MA303 Half Unit
Chaos in Dynamical Systems
This information is for the 2017/18 session.
Teacher responsible
Prof Graham Brightwell
Availability
This course is available on the BSc in Accounting and Finance, BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
Prerequisites
Mathematical Methods (MA100) is a prerequisite. Background in rigorous mathematical methods, such as provided in Introduction to Abstract Mathematics (MA103), is desirable. In particular, some familiarity with proving theorems would be useful.
Course content
Given a function f:X>X, what is the (iterative) behaviour of fn (x)=f(f(...(f(x)) )) (f applied n times). What do 'orbits' of f look like  an orbit has the form x, f(x), f(f(x)).,,, Particular emphasis is given to longterm evolution and stability analysis of such systems f:X>X. We explore connections with socalled fractal sets, which are roughly sets that look the same at any degree of magnification, and may have a dimension which is not an integer. We also discuss chaotic maps f, where fn (x) cannot be determined if there is any small uncertainty about x. Topics covered: Iteration of discrete maps. Orbit analysis. Contraction mapping theorem. Quadratic maps. Bifurcations. Definition of chaos. Sarkovskii's theorem. Fractal sets.
Teaching
21 hours of lectures and 10 hours of classes in the MT. 1 hour of lectures in the ST.
.
Formative coursework
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Full lecture notes will be provided. The following may prove useful, R Devaney, A First Course in Chaotic Dynamical Systems; R Devaney, An Introduction to Chaotic Dynamical Systems; E Scheinerman, Invitation to Dynamical Systems. A fun and interesting read might be Glieck, J.,Chaos: Making a New Science.
Assessment
Exam (100%, duration: 2 hours) in the main exam period.
Key facts
Department: Mathematics
Total students 2016/17: 10
Average class size 2016/17: 10
Capped 2016/17: No
Value: Half Unit
PDAM skills
 Selfmanagement
 Problem solving
 Application of information skills
 Communication
 Application of numeracy skills
 Specialist skills
Course survey results
(2014/15  2016/17 combined)
1 = "best" score, 5 = "worst" scoreThe scores below are average responses.
Response rate: 100%
Question 
Average  

Reading list (Q2.1) 
1.9  
Materials (Q2.3) 
1.8  
Course satisfied (Q2.4) 
1.6  
Lectures (Q2.5) 
1.5  
Integration (Q2.6) 
1.6  
Contact (Q2.7) 
1.7  
Feedback (Q2.8) 
1.8  
Recommend (Q2.9) 
