# Mathematics within Natural Sciences 2023-2024

This pages is primarily intended for existing students. It consists of modules available to Natural Sciences students, Joint-Honours regulations and general advice (which includes links to Departmental advice.)

The following lists the module code and the title of each module by the level of each module - clicking on the link will take you to further details listed in the Faculty Handbooks.

The last digit of the module code indicates whether the module is single, double or triple. The level indicates the year in which modules are normally taken, but it is often the case that students take modules from the adjacent level beneath the year of study. Visit the Subjects page for the general overarching rules and structure.

* Please note that the modules on offer and the requirements for progression can change from year to year and that the only combinations of modules that are guaranteed to fit in the timetable are those splits between the two departments on an approved Joint Honours route* (MSci and BSc).

Within Natural Sciences, Mathematics has BSc Joint-Honours programmes with: Biology; Chemistry; Computer Science; Economics; Philosophy; Physics; Psychology. There are also the following MSci Joint-Honours programmes with: Chemistry; Computer Science; Physics.

*In BSc students' final year, they are required to take no less than 20 credits and no more than 60 credits of Capstone Modules*. MSci student students are not required to take a capstone module, but rather take a Dissertation/Project in Year 4. Dissertation/Project/Capstone modules are denoted with G

#### Mathematics modules available to Natural Sciences students

**Level 1 modules **

Discrete Mathematics (MATH1031)

Analysis I (MATH1051)

Calculus I (MATH1061)

Linear Algebra I (MATH1071)

Maths For Engineers And Scientists (MATH1551)

Single Mathematics A (MATH1561)

Single Mathematics B (MATH1571)

Programming I (Term 1) (MATH1587)

Probability I (Term 1) (MATH1597)

Dynamics I (Term 2) (MATH1607)

Statistics I (Term 2) (MATH1617)

**Level 2 modules **

Complex Analysis II (MATH2011)

Analysis In Many Variables II (MATH2031)

Numerical Analysis II (MATH2051)

Mathematical Physics II (MATH2071)

Algebra II (MATH2581)

Elementary Number Theory II (Term 1) (MATH2617)

Mathematical Modelling II (Term 1) (MATH2637)

Probability II (Term 2) (MATH2647)

Special Relativity And Electromagnetism II (Term 2) (MATH2657)

Data Science And Statistical Computing II (Term 1) (MATH2687)

Statistical Modelling II (Term 2) (MATH2697)

Markov Chains II (Term 1) (MATH2707)

Statistical Inference II (MATH2711)

Topology II (Term 2) (MATH2727)

**Level 3 modules **

Analysis III^{*} (MATH3011)

Differential Geometry III^{*} (MATH3021)

Number Theory III (MATH3031)

Galois Theory III (MATH3041)

Decision Theory III (MATH3071)

Dynamical Systems III^{*} (MATH3091)

Fluid Mechanics III^{*} (MATH3101)

Quantum Mechanics III (MATH3111)

Operations Research III^{*} (MATH3141)

Mathematical Biology^{*} (MATH3171)

Geometry III (MATH3201)

Solitons III^{*} (MATH3231)

Stochastic Processes III (MATH3251)

Topology III^{*} (MATH3281)

Partial Differential Equations III^{*} (MATH3291)

Mathematical Finance III^{*} (MATH3301)

Project IIIG (MATH3382)

Quantum Computing III^{*} (MATH3391)

Cryptography And Codes III (MATH3401)

Advanced Statistical Modelling III (MATH3411)

Bayesian Computation And Modelling III (MATH3421)

Machine Learning And Neural Networks III (MATH3431)

Geometry Of Mathematical Physics III^{*} (MATH3471)

Mathematics Into Schools^{*}G (MATH3481)

Science EnterpriseG (NSCI3001)

**Level 4 modules **

General Relativity IV^{*} (MATH4051)

Advanced Quantum Theory IV^{*} (MATH4061)

Project IVG (MATH4072)

Topics In Algebra And Geometry IV (MATH4151)

Algebraic Topology IV^{*} (MATH4161)

Riemannian Geometry IV^{*} (MATH4171)

Statistical Mechanics IV^{*} (MATH4231)

Representation Theory IV (MATH4241)

Stochastic Analysis IV (MATH4261)

Deep Learning And Artificial Intelligence (MATH4267)

Superstrings IV^{*} (MATH4271)

Discrete & Continuous Probability IV (MATH4277)

Topics In Combinatorics IV (MATH4281)

High-dimensional Statistics (MATH4287)

Topics In Probability IV (MATH4327)

Uncertainty Quantification IV (MATH4337)

Spatio-temporal Statistics (MATH4341)

Ergodic Theory IV (MATH4361)

Functional Analysis And Applications IV^{*} (MATH4371)

Nonparametric Statistics IV (MATH4391)

Clinical Trials (MATH4407)

Geophysical And Astrophysical Fluids IV (MATH4421)

#### Requirements for Joint Honours (BSc and MSci Programmes)

Please note that these requirements are just for the B.Sc. degrees and the M.Sci. in Natural Sciences, requirements for the JH M.Sci. degrees involving Mathematics are detailed elsewhere.There are 3 routes within Mathematics: Maths with Statistics route, Maths with Physics route and Maths without Physics route.**Maths without Physics**

Designed to be timetabled with Chemistry and Philosophy.

Year 1 | 60 credits: Analysis I (MATH1051), Calculus I (MATH1061), Linear Algebra I (MATH1071) |

Year 2 | 60 credits: From the Level 2 Mathematics list. |

Year 3 | 40 credits: From the Level 3 Mathematics list. |

**Maths with Physics**

Year 1 | 60 credits: Analysis I (MATH1051), Calculus I (MATH1061), Linear Algebra I (MATH1071) |

Year 2 | 60 credits: Complex Analysis II (MATH2011), Analysis In Many Variables II (MATH2031) and 20 further credits from the Level 2 Mathematics list. Students must either take Mathematical Physics II (MATH2071) or Theoretical Physics 2 (PHYS2631) but both is not permitted. |

Year 3 | 40 credits: From the Level 3 Mathematics list. |

**Maths with Statistics**

Designed to be timetabled with Biology, Computer Science, Economics and Psychology.

Year 1 | 60 credits: Calculus I (MATH1061), Linear Algebra I (MATH1071), Probability I (MATH1597), Statistics I (MATH1617). |

Year 2 | 60 credits: From the Level 2 Mathematics list where at most 20 credits may be from the Level 1 Mathematics list. |

Year 3 | 40 credits: Modules taken from the Level 3 Mathematics list. |

#### Advice for progression and other aspects

**Department advice**: Handbook

**Natural Sciences advice**

Year 1 | Calculus I (MATH1061) and Linear Algebra I (MATH1071) gives some choice at level 2. To enhance further choice at Level 2 and beyond, either Analysis I (MATH1051) or (Probability I (MATH1597) and Statistics I (MATH1617)) is |

Year 2 | Students who are unable to take Analysis I (MATH1051) can take any from Algebra II (MATH2581), Elementary Number Theory II (MATH2617) or (Mathematical Physics II (MATH2071) if Foundations Of Physics 1 (PHYS1122) has been taken.) |

Year 3 | Decision Theory III (MATH3071) and Operations Research III (MATH3141) have no Level 2 prerequisites but do require students to have taken Probability I (MATH1597). |

For more information about the Natural Sciences degree programme, please contact:

Dr. James Blowey

Deputy Head of Faculty

Faculty of Science Office

Level 3 Chemistry Building

Durham University

DH1 3LE

UK

Email: Natural Sciences Director

WWW: Natural Sciences home page

The Natural Sciences web pages are maintained by James Blowey