Unit information: Topics in Discrete Mathematics 34 in 2020/21

Unit name	Topics in Discrete Mathematics 34
Unit code	MATHM0009
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 2C (weeks 13 - 18)
Unit director	Dr. Ellis
Open unit status	Not open
Pre-requisites	At least two of the following units: MATH20006 Metric Spaces, MATH21800 Algebra 2, MATH21400 Linear Algebra 2 For joint Mathematics and Computer Science students, it would be desirable to have taken COMS21103 Data Structures and Algorithms
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Lecturers: Heilbronn Fellows (to be confirmed)

Unit Aims

This is a topics course aimed at deepening and broadening the students' knowledge of various aspects of discrete mathematics, as well as illustrating connections between discrete mathematics and other areas such as algebra, probability, number theory, analysis and computer science.

Unit Description

Discrete mathematics refers to the study of mathematical structures that are discrete in nature rather than continuous, for example graphs, lattices, partially ordered sets, designs and codes. It is a classical subject that has become very important in real-world applications, and consequently it is a very active research topic.

This topics course exposes the students to a selection of advanced topics in discrete mathematics. These may include (but are not restricted to) advanced topics in graph and hypergraph theory, design and coding theory, combinatorial topics in group theory, as well as probabilistic, algebraic and Fourier-analytic methods throughout discrete mathematics.

While results and problems of recent origin may be included in the syllabus, the instructors aim to make the material accessible to all students fulfilling the prerequisites by providing complete lectures notes and including all necessary background material.

The unit is suitable for students with a firm grasp of the basic concepts in Combinatorics, and likely of interest to those with an interest in number theory, algebra, probability and/or theoretical computer science.

Relation to Other Units

The course follows on from Combinatorics. It complements Complex Networks and the Data Structures and Algorithms unit in Computer Science. Students may not take this unit if they have taken the corresponding Level H/6 unit MATH30002 Topics in Discrete Mathematics 3.

Intended Learning Outcomes

Learning Objectives

In accordance with the specific syllabus taught in any particular year, students who successfully complete the unit should:

• have developed a solid understanding of the advanced concepts covered in the course;
• be able to use techniques from algebra, analysis and probability to solve problems in discrete mathematics;
• have a good grasp of the applications of combinatorial techniques in other areas of mathematics and to real-world problems.

By pursuing an individual project on a more advanced topic students should have:

• developed an awareness of a broader literature;
• gained an appreciation of how the basic ideas may be further developed;
• learned how to assimilate material from several sources into a coherent document.

Transferable Skills

The ability to think clearly about discrete structures and the ability to analyse complex real-world problems using combinatorial abstractions.

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

90% Timed, open-book examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Further

• Ian Anderson, A First Course in Discrete Mathematics, Springer, 2001
• Peter J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1995
• Dieter Jungnickel, Graphs, Networks, and Algorithms, Springer, 2005