Module Title  Combinatorics and Communication Theory 
School  Mathematics 
Department  Mathematics 
Module Code  06 19608 
Module Lead  Deryk Osthus 
Level  Masters Level 
Credits  20 
Semester  Semester 2 
Prerequisites 
LC Algebra & Combinatorics 1  (06 25659)

Corequisites 

Restrictions  Optional for all MSci programmes in Mathematics and MSci JH programmes including mathematics 
Contact Hours 
Lecture46 hours
Tutorial10 hours
Total: 56 hours

Exclusions  
Description  The first part of the module will give an introduction to several combinatorial structures, which have applications in different areas. Topics are likely to include combinatorial games, applications of counting principles to discrete probability and basic Ramsey theory. (Here Ramsey theory can be viewed as a formalization of the notion that `complete disorder is impossible’ – this surprising phenomenon will be investigated for graph colourings and arithmetic properties of the integers). The second part of the module consists of an introduction to information theory and coding theory. The aim here is to transmit information (i) efficiently and (ii) reliably over a noisy channel. For (i), the main result will be Shannon’s noiseless coding theorem, which relates coding efficiency to the entropy of a source. For (ii), we will discuss error correcting codes, including several linear codes, such as Hamming codes. Both parts of the module are linked by the methods and ideas that are used. 
Learning Outcomes  By the end of the module the student should be able to: Apply counting principles in various settings, including discrete probability
 Be familiar with basic combinatorial structures and arguments, be able to prove simple results in Ramsey theory.
 Understand and be able to apply fundamental results on codes and communication over a noisy channel.
 Apply the basic coding techniques such as Huffman codes and linear codes.
 Level M students will explore the subject beyond the taught syllabus.

Assessment 
1960801 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions  3 hour Written Unseen Examination (80%); Incourse Assessment (20%). 
Other  
Reading List 
Welsh, D. 1988. Codes and Cryptography. Oxford University Press.
Jukna, S. 2001. Extremal Combinatorics. SpringerVerlag.
