The Department of Mathematics offers a number of specific Ancillary modules which are designed to be taken by students who are based in other departments at UCL. For more information on these courses, please see the syllabi linked below under "Choice of Module". For details regarding eligibility and how to register for these modules, please see the "Ancillary Registration" section.

- Choice of Module
You are most likely to find a suitable module from the following modules intended for students from other departments. These are as follows:

**Level 4 Ancillary Mathematics modules:**MATH0039 Differential and Integral Calculus: This module provides a rapid introduction to calculus a little above A-level standard suitable for students who do not have a good Maths A Level or equivalent.

MATH0040 Mathematics for Science 1: This module requires a grade A in A-level Mathematics and continues from A-level, including further differentiation and integration, curve sketching, complex numbers and series. It is aimed mainly at students studying physical science (in particular Chemistry).

MATH0041 Mathematics for Science 2: This module continues from MATH0040 (which is the normal pre-requisite), providing a foundation course in 3-dimensional geometry, calculus of several variables, differential operators and eigenvalue problems. It is aimed mainly at students studying physical science (in particular Chemistry).

MATH0012 Mathematical Methods for Arts and Sciences: This module covers complex numbers, standard functions of a real variable, methods of integration and an introduction to ordinary differential equations.

**It is only available to BASc students.**MATH0045 Calculus and Linear Algebra: The topics covered in this module include differentiation, integration, infinite series, functions of several variables, and elementary matrix theory. It is intended mainly for Statistics students or SSEES students with an A grade in A-level Mathematics.

MATH0046 Calculus in Several Dimensions: The topics covered in this module include optimisation with a constraint, complex numbers, differential equations, multiple integrals, eigenvalues and eigenvectors and quadratic forms. It is intended mainly for Statistics students or SSEES students, following on from MATH0045.

MATH0049 Mathematics for Engineers 1: A slightly post-A-level module, requiring some background in A-level type Maths. Topics covered include differentiation and integration with applications, some differential equations, basic vectors, numerical methods and some statistics and probability.

**Level 5 Ancillary Mathematics modules:**MATH0042 Mathematical Methods in Chemistry: This is a course designed for second year Chemistry students who have previously taken MATH0040/41, dealing with some of the mathematics useful for physical chemistry including series solution of ODEs, Legendre polynomials, group theory, some matrix theory and some applications of the methods to problems in Chemistry.

MATH0043 Mathematics for Physics and Astronomy: This module teaches some of the mathematical methods suitable for advanced study in Theoretical Physics, including complex analysis, calculus of variations and group theory. It is intended mainly for Physics students who have taken the maths modules PHAS0002/0009 and PHAS0025 and also for Chemistry students who have taken MATH0042.

MATH0047 Advanced Linear Algebra: This course aims to develop the theory of matrices and give an introduction to the theory of vector spaces and the theory of linear maps, subjects with applications in many areas, including Economics and Statistics. It is intended mainly for second years Statistics students (following on from MATH0045/0046) and Economics students (following on from ECON0006/0010).

MATH0048 Mathematical Analysis: This module is an introduction to mathematical analysis, one of the most important and well-developed strands of pure mathematics, with applications to many areas of mathematics, theoretical statistics, econometrics, and optimisation. It is intended for first, second or third year Statistics or Economics students with Further Maths A-level or strong results in UCL Mathematics modules.

MATH0101 Linear Algebra for Data Science: This module provides an introduction to vectors, matrices, and least square methods, all basic topics in linear algebra, in the context of data science. It is aimed mainly at Neuroscience students but may be suitable for others such as Social Sciences or BASc students.

MATH0103 Discrete Mathematics: This module introduces important ideas in mathematics, including set theory and proof, group theory, number theory and field theory. It is aimed mainly at second year BASc or Natural Sciences students but may be suitable for others.

**Level 6 Ancillary Mathematics modules:**MATH0050 Logic: This module introduces a language for (first order predicate) mathematical logic and studies the interplay between the notions of ‘truth’ and ‘provability’. It then looks at computability, via register machines, recursive functions and coding, and uses these concepts to show the undecidability of first order predicate logic. It is suitable for third year students from outside mathematics department with good results in previous maths modules (normally 70%+ in MATH0047 or MATH0048 taken).

[MATH0100 Quantitative Physiology: Mathematical Methods: An introduction to mathematical modelling for biologists, intended mainly for Biosciences students.

*Not available in 2021/22*.]**Honours Mathematics modules:**These are modules taken mostly by students on Mathematics degrees. It is also possible that you might find a suitable honours module (i.e. one not listed above). However, please be aware that:

(i) honours modules tend to be mathematically sophisticated and demanding;

(ii) places on these modules may be very limited.

For more information about the modules offered by the department, including detailed syllabi, module descriptions and further details, please refer to the module webpage here. Ancillary modules are located at the bottom of the page.

- Students from other Departments - Ancillary Registration for Mathematics modules
This applies to students on honours degrees from departments other than mathematics who are going to take a mathematics module in the upcoming year. (Affiliate students from other universities should contact the Mathematics Department Affiliate Tutor, Dr Lars Louder, l.louder@ucl.ac.uk.) Syllabi can be found on the Mathematics Department webpage, and timetables on the UCL common timetable using the custom feature and the module code. Please see above for the list of Ancillary modules, and suitability guidelines.

UCL provides guidance on module selection here.

**1. If your module is compulsory and appears on Portico you need take no further action.****2.****In the following cases, you just need to put the module on Portico:**(a) You are a second or third year student from

*Economics*choosing MATH0047 Advanced Linear Algebra as advised by your home department(b) You are a first year student from

*Chemistry*choosing MATH0040 Mathematics for Science 1 or MATH0041 Mathematics for Science 2 as advised by your home department(c) You are a second year student from

*Chemistry*taking MATH0042 Mathematical Methods in Chemistry as advised by your home department(d) You are a second year student from

*Neuroscience*or*Biomedical Sciences*choosing MATH0040 Mathematics for Science 1 as advised by your home department(e) You are a second year student from

*Physics*taking MATH0043 Mathematics for Physics and Astronomy as advised by your department(f) You are a third year student from

*Physics*taking MATH0025 Mathematics for General Relativity as advised by your department(g) You are a

*SSEES*student choosing one of the standard options MATH0039 Differential and Integral Calculus and/or MATH0045 Calculus and Linear Algebra and are sure you have the right prerequisites (neither under-qualified nor overqualified)(h) You are a student from

*Geology, Earth Sciences*or*Management*taking MATH0049 Mathematics for Engineers 1 as advised by your department(i) You are a

*BASc*student choosing modules as advised by your department*Normal prerequisites for these modules:*MATH0039: A-level grade below A or lower qualification

MATH0040: grade A in A-level Maths, OR good result in MATH0039 in previous year

MATH0041: MATH0040

MATH0045: grade A in A-level Maths

MATH0046: MATH0045

MATH0042: MATH0040/MATH0041

MATH0043: first year Mathematics modules offered by Physics

**3.****In other cases, you can put the module on Portico, but should seek advice**either by e-mail to m.l.roberts@ucl.ac.uk or at the induction week advice sessions. If you e-mail, please use the subject line MATHEMATICS OPTION and include in your e-mail your name and student number, your degree, and your background in Mathematics (A-level results, results in UCL Maths modules, etc). The induction week sessions will be in the Mathematics Department during the first week of term. It is particularly important to get advice if you are choosing an honours Mathematics module, i.e. not one of those appearing on the Ancillary Mathematics Modules list.Please note that all choices of mathematics modules will need to be approved on Portico by both the Maths department and by your home department before your module registration is confirmed. Preference is given to certain groups of students on some modules, but otherwise earlier registration on Portico will make it more likely that you get a place. You may be rejected by the teaching department (Mathematics) either if you have an unsuitable background for the module or it is full.

Late choice/problems: please contact the Departmental Tutor Dr Mark Roberts on m.l.roberts@ucl.ac.uk.