UNIVERSITY OF KENT
Confirmation that this version of the module specification has been approved by the School Learning and
Teaching Committee:
……25th March 2015……………………….(date)
MODULE SPECIFICATION
1.
Title of the module: Graphs and Combinatorics (MA595 and MA995).
2.
School or partner institution which will be responsible for management of the module: School of
Mathematics, Statistics and Actuarial Science
3.
Start date of the module: September 2015
4.
The number of students expected to take the module: 50
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with other
relevant Schools and Faculties regarding the withdrawal: None – this is a new module.
6.
The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M])
MA595 – H-level; MA995 – M-level
7.
The number of credits and the ECTS value which the module represents: 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern)
Autumn Term or Spring Term
9.
Prerequisite and co-requisite modules
Prerequisite module: MA322 Proofs and Numbers or equivalent.
10. The programmes of study to which the module contributes
For H-level module: BSc (Hons) Mathematics, BSc Mathematics and Statistics (including
programmes with a year in industry), BSc (Hons) Mathematics with a Foundation Year, MMath
Mathematics, MMathStat Mathematics and Statistics, Graduate Diploma in Mathematics
For M-level module: International MSc in Mathematics and its Applications, MSc in Mathematics and
its Applications, MMath Mathematics, MMathStat Mathematics and Statistics
For the MMath Mathematics and MMathStat Mathematics and Statistics programmes, either the Hlevel or the M-level module may be offered, but not both.
11. The intended subject specific learning outcomes
On successful completion of this module, H-level students will:
11.1 have gained knowledge of the fundamental concepts and results in graph theory and
combinatorics;
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11.2 be able to describe and solve a mathematical problem using graphs and combinatorial
arguments;
11.3 have gained further knowledge of discrete structures in mathematics;
11.4 have gained a working knowledge of various fundamental graph algorithms;
11.5 have an ability to understand constructive proofs and to be able to use them to design
algorithms.
On successful completion of this module, M-level students will also:
11.6 have a systematic understanding of an advanced topic in graph theory or combinatorics at the
forefront of the discipline.
12. The intended generic learning outcomes
On successful completion of this module, H-level students will have:
12.1 enhanced mathematical problem solving skills;
12.2 gained further appreciation of proofs in mathematics;
12.3 gained understanding of constructive proofs;
12.4 strengthened their skills in designing and working with algorithms;
12.5 an enhanced ability to communicate complex mathematical concepts.
On successful completion of this module, M-level students will also have:
12.6 an enhanced ability to master and communicate mathematics independently.
13. A synopsis of the curriculum
Combinatorics is a field in mathematics that studies discrete, usually finite, structures, such as
graphs. It not only plays an important role in numerous parts of mathematics, but also has real
world applications. In particular, it underpins a variety of computational processes used in digital
technologies and the design of computing hardware.
Among other things, this module provides an introduction to graph theory. Graphs are discrete
objects consisting of vertices that are connected by edges. We will discuss a variety of concepts
and results in graph theory, and some fundamental graph algorithms. Topics may include, but
are not restricted to: trees, shortest paths problems, walks on graphs, graph colourings and
embeddings, flows and matchings, and matrices and graphs.
In addition to graphs, the module may cover other topics in combinatorics such as: problems in
extremal set theory, enumerative problems, Principle of Inclusion and Exclusion, and, for M-level
students, Ramsey theory, computational complexity and the P versus NP problem.
14. Indicative Reading List
P. Cameron, Combinatorics, Topics, Techniques Algorithms, Cambridge Press, (1994)
L. Lovasz, J. Pelikan, and K. Vesztergombi, Discrete Mathematics: Elementary and Beyond.
Springer-Verlag, (2003).
D. B. West, Introduction to Graph Theory, Prentice Hall, (1996).
R.J. Wilson, Introduction to Graph Theory, Fourth edition. Longman, Harlow, (1996).
In addition, for M-level students:
J.A. Bondy and U.S.R. Murty, Graph Theory, Graduate Text in Math. 244, Springer-Verlag,
(2008).
B. Ballobas, Modern Graph Theory, Graduate Text in Math., 184, Springer-Verlag, 1998.
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15. Learning and Teaching Methods, including the nature and number of contact hours and the total
study hours which will be expected of students, and how these relate to achievement of the intended
module learning outcomes
Learning and Teaching Methods:
Number of contact hours: 42-48 hours, including approx. 36 lectures and 6-12 example classes (1hour)
Number of independent learning hours: 102-108 hours
Total study hours: 150.
The lectures will address learning outcomes: 11.1,11.3-11.5,12.2,12.3.
The exercise classes will address learning outcomes: 11.2,12.1,12.4,12.5.
In addition, for M-level students, directed reading will cover learning outcomes 11.6 and 12.6.
16. Assessment methods and how these relate to testing achievement of the intended module learning
outcomes:
The module will be assessed by examination (80%) and coursework (20%).
Coursework: There will be up to two assignments assessing learning outcomes 11.1, 11.2, 11.4,
11.5 and 12.1, 12.5. Different open book assignments will be provided for M-level students, which
will additionally assess learning outcomes 11.6 and 12.6.
Examination: This will be a 3-hour written examination in the Summer term that consists of multi-part
questions requiring a mix of short and long answers that test at varying levels of proficiency learning
outcomes 11.1-11.4, and 12.1-12.4. The examination set for M-level students will assess their level
of understanding to an enhanced level, additionally assessing learning outcome 12.6.
17. Implications for learning resources, including staff, library, IT and space
For the lectures and the workshops a room with plenty of white (or black) board space. Additional
books and ebooks should be acquired by the Library.
18. The School recognises and has embedded the expectations of current disability equality legislation,
and supports students with a declared disability or special educational need in its teaching. Within
this module we will make reasonable adjustments wherever necessary, including additional or
substitute materials, teaching modes or assessment methods for students who have declared and
discussed their learning support needs. Arrangements for students with declared disabilities will be
made on an individual basis, in consultation with the University’s disability/dyslexia support service,
and specialist support will be provided where needed.
19. Campus(es) where module will be delivered:
Canterbury
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