Discrete
Mathematics
BSc Hons
“Warwick University has a
great community and there are
always lots of opportunities to
get involved in a diverse range
of activities and events.”
Rhys Davis (2009-2012)
Discrete Mathematics
(BSc Hons)
What is Discrete Mathematics?
Discrete Mathematics is a dynamic and
interesting branch of Mathematics with many
existing and emerging applications. It deals
with mathematical structures and problems
that are "discrete" in nature, as opposed to
problems that exhibit continuous properties.
Discrete Mathematics is used in all areas of
algorithm and information structure design,
which means our graduates are in demand
in areas concerned with topics in computer
security, coding theory, cryptography, electronic
banking, telecommunications and web search
engines.
Many optimisation and planning problems also
give rise to questions addressed by Discrete
Mathematics. For instance, the road map in
a GPS in your car is stored as a list of crossings
with mutual links describing how it is possible
to drive from one crossing to another. When
you enter a desired destination, a complex
mathematical algorithm is invoked to compute
an optimal route from your current place to the
destination. It is important that the algorithm
computing the route is fast enough to be
useful in navigation, which is exactly why we
should be concerned with the complexity of
algorithms.
Discrete Mathematics was essential to the
breaking of German codes during World War
II. Bill Tutte, a key contributor to the cracking
of the Enigma code, set the foundations of
modern Discrete Mathematics. Discrete
Mathematics is also linked to the legacy of Paul
Erdos, one of the most famous mathematicians
of the 20th century. It gave foundations of
modern public-key cryptography used in today
e-banking and e-commerce applications.
Formal verification provides framework for
testing logic statements about safety-essential
software systems such as those in the planes.
On the theoretical side, one of the greatest
unsolved problems of theoretical Computer
Science is the $1m Millennium Prize Problem "P
vs. NP" on the existence of efficient algorithms
for many intriguing Discrete Mathematics
problems.
Discrete Mathematics
at Warwick
Discrete Mathematics is an honours degree
taught jointly by the Department of Computer
Science and the Warwick Mathematics Institute
since 2008. This distinctive course provides a
firm grounding in modern Computer Science
and Mathematics, building on the expertise
of the Centre for Discrete Mathematics and
its Applications (DIMAP), a research centre
established at the University of Warwick in
2007. Our Discrete Mathematics degree equips
students with a fundamental understanding
of Mathematics and a comprehensive set of
skills in Computer Science, which make our
graduates particularly attractive to the world’s
most reputable employers.
Discrete Maths at Warwick
“Studying
was no easy task but, with the help
and support of the staff, I was able
to graduate with exactly the set of
skills I needed to pursue a career in a
competitive industry. The course also
offered me great flexibility, allowing
me to choose the Computer Science and
Mathematics modules I found more
interesting." Jess Fan (2009-2012)
The course involves learning about and solving
interesting problems. You will be taught how
to create and analyse algorithms and have
the opportunity to develop software systems
individually and as part of a team. Your finalyear project will allow you to explore a topic
that you find particularly interesting, building
on the expertise and skills you’ve developed in
previous years.
DISCRETE MATHEMATICS 3
www.warwick.ac.uk/go/statistics
warwick.ac.uk/dmaths
Meet Our Academics
Dr. Andrzej S. Murawski
(Course Manager,
Computer Science)
Research Interests:
Programming languages, software
verification, automata theory
2005-2010 EPSRC Advanced Research
Fellow, Oxford
2002-2006 Junior Research Fellow,
St John's College, Oxford
2001 DPhil in Computation, Oxford
Dr. Alina R. Ene
(Computer Science)
Research Interests:
Discrete and combinatorial optimization,
approximation algorithms
2013-14, Postdoc, Princeton University
2013 PhD in Computer Science, University
of Illinois at Urbana-Champaign
2008 BSE in Computer Science
(magna cum laude), Princeton University
Professor
Oleg Pikhurko
(Mathematics)
Research Interests:
Extremal combinatorics, graph limits
2003-2011 Assistant and Associate
Professor, Carnegie Mellon University
2000-2003 Junior Research Fellow,
St John's College, Cambridge
2000 PhD in Pure Mathematics,
Cambridge University
Course Structure
The Discrete Mathematics course develops
the rigorous mathematical methods and
practical skills that are demanded by a variety
of technical roles, including those in scientific
research. This is achieved through three
years of study, where each year builds on
the previous to provide breadth and depth in
Mathematics and Computer Science.
First year
The first year of the course focuses on essential
Computer Science and Mathematics skills.
Students take modules in the fundamental
areas of pure mathematics, such as
mathematical analysis, linear algebra and
probability. They also experience computer
programming in Java and learn how to solve
fundamental problems using algorithms and
data structures. The normal load consists of
around 25% Computer Science modules, 20%
pure mathematics modules, 20% Discrete
Mathematics modules and 5% statistics
modules. 10% of the normal load is left for
optional modules. Some of the modules are
specifically designed for and taken only by
the students studying Discrete Mathematics,
whilst others are taken with the first-year
students in Computer Science, Mathematics
and Statistics.
Second year
The second year places emphasis on applying
mathematical skills developed during the first
year in Computer Science. The core consists
of those related to Discrete Mathematics and
advanced algorithm and data structure design,
including theoretical concepts related to the
structure of programming languages. Optional
modules offer a wide range of mathematical
and statistical subjects related to optimisation
and stochastic methods. More than 40% of
the normal load is left as optional modules for
students to choose.
Final year
The final year gives students the freedom to
choose modules to suit their interests and
shape their graduate profile. The students
are required to take two Computer Science
modules. The first is a module on analysing the
complexity of computational problems, whilst
the second module is an individual project. In
most cases, the projects consist of designing
and implementing software to solve a studentspecified problem, though students can also
choose to develop entirely mathematical
projects.
Careers
The students graduating from Department
of Computer Science and the Warwick
Mathematics Institute are highly demanded
by employers.
Discrete Mathematics plays an essential
role in modelling and in designing efficient
solutions of everyday problems in the digital
economy, allowing our graduates find jobs
in a wide range of areas, including:
• Consultancy
• Finance
Flexible study
• Scientific Research
The Discrete Mathematics course offers great
flexibility, which increases from the first year
to the third. Most of the modules taken by
the students are taught by Department of
Computer Science,Department of Statistics,
Warwick Business School, and Warwick
Mathematics Institute. However, there is no
restriction on some of the modules taken as
part of the normal load in the second and third
years and the choices of the modules taken
often include those offered by Department of
Philosophy, Economics Department, Language
Centre and others. Additional modules may also
be taken by students opting to take higher than
the normal load.
• Software Engineering
As with all degree courses offered by the
Department of Computer Science, Discrete
Mathematics students have the option of
taking an intercalated year between the second
and third years of their degree. This can be used
to work in industry or to study at a university
in another country for a year. Our students
have spent intercalated years at companies
such as Barclays Capital, BT, HSBC, IBM, Intel,
PwC, Siemens and many other prestigious
organisations. Another way of getting an
industrial experience during the course are
summer internships which sometimes lead to
employment offers after the graduation.
• Telecommunications
Other career options include teaching
mathematics and Computer Science related
subjects at schools, where the shortage
of Mathematics teachers remains an
issue. Some graduates also continue on to
study for postgraduate degrees that allow
them to take up research positions within
companies or universities.
I started my first year of
“When
Discrete Mathematics, I wasn't
entirely sure what to expect.
However, you have the freedom to
explore your options and find out
what suits you best. After my second
year, I took part in an Internship
at PwC under Data Assurance. This
allowed me to put skills developed
during my degree to use and
highlighted how relevant DM is
in a financial and technological
environment. Overall, the degree
is an interesting mix of theoretical
concepts and real life applications
which develops your natural abilities
such as problem solving."
Jon Buckler (2011-2014)
DISCRETE MATHEMATICS 5
www.warwick.ac.uk/go/statistics
warwick.ac.uk/dmaths
Mathematics and Computer
Science at Warwick
Since its foundation as one of the new
universities in 1965, Warwick has grown
into one of the strongest universities for
mathematical science in Europe. Warwick
Mathematics Institute is home to many
internationally renowned researchers from all
areas of pure and applied Mathematics. One of
its members, Ian Stewart, is also a well-known
author in popular science.
Department of Computer Science was
established in 1969. It has steadily grown
in size with the increasing numbers of its
undergraduate and graduate students. The
Department is consistently ranked among the
top UK Computer Science departments.
Discrete Mathematics at Warwick
In response to the growing importance
of Discrete Mathematics, the University
of Warwick set up the Centre for Discrete
Mathematics and its Applications (DIMAP)
in 2007. The centre is a joint venture of the
Department of Computer Science, the Warwick
Mathematics Institute and the Warwick
Business School. In its first years of existence,
it was supported by the EPSRC Science and
Innovation Award of nearly £4M. The centre
attracted many world leading experts to
Warwick and turned Warwick in one of the
strongest places for Discrete Mathematics in
Europe.
The Discrete Mathematics course is
administered by the Department of Computer
Science, which has a strong tradition in
multidisciplinary degrees. Every student is
assigned a personal tutor to provide pastoral
care and help deal with any issues. The modules
taught are delivered by specialists from relevant
departments. Mathematical supervisions
held twice a week for groups of 4 or 5 students
assist the first-year students to cope with their
mathematical modules. Computer Science
classes are supplemented by small group
tutorials. Since the first year, all students are
able to shape the structure of the modules they
take based on their own interests.
Discrete Mathematics is one of several
mathematics oriented honours degrees at the
University of Warwick. Allied courses include:
• Computer Science
• Data Science
• Mathematics
• Mathematics and Physics
• Mathematics and Statistics
• MORSE (Mathematics, Operational
Research, Statistics and Economics)
The Discrete Mathematics degree focuses on
(discrete) mathematics methods underpinning
Computer Science applications, leading to
applications in algorithm and data structure
design and in planning and optimisation
tasks. At the same time the degree provides
large flexibility by offering a wide range of
mathematical and Computer Science modules.
Entry Requirements
Our typical A-level offer is A*AA including an
A* in Mathematics or Further Mathematics.
No previous knowledge of Computer Science is
required.
Our minimum language requirements is a
grade C in GCSE English or IELTS 6.0.
About the University
The University of Warwick was established
in 1965 and it quickly gained a reputation
for excellence in research and teaching. It
has regularly been appearing among the
top 20 world universities in the "under 50"
lists (consisting of the universities under
the age of 50) both in QS World University
Rankings and the Times Higher Education
World University Rankings. The Government
Teaching Quality Assessment has rated
as excellent both Computer Science and
Mathematics.
The modern main campus of the University
is located in the southern part of Coventry
and partly in the county of Warwickshire.
Its central location means that Birmingham
and its busy international airport are within
easy reach. It is also one hour train ride
or 90 minute motorway ride to London.
The University of Warwick is a place of
study for over 23,000 students with 55%
being undergraduates. In January 2013,
the University also opened Learning Grid
in Leamington Spa to offer supportive
environment to its many students living in
the town.
The Warwick Arts Centre is the largest arts
centre in the UK outside London. It combines
art gallery, cinema, a concert hall, cinema,
theatres and Music Centre. The University
campus also offers first class sports facilities
including a Sports Centre, Games Hall, Bear
Rock Climbing Centre, playing fields and
running tracks.
Over 200 clubs and societies are organised
by a dynamic Students Union (one of the
biggest in the UK) providing a vast range
of activities and entertainment options for
student life at Warwick.
DISCRETE MATHEMATICS 7
warwick.ac.uk/datsci
warwick.ac.uk/dmaths
xx
For further information contact:
Undergraduate Admissions
Computer Science
University of Warwick
Coventry CV4 7AL UK
Tel:
+44 (0)24 7652 3193
Fax:
+44 (0)24 7652 3024
Email:[email protected]
Designed by WarwickDesign, www.designatwarwick.com
Printed by WarwickPrint, www.warwickprint.co.uk