Natural Sciences

# Mathematics within Natural Sciences 2022-2023

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 (MATH1587)
Probability I (MATH1597)
Dynamics I (MATH1607)
Statistics I (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 (MATH2617)
Geometric Topology II (MATH2627)
Mathematical Modelling II (MATH2637)
Probability II (MATH2647)
Special Relativity And Electromagnetism II (MATH2657)
Data Science And Statistical Computing II (MATH2687)
Statistical Modelling II (MATH2697)
Markov Chains II (MATH2707)
Statistical Inference II (MATH2711)

##### 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)
Topics In Statistics IV (MATH4071)
Project IVG (MATH4072)
Probability IV (MATH4131)
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)
Superstrings IV (MATH4271)
Topics In Combinatorics IV (MATH4281)
Ergodic Theory IV (MATH4361)
Functional Analysis And Applications IV (MATH4371)
Topics In Applied Mathematics IV* (MATH4381)

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

 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 strongly recommended.Progression from: MATH1061; MATH1071; MATH1051; MATH1597; MATH1617. 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.)Students taking Biology, Economics or Psychology are recommended to take Statistical Inference (MATH2671).In 2023/24, students taking Chemistry on the BSc pathway may wish to take Programming I (MATH1587). In 2023/24, Advanced Quantum Theory IV (MATH4061) will become an excluded combination with Particle Theory (PHYS4181). A new module taught by Mathematics on Superstrings should become available to account for this reduction in choice.Progression from: MATH1051; MATH2581; MATH2617; MATH2627; MATH2071; MATH2671; MATH1587; MATH4061; PHYS1122; PHYS4181. 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). In 2023/24, Advanced Quantum Theory IV (MATH4061) will become an excluded combination with Particle Theory (PHYS4181). A new module taught by Mathematics on Superstrings should become available to account for this reduction in choice.Progression from: MATH3071; MATH3141; MATH1597; MATH4061; PHYS4181.

Dr. James Blowey
Deputy Head of Faculty
Faculty of Science Office
Level 3 Chemistry Building
Durham University
DH1 3LE
UK

Email: Natural Sciences Director

The Natural Sciences web pages are maintained by James Blowey