; sensitivity of the solution; discovery of the solution to small problems by graphical methods, and proof of optimality by testing the sufficient conditions. The transportation problem. Modelling real world problems using linear optimisation. Various other operational research techniques including: Shortest Paths, Critical Path Analysis, Markov Chains, Stable Matchings, Queueing Theory, Simulation, Inventory Management, Dynamic Programming, Decision Theory, Game Theory. The course includes an assessed software component. The software used will be "Microsoft Excel" and the add-on packages "LP solve" to solve linear optimisation problems and "@ risk" to perform Monte Carlo simulation.

Syllabus

CAAM 3XX: DEPT APPROVED TRANSFER CREDIT

University of Edinburgh

MATH08068: Facets of Mathematics

This course aims to explore the wide range of applications of mathematics, and links to other areas that are present in today's world. This course is centred around three components in different areas of mathematics. The content of the components is not fixed, but there will normally be one each in Pure mathematics, Mathematical Modelling and Operational Research. In each component, some basic techniques from the chosen area will be studied and there will also be some exploration of their applications in the modern world. Applications of the area in general and its relationship to other topics will also be discussed. Another aim of the course is to develop important skills in teamwork and in presenting mathematics. Some instruction in producing mathematical documents, particularly posters, in LaTeX will be given and students will undertake a group research project that builds on the content of one of the components. The outcome of the project will be a poster.

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CAAM 423: PARTIAL DIFFERENTIAL EQNS I

Politecnico di Milano

Fredholm alternative, spectrum of a compact operator in Hilbert spaces. Application to abstract variational problems. Weak formulation of evolution problems. Method of Faedo-Galerkin. Fixed point theorems of Shauder and Leray-Shauder. Stationary Navier Stokes equations. Conservation laws. Generalized solutions. Rankine-Hugoniot conditions. Rarefaction waves and shocks. Entropy conditions. Riemann invariants. Riemann problem. Local existence. Application to the shallow waters system, gas dynamics and p-system. Optimal control problems. Existence and uniqueness for quadratic functionals. Lagrange multipliers and optimality conditions.

Syllabus

CAAM 453: NUMERICAL ANALYSIS I

Indian Institute of Technology Kanpur

ME685: Applied Numerical Methods

This course deals with how functions, derivatives, integrals, matrices and differential equations are evaluated as strings of numbers in the computer. It studies the speed of convergence of Taylor, Fourier, and other series expansions and their utility. Applications of these techniques in solving model engineering problems are included. Finally, it expects the students to write a computer program for several of the numerical techniques covered in the course.

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CAAM 454: NUMERICAL ANALYSIS II

London School of Econ & Political Science

MA208: Optimisation Theory

Based on the relevant mathematical theory, the course describes various techniques of optimisation and shows how they can be applied. More precisely, the topics covered are: Introduction and review of mathematical background. Introduction to combinatorial optimisation; shortest paths in directed graphs; algorithms and their running time. Classical results on continuous optimisation: Weierstrass's Theorem on continuous functions on compact set; optimisation of differentiable functions on open sets; Lagrange's Theorem on equality constrained optimisation; Kuhn and Tucker's Theorem on inequality constrained optimisation. Linear programming and duality theory.

Syllabus

CAAM 470: INTRODUCTION TO GRAPH THEORY

Indian Institute of Technology

CS 408: Graph Theory

Graph theory applied to the design of parallel computer networks. Measures such as diameter, bisection width of popular networks. Graph embedding for comparing networks. Graph embedding and partitioning for designing divide and conquer algorithms. Network flow and applications. Matchings in general graphs. Page rank algorithm for web search. Random walks on graphs with applications to graph drawing and graph partitioning.

Course Description