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 JM Woolf
Mathematical Sciences
Jonathan.Woolf@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 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

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.
Explanation of Reading List:

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

MATH101; MATH102; MATH103  

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:

Programme:G100 Year:3 Programme:G101 Year:3,4 Programme:G110 Year:3 Programme:G1F7 Year:3 Programme:G1N2 Year:3 Programme:G1R9 Year:4 Programme:G1X3 Year:3 Programme:GG13 Year:3 Programme:GN11 Year:3 Programme:GG14 Year:3 Programme:GL11 Year:3 Programme:GR11 Year:4 Programme:GV15 Year:3 Programme:BCG0 Year:3 Programme:L000 Year:3 Programme:Y001 Year:3 Programme:MMAS Year:1

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Written Exam  2.5 hours  First semester  90  Standard University Policy    Assessment 2 Notes (applying to all assessments) Homeworks This work is not marked anonymously. Candidates may attempt all questions. The best FIVE will be taken into account. Each question carries the same weight.  
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework    First semester  10  Standard University Policy  University policy.  Assessment 1