Numerical Analysis Pathway
If you are an undergraduate student at Manchester and are interested in Numerical Analysis, then here is some guidance for you. The NA Pathway lists the courses in Mathematics on or related to Numerical Analysis.
Note: course codes are of the form MATHYABCS, where Y is the year of study and S is the semester.
Year 2 Courses
Numerical Analysis 1 (MATH24411)
Description: This course introduces students to numerical methods for solving mathematical problems that arise in science and engineering. Topics include iteration, interpolation, and quadrature.
Topics Covered: Iterative methods for solving equations, polynomial interpolation, numerical integration, and error analysis.
Programming with Python (MATH20621)
Description: This course teaches the fundamentals of programming using Python, with applications in mathematics and numerical analysis.
Topics Covered: Python syntax, data structures, functions, and libraries for numerical computing.
Year 3 Courses
Numerical Analysis 2 (MATH36022)
Description: This course builds on the concepts introduced in Numerical Analysis 1, focusing on more advanced numerical methods for approximating functions, evaluating integrals, and solving ordinary differential equations.
Topics Covered: Best approximation, numerical integration, initial value problems for ODEs, and stability analysis.
Matrix Analysis (MATH36001)
Description: This course covers the theory and applications of matrices in various mathematical contexts, including linear algebra and numerical analysis.
Topics Covered: Matrix decompositions, eigenvalues and eigenvectors, and applications in solving linear systems.
Mathematics and Applications of Machine Learning (MATH36160)
Description: This course explores the mathematical foundations of machine learning and its applications in various fields.
Topics Covered: Supervised and unsupervised learning, neural networks, and optimization techniques.
Problem Solving By Computer (MATH36031)
Description: This course introduces students to computational problem-solving techniques using programming languages and software tools.
Topics Covered: Algorithm design, programming in Python, and applications in numerical analysis.
Year 4 Courses
Numerical Linear Algebra (MATH46101)
Description: This course covers numerical methods for solving linear systems, eigenvalue problems, and singular value decomposition.
Topics Covered: Direct and iterative methods for linear systems, QR factorization, and applications in scientific computing.
Approximation Theory and Finite Element Analysis (MATH46052)
Description: This course introduces students to approximation theory and its applications in finite element analysis.
Topics Covered: Polynomial approximation, finite element methods, and error estimation.
Numerical Optimisation & Inverse Problems (MATH46132)
Description: This course covers numerical methods for solving optimization problems and inverse problems in various scientific and engineering contexts.
Topics Covered: Gradient-based methods, Newton's method, regularization techniques, and applications in inverse problems.
Scientific Computing (MATH49111)
Description: This course focuses on the use of numerical simulation to study natural phenomena, complementing experimental and theoretical approaches.
Topics Covered: Numerical methods for PDEs, finite element methods, and high-performance computing.
Introduction to Uncertainty Quantification (MATH44071)
Description: This course introduces students to the methods and algorithms used to quantify uncertainty in mathematical models.
Topics Covered: Probabilistic modeling, Bayesian inference, and Monte Carlo methods.
Advanced Uncertainty Quantification (MATH44082)
Description: This course builds on the concepts introduced in Introduction to Uncertainty Quantification, focusing on more advanced techniques and applications.
Topics Covered: Advanced probabilistic modeling, stochastic processes, and applications in engineering and science.