# Mathematics within Natural Sciences 2020-2021

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).

**Further, as we are unable to fully anticipate the impact of COVID-19 this information should be viewed as being provisional and understood in the context that the University will test the feasibility of delivering each module within the timetable while applying government advice.**

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 (MATH1587)

Probability I (MATH1597)

Dynamics I (MATH1607)

Statistics I (MATH1617)

**Level 2 modules **

Complex Analysis II (MATH2011)

Analysis In Many Variables II (MATH2031)

Statistical Concepts II (MATH2041)

Numerical Analysis II (MATH2051)

Mathematical Physics II (MATH2071)

Algebra II (MATH2581)

Elementary Number Theory II (MATH2617)

Geometric Topology II (MATH2627)

Mathematical Modelling II (MATH2637)

Probability II (MATH2647)

Special Relativity And Electromagnetism II (MATH2657)

Monte Carlo II (MATH2667)

**Level 3 modules **

Analysis III^{*} (MATH3011)

Differential Geometry III^{*} (MATH3021)

Number Theory III (MATH3031)

Galois Theory III (MATH3041)

Statistical Methods III (MATH3051)

Decision Theory III (MATH3071)

Numerical Differential Equations III (Available 2021-2022) (MATH3081)

Dynamical Systems III^{*} (MATH3091)

Fluid Mechanics III^{*} (MATH3101)

Quantum Mechanics III (MATH3111)

Mathematics Teaching III^{*} (unlikely to be offered in 2020-2021)G (MATH3121)

Operations Research III^{*} (MATH3141)

Mathematical Biology^{*} (MATH3171)

Geometry III (Available 2020-2021) (MATH3201)

Probability III (Available 2020-2021) (MATH3211)

Solitons III^{*} (MATH3231)

Stochastic Processes III (Available 2021-2022) (MATH3251)

Topology III^{*} (MATH3281)

Partial Differential Equations III^{*} (MATH3291)

Mathematical Finance III^{*} (MATH3301)

Bayesian Statistics III (Available 2021-2022) (MATH3341)

Statistical Mechanics III^{*} (Available 2020-2021) (MATH3351)

Topics In Statistics III (Available 2020-2021) (MATH3361)

Representation Theory III (Available 2021-2022) (MATH3371)

Project IIIG (MATH3382)

Quantum Computing III^{*} (MATH3391)

Cryptography And Codes III (MATH3401)

Public Engagement In Mathematical SciencesG (MATH3461)

Science EnterpriseG (NSCI3001)

**Level 4 modules **

Bayesian Statistics IV (Available 2021-2022) (MATH4031)

Partial Differential Equations IV^{*} (MATH4041)

General Relativity IV^{*} (MATH4051)

Advanced Quantum Theory IV^{*} (MATH4061)

Topics In Statistics IV (Available 2020-2021) (MATH4071)

Project IVG (MATH4072)

Stochastic Processes IV (Available 2021-2022) (MATH4091)

Probability IV (Available 2020-2021) (MATH4131)

Geometry IV (Available 2020-2021) (MATH4141)

Topics In Algebra And Geometry IV (MATH4151)

Algebraic Topology IV^{*} (MATH4161)

Riemannian Geometry IV^{*} (MATH4171)

Mathematical Finance IV^{*} (MATH4181)

Numerical Differential Equations IV (Available 2020-2021) (MATH4221)

Statistical Mechanics IV^{*} (MATH4231)

Representation Theory IV (MATH4241)

#### 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 at least 20 credits taken from the Level 2 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. If 60 credits or more are taken, 20 credits can be at Level 2. |

**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 at Level 1. |

Year 3 | 40 credits: Modules taken from the Level 3 Mathematics list. If 60 credits or more are taken, 20 credits can be at Level 2 Mathematics. |

#### Advice for progression and other aspects

**Department advice**: See Mathematics 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), Geometric Topology II (MATH2627) or (Mathematical Physics II (MATH2071) if Foundations Of Physics 1 (PHYS1122) has been taken) and for 2019/20 |

Year 3 | Decision Theory III (MATH3071) and Operations Research III (MATH3141) have no Level 2 prerequisites, but do require students to have taken Calculus I (MATH1061) and Linear Algebra I (MATH1071). |

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