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 |
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Year | CATS Level | Semester | CATS Value |
Session 2016-17 | Level 6 FHEQ | First Semester | 15 |
Aims |
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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 |
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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 |
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1 |
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 |
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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 |
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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 |