# 2019/20 Undergraduate Programme Catalogue

## MMath, BSc Mathematics *(Single degree scheme)*

*(Single degree scheme)*

Programme code: | MMBS-MATH | UCAS code: | G101 |
---|---|---|---|

Duration: | 4 Years |
Method of Attendance: | Full Time |

Programme manager: | Professor Jonathan Partington | Contact address: | j.r.partington@leeds.ac.uk |

### Total credits: 480

### Entry requirements:

Typical offers are AAA with A in Mathematics or A*AB with A* in Mathematics. Other alternative offers are available.

### School/Unit responsible for the parenting of students and programme:

School of Mathematics

### Examination board through which the programme will be considered:

School of Mathematics

### Relevant QAA Subject Benchmark Groups:

Mathematics, Statistics and Operational Research

### Programme specification:

This Integrated Masters programme is for students who have entered University in 2007 or after.

The programme will aim to:

- introduce students to the major branches of mathematics;

- meet the needs of students with varied mathematical backgrounds and with different aspirations within mathematics;

- enable the student to appreciate the coherence, logical structure, and broad applicability of mathematics;

- impart an awareness of the values of research and scholarship in mathematics;

- accustom students to the use of tools, including libraries and computers, that are available to mathematicians;

- provide a thorough training in the intellectual skills and advanced techniques of modern mathematics;

- develop the ability of students to abstract and generalize, to model various phenomena, and to interpret numerical data;

- enable future mathematicians to develop the skills associated with problem solving, rigorous argument and communication;

- educate new mathematicians to meet the needs of employers, including those in industry, finance, education and the public services;

- broaden and deepen the mathematical background of students;

- prepare students to work in fields where specific and broadly based advanced mathematical knowledge is required;

- enable students to embark on research in some area of mathematics or statistics;

- give students the opportunity to experience a wide and deep mathematics curriculum;

- give students the chance to undertake a substantial project.

**Year1** - View timetable

[Learning Outcomes, Transferable (Key) Skills, Assessment]

Students must enrol on exactly 120 or 125 credits in each academic year.

**Compulsory modules:**

Students will be required to take the following compulsory modules.

MATH1010 | Mathematics 1 | 25 credits | Semester 1 | |

MATH1012 | Mathematics 2 | 25 credits | Semester 2 | |

MATH1025 | Number Systems | 15 credits | Semester 1 | |

MATH1026 | Sets, Sequences and Series | 15 credits | Semester 2 | |

MATH1710 | Probability and Statistics I | 10 credits | Semester 1 | |

MATH1712 | Probability and Statistics II | 10 credits | Semester 2 |

**Optional modules:**

Candidates may take up to 25 credits from the optional modules below:

MATH1225 | Introduction to Geometry | 10 credits | Semester 1 | |

MATH1510 | Financial Mathematics 1 | 15 credits | Semester 2 |

In all cases the choice of modules is subject to the approval of the Head of the School of Mathematics.

**Discovery modules:**

Candidates may study up to 20 credits of level 1 discovery modules. Choices are subject to the approval of the Programme Manager.

**Year2** - View timetable

[Learning Outcomes, Transferable (Key) Skills, Assessment]

Students must enrol on exactly 120 or 125 credits in each academic year.

Students must achieve an average of at least 58 (on the 0 to 100 scale) in their second year to progress to the third year of the MMath, BSc programme. Students with lower averages normally have to switch to the BSc Mathematics programme.

**Compulsory modules:**

Students are required to study the following compulsory modules.

MATH2017 | Real Analysis | 15 credits | Semester 2 | |

MATH2022 | Groups and Vector Spaces | 15 credits | Semester 1 | |

MATH2365 | Vector Calculus | 15 credits | Semester 1 | |

MATH2375 | Linear Differential Equations and Transforms | 15 credits | Semester 2 | |

MATH2920 | Computational Mathematics | 10 credits | Semester 1 |

**Optional modules:**

Students are required to take at least 30 credits from the following optional module lists:

List A

Students must take at least 20 credits from List A:

MATH2027 | Rings and Polynomials | 10 credits | Semester 2 | |

MATH2041 | Logic | 10 credits | Semester 2 | |

MATH2042 | Logic with Computation | 15 credits | Semester 2 | |

MATH2051 | Geometry of Curves and Surfaces | 10 credits | Semester 1 | |

MATH2230 | Discrete Mathematics | 10 credits | Semester 2 | |

MATH2231 | Discrete Mathematics with Computation | 15 credits | Semester 2 | |

MATH2340 | The Mathematics of Music | 10 credits | Semester 1 | |

MATH2391 | Nonlinear Differential Equations | 10 credits | Semester 2 | |

MATH2530 | Financial Mathematics 2 | 10 credits | Semester 1 | |

MATH2540 | Financial Mathematics 3 | 10 credits | Semester 2 | |

MATH2600 | Numerical Analysis | 10 credits | Semester 2 | |

MATH2601 | Numerical Analysis with Computation | 15 credits | Semester 2 | |

MATH2620 | Fluid Dynamics 1 | 10 credits | Semester 2 | |

MATH2640 | Introduction to Optimisation | 10 credits | Semester 1 | |

MATH2650 | Calculus of Variations | 10 credits | Semester 2 | |

MATH2715 | Statistical Methods | 10 credits | Semester 1 | |

MATH2735 | Statistical Modelling | 10 credits | Semester 1 | |

MATH2740 | Environmental Statistics | 10 credits | Not running in 201920 | |

MATH2750 | Introduction to Markov Processes | 10 credits | Semester 2 | |

MATH2775 | Survival Analysis | 10 credits | Semester 2 |

Further modules can be chosen from List B:

EDUC2091 | School Mathematics | 10 credits | Semester 2 | |

MATH2800 | Mathematics into Schools | 10 credits | Semesters 1 & 2 | |

MATH2900 | Maths at Work | 10 credits | Semesters 1 & 2 |

**Discovery modules:**

At most 20 credits may be chosen as discovery modules. Discovery modules may be chosen at Level 1 or Level 2.

!! IMPORTANT !! When choosing options, students must take into account which modules they intend to take in Year 3 to make sure that they have the necessary prerequisites. Please refer to the information from the Programme Meetings.

Altogether students may not take more than 20 credits in Level 1 modules. Choices are subject to the approval of the Programme Manager.

**Year3** - View timetable

[Learning Outcomes, Transferable (Key) Skills, Assessment]

Students should normally enrol on exactly 120 or 125 credits in each academic year. Students are permitted to enrol for 110 (115) credits in either of the final 2 years of the programme, provided they register for 130 (125) credits in the other year. Over the final 2 years of the programme, students can enrol on at most 20 credits of Level 1 and 2 modules.

Over the final 2 years, students have to take at least 120 credits of Level 5 modules.

Students need to have passed at least 100 credits in their penultimate year and have a year average of at least 50 (on the 0 to 100 scale) to progress to the final year of the programme.

**Optional modules:**

Students must choose at least 100 credits from the modules in Lists A and B, with at least 80 credits from List A.

List A

COMP3910 | Combinatorial Optimisation | 10 credits | Semester 2 | |

COMP3940 | Graph Algorithms and Complexity Theory | 10 credits | Semester 1 | |

COMP5940M | Graph Theory: Structure and Algorithms | 15 credits | Semester 2 | |

MATH3001 | Project in Mathematics | 20 credits | Semesters 1 & 2 | |

MATH3015 | History of Mathematics | 15 credits | Semester 2 | |

MATH3017 | Calculus in the Complex Plane | 15 credits | Semester 1 | |

MATH3021 | Philosophy of Logic and Mathematics | 20 credits | Semester 2 | |

MATH3033 | Graph Theory | 15 credits | Semester 1 | |

MATH3044 | Number Theory | 15 credits | Semester 2 | |

MATH3071 | Groups and Symmetry | 15 credits | Semester 1 | |

MATH3104 | Proof and Computation | 15 credits | Semester 2 | |

MATH3113 | Differential Geometry | 15 credits | Semester 2 | |

MATH3120 | Models and Sets | 15 credits | Semester 1 | |

MATH3143 | Combinatorics | 15 credits | Semester 2 | |

MATH3153 | Coding Theory | 15 credits | Semester 1 | |

MATH3195 | Commutative Rings and Algebraic Geometry | 15 credits | Semester 2 | |

MATH3211 | Metric and Function Spaces | 15 credits | Semester 1 | |

MATH3216 | Hilbert Spaces and Fourier Analysis | 15 credits | Semester 2 | |

MATH3225 | Topology | 15 credits | Semester 2 | |

MATH3232 | Transformation Geometry | 15 credits | Semester 1 | |

MATH3355 | Hamiltonian Systems | 15 credits | Semester 2 | |

MATH3365 | Mathematical Methods | 15 credits | Semester 1 | |

MATH3374 | Linear and Non-Linear Waves | 15 credits | Not running in 201920 | |

MATH3375 | Hydrodynamic Stability | 15 credits | Not running in 201920 | |

MATH3385 | Quantum Mechanics | 15 credits | Semester 1 | |

MATH3396 | Dynamical Systems | 15 credits | Not running in 201920 | |

MATH3397 | Nonlinear Dynamics | 15 credits | Semester 1 | |

MATH3414 | Analytic Solutions of Partial Differential Equations | 15 credits | Semester 1 | |

MATH3424 | Introduction to Entropy in the Physical World | 15 credits | Not running in 201920 | |

MATH3458 | Geophysical Fluid Dynamics | 15 credits | Semester 2 | |

MATH3459 | Astrophysical Fluid Dynamics | 15 credits | Semester 2 | |

MATH3474 | Numerical Methods | 10 credits | Semester 1 | |

MATH3475 | Modern Numerical Methods | 15 credits | Not running in 201920 | |

MATH3491 | Discrete Systems and Integrability | 15 credits | Not running in 201920 | |

MATH3510 | Actuarial Mathematics 1 | 15 credits | Semester 1 | |

MATH3520 | Actuarial Mathematics 2 | 15 credits | Semester 2 | |

MATH3532 | Relativity and Cosmology | 15 credits | Semester 2 | |

MATH3565 | Mathematical Biology | 15 credits | Semester 1 | |

MATH3567 | Evolutionary Modelling | 15 credits | Semester 2 | |

MATH3620 | Fluid Dynamics 2 | 15 credits | Semester 1 | |

MATH3714 | Linear Regression and Robustness | 15 credits | Semester 1 | |

MATH3723 | Statistical Theory | 15 credits | Semester 2 | |

MATH3734 | Stochastic Calculus for Finance | 15 credits | Semester 2 | |

MATH3772 | Multivariate Analysis | 10 credits | Semester 1 | |

MATH3802 | Time Series | 10 credits | Semester 1 | |

MATH3820 | Bayesian Statistics | 10 credits | Semester 2 | |

MATH3823 | Generalised Linear Models | 10 credits | Semester 2 | |

MATH5021M | Philosophy of Logic and Mathematics | 20 credits | Semester 2 | |

MATH5071M | Groups, Symmetry and Galois Theory | 20 credits | Semester 1 | |

MATH5104M | Advanced Proof and Computation | 20 credits | Semester 2 | |

MATH5113M | Advanced Differential Geometry | 20 credits | Semester 2 | |

MATH5120M | Advanced Models and Sets | 20 credits | Semester 1 | |

MATH5195M | Advanced Commutative Rings and Algebraic Geometry | 20 credits | Semester 2 | |

MATH5211M | Metric Spaces and Functional Analysis | 20 credits | Semester 1 | |

MATH5216M | Hilbert Spaces and Advanced Fourier Analysis | 20 credits | Semester 2 | |

MATH5325M | Models in Actuarial Science | 15 credits | Semester 2 | |

MATH5356M | Advanced Hamiltonian Systems | 20 credits | Semester 2 | |

MATH5366M | Advanced Mathematical Methods | 20 credits | Semester 1 | |

MATH5373M | Advanced Linear and Nonlinear Waves | 20 credits | Not running in 201920 | |

MATH5376M | Advanced Hydrodynamic Stability | 20 credits | Not running in 201920 | |

MATH5386M | Advanced Quantum Mechanics | 20 credits | Semester 1 | |

MATH5395M | Advanced Dynamical Systems | 20 credits | Not running in 201920 | |

MATH5398M | Advanced Nonlinear Dynamics | 20 credits | Semester 1 | |

MATH5424M | Advanced Entropy in the Physical World | 20 credits | Not running in 201920 | |

MATH5458M | Advanced Geophysical Fluid Dynamics | 20 credits | Semester 2 | |

MATH5459M | Advanced Astrophysical Fluid Dynamics | 20 credits | Semester 2 | |

MATH5476M | Advanced Modern Numerical Methods | 20 credits | Not running in 201920 | |

MATH5492M | Advanced Discrete Systems and Integrability | 20 credits | Not running in 201920 | |

MATH5566M | Advanced Mathematical Biology | 20 credits | Semester 1 | |

MATH5567M | Advanced Evolutionary Modelling | 20 credits | Semester 2 | |

MATH5714M | Linear Regression, Robustness and Smoothing | 20 credits | Semester 1 | |

MATH5734M | Advanced Stochastic Calculus and Applications to Finance | 20 credits | Semester 2 | |

MATH5772M | Multivariate and Cluster Analysis | 15 credits | Semester 1 | |

MATH5802M | Time Series and Spectral Analysis | 15 credits | Semester 1 | |

MATH5820M | Bayesian Statistics and Causality | 15 credits | Semester 2 | |

MATH5824M | Generalised Linear and Additive Models | 15 credits | Semester 2 | |

MATH5835M | Statistical Computing | 15 credits | Semester 1 |

List B

EDUC3060 | Mathematics Education | 10 credits | Semester 2, Semester 1 | |

EPIB3036 | Introduction to Clinical Trials | 15 credits | Semester 2 | |

MATH2051 | Geometry of Curves and Surfaces | 10 credits | Semester 1 | |

MATH2231 | Discrete Mathematics with Computation | 15 credits | Semester 2 | |

MATH2601 | Numerical Analysis with Computation | 15 credits | Semester 2 | |

MATH2650 | Calculus of Variations | 10 credits | Semester 2 | |

MATH2775 | Survival Analysis | 10 credits | Semester 2 | |

MATH2920 | Computational Mathematics | 10 credits | Semester 1 |

For questions concerning prerequisites for COMP modules, please contact the School of Computing or the relevant module manager.

**Discovery modules:**

Candidates may study up to 20 credits of discovery modules at Level 2, 3 or 5M, including Mathematics modules and Level 1 Skills Modules. Over years 3 and 4 of the programme, students can enrol on at most 20 credits of Level 1 and 2 modules. Module choices are subject to the approval of the Programme Manager.

**Year4** - View timetable

[Learning Outcomes, Transferable (Key) Skills, Assessment]

Students should normally enrol on exactly 120 or 125 credits in each academic year. Students are permitted to enrol for 110 (115) credits in either of the final 2 years of the programme, provided they register for 130 (125) credits in the other year. Over the final 2 years of the programme, students can enrol on at most 20 credits of level 1 and 2 modules.

Over the final 2 years,, students have to take at least 120 credits of level 5 modules.

**Optional modules:**

Students must take at least 100 credits from Lists A and B with exactly one of the project modules in List A.

List A

MATH5003M | Assignment in Mathematics (30cr) | 30 credits | Semesters 1 & 2 | |

MATH5004M | Assignment in Mathematics (40cr) | 40 credits | Semesters 1 & 2 |

List B

COMP3910 | Combinatorial Optimisation | 10 credits | Semester 2 | |

COMP3940 | Graph Algorithms and Complexity Theory | 10 credits | Semester 1 | |

COMP5940M | Graph Theory: Structure and Algorithms | 15 credits | Semester 2 | |

MATH3015 | History of Mathematics | 15 credits | Semester 2 | |

MATH3017 | Calculus in the Complex Plane | 15 credits | Semester 1 | |

MATH3021 | Philosophy of Logic and Mathematics | 20 credits | Semester 2 | |

MATH3033 | Graph Theory | 15 credits | Semester 1 | |

MATH3044 | Number Theory | 15 credits | Semester 2 | |

MATH3071 | Groups and Symmetry | 15 credits | Semester 1 | |

MATH3104 | Proof and Computation | 15 credits | Semester 2 | |

MATH3113 | Differential Geometry | 15 credits | Semester 2 | |

MATH3120 | Models and Sets | 15 credits | Semester 1 | |

MATH3143 | Combinatorics | 15 credits | Semester 2 | |

MATH3153 | Coding Theory | 15 credits | Semester 1 | |

MATH3195 | Commutative Rings and Algebraic Geometry | 15 credits | Semester 2 | |

MATH3211 | Metric and Function Spaces | 15 credits | Semester 1 | |

MATH3216 | Hilbert Spaces and Fourier Analysis | 15 credits | Semester 2 | |

MATH3225 | Topology | 15 credits | Semester 2 | |

MATH3232 | Transformation Geometry | 15 credits | Semester 1 | |

MATH3355 | Hamiltonian Systems | 15 credits | Semester 2 | |

MATH3365 | Mathematical Methods | 15 credits | Semester 1 | |

MATH3374 | Linear and Non-Linear Waves | 15 credits | Not running in 201920 | |

MATH3375 | Hydrodynamic Stability | 15 credits | Not running in 201920 | |

MATH3385 | Quantum Mechanics | 15 credits | Semester 1 | |

MATH3396 | Dynamical Systems | 15 credits | Not running in 201920 | |

MATH3397 | Nonlinear Dynamics | 15 credits | Semester 1 | |

MATH3414 | Analytic Solutions of Partial Differential Equations | 15 credits | Semester 1 | |

MATH3424 | Introduction to Entropy in the Physical World | 15 credits | Not running in 201920 | |

MATH3458 | Geophysical Fluid Dynamics | 15 credits | Semester 2 | |

MATH3459 | Astrophysical Fluid Dynamics | 15 credits | Semester 2 | |

MATH3474 | Numerical Methods | 10 credits | Semester 1 | |

MATH3475 | Modern Numerical Methods | 15 credits | Not running in 201920 | |

MATH3491 | Discrete Systems and Integrability | 15 credits | Not running in 201920 | |

MATH3510 | Actuarial Mathematics 1 | 15 credits | Semester 1 | |

MATH3520 | Actuarial Mathematics 2 | 15 credits | Semester 2 | |

MATH3532 | Relativity and Cosmology | 15 credits | Semester 2 | |

MATH3565 | Mathematical Biology | 15 credits | Semester 1 | |

MATH3567 | Evolutionary Modelling | 15 credits | Semester 2 | |

MATH3620 | Fluid Dynamics 2 | 15 credits | Semester 1 | |

MATH3714 | Linear Regression and Robustness | 15 credits | Semester 1 | |

MATH3723 | Statistical Theory | 15 credits | Semester 2 | |

MATH3734 | Stochastic Calculus for Finance | 15 credits | Semester 2 | |

MATH3772 | Multivariate Analysis | 10 credits | Semester 1 | |

MATH3802 | Time Series | 10 credits | Semester 1 | |

MATH3820 | Bayesian Statistics | 10 credits | Semester 2 | |

MATH3823 | Generalised Linear Models | 10 credits | Semester 2 | |

MATH5021M | Philosophy of Logic and Mathematics | 20 credits | Semester 2 | |

MATH5071M | Groups, Symmetry and Galois Theory | 20 credits | Semester 1 | |

MATH5104M | Advanced Proof and Computation | 20 credits | Semester 2 | |

MATH5113M | Advanced Differential Geometry | 20 credits | Semester 2 | |

MATH5120M | Advanced Models and Sets | 20 credits | Semester 1 | |

MATH5195M | Advanced Commutative Rings and Algebraic Geometry | 20 credits | Semester 2 | |

MATH5211M | Metric Spaces and Functional Analysis | 20 credits | Semester 1 | |

MATH5216M | Hilbert Spaces and Advanced Fourier Analysis | 20 credits | Semester 2 | |

MATH5325M | Models in Actuarial Science | 15 credits | Semester 2 | |

MATH5356M | Advanced Hamiltonian Systems | 20 credits | Semester 2 | |

MATH5366M | Advanced Mathematical Methods | 20 credits | Semester 1 | |

MATH5373M | Advanced Linear and Nonlinear Waves | 20 credits | Not running in 201920 | |

MATH5376M | Advanced Hydrodynamic Stability | 20 credits | Not running in 201920 | |

MATH5386M | Advanced Quantum Mechanics | 20 credits | Semester 1 | |

MATH5395M | Advanced Dynamical Systems | 20 credits | Not running in 201920 | |

MATH5398M | Advanced Nonlinear Dynamics | 20 credits | Semester 1 | |

MATH5424M | Advanced Entropy in the Physical World | 20 credits | Not running in 201920 | |

MATH5458M | Advanced Geophysical Fluid Dynamics | 20 credits | Semester 2 | |

MATH5459M | Advanced Astrophysical Fluid Dynamics | 20 credits | Semester 2 | |

MATH5476M | Advanced Modern Numerical Methods | 20 credits | Not running in 201920 | |

MATH5492M | Advanced Discrete Systems and Integrability | 20 credits | Not running in 201920 | |

MATH5566M | Advanced Mathematical Biology | 20 credits | Semester 1 | |

MATH5567M | Advanced Evolutionary Modelling | 20 credits | Semester 2 | |

MATH5714M | Linear Regression, Robustness and Smoothing | 20 credits | Semester 1 | |

MATH5734M | Advanced Stochastic Calculus and Applications to Finance | 20 credits | Semester 2 | |

MATH5772M | Multivariate and Cluster Analysis | 15 credits | Semester 1 | |

MATH5802M | Time Series and Spectral Analysis | 15 credits | Semester 1 | |

MATH5820M | Bayesian Statistics and Causality | 15 credits | Semester 2 | |

MATH5824M | Generalised Linear and Additive Models | 15 credits | Semester 2 | |

MATH5835M | Statistical Computing | 15 credits | Semester 1 |

Additional modules may be chosen from:

EDUC3060 | Mathematics Education | 10 credits | Semester 2, Semester 1 | |

EPIB3036 | Introduction to Clinical Trials | 15 credits | Semester 2 | |

MATH2051 | Geometry of Curves and Surfaces | 10 credits | Semester 1 | |

MATH2231 | Discrete Mathematics with Computation | 15 credits | Semester 2 | |

MATH2601 | Numerical Analysis with Computation | 15 credits | Semester 2 | |

MATH2650 | Calculus of Variations | 10 credits | Semester 2 | |

MATH2775 | Survival Analysis | 10 credits | Semester 2 | |

MATH2920 | Computational Mathematics | 10 credits | Semester 1 |

For questions concerning pre-requisites for COMP modules, please contact the School of Computing or the relevant Module Manager.

**Discovery modules:**

Students may study up to 20 credits of discovery modules at Level 2, 3 or 5M, including Mathematics modules and Level 1 Skills Modules. Module choices are subject to the approval of the Programme Manager.

Over Years 3 and 4 of the programme, at most 20 credits of Level 1 Skills Discovery modules or level 2 modules may be chosen.

Last updated: 17/05/2019

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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