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# 160

### Mathematics

160.101 Calculus 15 credits

A course focusing on the fundamental techniques and applications of calculus including differentiation and integration of functions of one real variable, differential equations, numerical methods, and an introduction to power series with applications to mathematical models. 160.101, alongside 160.102, forms a foundation for further study in mathematics. It is essential for students intending to study Mathematics, Physics, Food Technology or Engineering, or for anyone who wants a strong mathematical component to their degree.

160.102 Algebra 15 credits

A course focusing on the fundamental techniques and applications of linear algebra including vector and matrix algebra, vector representation of lines and planes, projections, Gaussian elimination, eigenvectors and complex numbers. 160.102, alongside 160.101, forms a foundation for further study in mathematics. It is essential for students intending to study Mathematics, Physics, Food Technology or Engineering, or for anyone who wants a strong mathematical component to their degree.

160.103 Introductory University Mathematics 15 credits

A course designed to increase the confidence of students in handling mathematical concepts and skills. Content includes algebraic skills, functions and graphs, and an introduction to matrices and calculus.

160.104 Introductory Mathematics for Science 15 credits

An introductory course focusing on the development of mathematical problem solving skills in science contexts. The use of number, algebra, trigonometry, and curve sketching will be employed in different situations to solve problems and interpret results.

160.105 Methods of Mathematics 15 credits

An introductory course designed to increase the confidence of students in handling mathematical concepts and skills. Content includes algebraic skills, functions and graphs, and an introduction to calculus.

160.111 Mathematics 1A 15 credits

This course provides a solid mathematical foundation for further studies in mathematics, science and engineering. It consolidates basic concepts and introduces more advanced material on differentiation and numerical techniques, enabling the formation of mathematical models of real-world problems. The course blends topics from calculus with those from linear algebra and includes matrices, linear equations, vectors and geometry.

160.112 Mathematics 1B 15 credits

This course builds on the foundation provided by 160.111. Together these courses provide a mathematical platform for more advanced studies in mathematics, science and engineering.. The topics are a blend of calculus and linear algebra, including complex numbers, linear transformations, eigenvectors, advanced techniques of integration, differential equations and applications.

160.131 Mathematics for Business I 15 credits

Development of algebraic skills. An introduction to linear equations and matrices, including graphical linear programming. Graphs. An introduction to calculus. Use of spreadsheets and/or other mathematical software.

160.132 Concepts in Mathematics 15 credits

At the heart of this course are three mathematical questions: what is an equation, what is a solution and what is a function? Through exploring these three themes, students will be exposed to different types of equations, different types of solutions and mathematical functions. Students will also learn to differentiate, integrate and manipulate simple equations and develop problem solving skills.

160.133 Processes in Mathematics 15 credits

A mathematical foundation for further studies in mathematics, statistics, natural and computing sciences, business and education. It combines a blend of concepts, techniques and applications. Topics from algebra and calculus include matrices, vectors and geometry, complex numbers, techniques and applications of differentiation and integration. The course follows from 160.132; well-prepared students from high school can enter 160.133 directly.

160.203 Multivariable Calculus 15 credits

The techniques of 100-level calculus are applied and extended in the study of infinite series, vector-valued functions and functions of two or more variables. Topics include convergence of power series, partial derivatives, double and triple integrals with applications to surface area and volumes, line and surface integrals.

160.204 Differential Equations I 15 credits

Exact solution methods for ordinary differential equations including the use of the Laplace transform. Systems of differential equations, matrix methods, phase plane techniques. Numerical methods for differential equations.

160.211 Linear Algebra 15 credits

Vector spaces, linear transformation, matrix representation, inner product spaces, isometries, least squares, generalised inverse, eigen theory, quadratic forms, norms, numerical methods.

160.212 Discrete Mathematics 15 credits

Sets, logic, mathematical induction, functions and equivalence relations. Partial orderings, algebraic structures and morphisms. Error correcting codes and public key cryptography. Graph theory.

160.301 Real and Complex Analysis 15 credits

Real analysis: inequalities, the continuum property, induction, sequences, functions and limits, continuity, contraction mappings and fixed points, differentiation, mean value theorems and Taylor's theorem. Complex analysis: geometry in the complex plane, limits and continuity, holomorphic functions, line integrals, Cauchy's theorem and some elementary consequences, singularities and Laurent's theorem, the calculus of residues and some applications.

160.302 Modern Algebra 15 credits

Group theory - basic properties, permutation groups, finite Abelian groups, cosets, normal subgroups, homomorphism theorems, representation. Ring theory - integral domains and fields, ideals, homomorphism theorems, factorisation, extension fields.

160.303 Mathematical Physics 15 credits

An integrated course on mathematical methods for solving problems in physics. Fundamental principles of vector calculus including the divergence theorem, Stokes' theorem, and curvilinear coordinates, an introduction to fluid dynamics, and a study of wave phenomena and electrodynamics, including Maxwell's equations.

160.314 Combinatorics 15 credits

Permutations and combinations, binomial coefficients, the inclusion-exclusion principle, generating functions, recurrence relations, Polya's theorem, topics in graph theory.

160.318 Differential Equations II 15 credits

Ordinary differential equations: series solutions, special functions, Sturm-Liouville problems, Green's functions. Qualitative analysis of non-linear equations. Partial differential equations: method of characteristics, classification of second order equations, separation of variables, Fourier transforms. Introduction to numerical methods and software.

160.319 Mathematical Modelling 15 credits

The mathematical modelling process and methodologies examined through a variety of case studies. Application of analytical techniques, numerical methods and computer software packages to the solution of differential equations, difference equations and linear and nonlinear systems.

160.320 Mathematics in Education 15 credits

A discussion of the fundamental questions in mathematics education concerning the nature of mathematics and the purposes of teaching mathematics.

160.380 Project 15 credits

160.702 Advanced Algebra 15 credits

A selection of topics in advanced algebra which may include the following: isomorphism theorems, series of groups, Sylow theorems, classification of finitely generated abelian groups, free groups, group representations, matrix representations and characters of groups; extension fields, Galois correspondence, solvability of polynomial equations; semigroups, Green's equivalence, regular semigroups, inverse semigroups.

160.703 Advanced Analysis 15 credits

A selection of advanced topics from real, complex, abstract and functional analysis, with applications, e.g. Fourier series, approximation theory.

160.704 Studies in Theoretical Mathematics 15 credits

Selected advanced topics from geometry, topology, number theory, analysis and combinatorics.

160.715 Advanced Computational Methods 15 credits

Advanced study of computational solution methods with topics selected from approximation theory, sparse linear systems, matrix eigenproblems, initial value problems and boundary value problems in ordinary differential equations and partial differential equations.

160.733 Methods of Applied Mathematics 15 credits

A selection of topics which may include asymptotic analysis, the calculus of variations, integral equations and partial differential equations. Some applications to problems in engineering and physics will be discussed.

160.734 Studies in Applied Differential Equations 15 credits

Topics in the advanced study of ordinary and partial differential equations selected from dynamical systems, chaos, Lie symmetries, and applications to mathematical modelling, physics and engineering.

160.737 Studies in Mathematical Physics 15 credits

Studies of the mathematical formulation of the physical principles required for the development of modern theories in mathematical physics. A topic or topics will be selected from areas such as Lie groups and algebras, analytical mechanics, electrodynamics, quantum mechanics and kinetic theory, together with suitable applications.

160.783 Mathematics Project 30 credits

160.870 Research Report 60 credits

160.871 Thesis 90 Credit Part 1 45 credits

A supervised and guided independent study resulting in a published work.

160.872 Thesis 90 Credit Part 2 45 credits

A supervised and guided independent study resulting in a published work.

160.875 Thesis 90 credits

A supervised and guided independent study resulting in a published work.

160.897 Thesis 120 Credit Part 1 60 credits

A supervised and guided independent study resulting in a published work.

160.898 Thesis 120 Credit Part 2 60 credits

A supervised and guided independent study resulting in a published work

160.899 Thesis 120 credits

A supervised and guided independent study resulting in a published work.

160.900 PhD Mathematics 120 credits

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Last updated on Monday 20 September 2021