Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title COMBINATORICS
Code MATH344
Coordinator Dr V Guletskii
Mathematical Sciences
vladimir.guletskii@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2019-20 Level 6 FHEQ First Semester 15

Aims

To provide an introduction to the problems and methods of Combinatorics, particularly to those areas of the subject with the widest applications such as pairings problems, the inclusion-exclusion principle, recurrence relations, partitions and the elementary theory of symmetric functions.

Learning Outcomes

(LO1) After completing the module students should be able to: understand of the type of problem to which the methods of Combinatorics apply, and model these problems; solve counting and arrangement problems; solve general recurrence relations using the generating function method; appreciate the elementary theory of partitions and its application to the study of symmetric functions.

Syllabus
 

Introduction to the problem of Combinatorics. Selection and binomial coefficients. Pairings problems. The inclusion-exclusion principle. Recurrence including the Fibonacci sequence. Generating functions. Partitions and their Ferrers graphs Symmetric functions.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 2 Assessment Schedule (When) :First semester  2.5 hours    90       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 1 Assessment Schedule (When) :First semester      10