Probabilistic Method in Combinatorics (MATH0107)

Key information

Faculty: Faculty of Mathematical and Physical Sciences
Teaching department: Mathematics
Credit value: 15

Restrictions: This module is normally taken by fourth-year students on single or combined Mathematics degrees who have previously taken MATH0029 Graph Theory and Combinatorics and/or MATH0028 Combinatorial Optimisation. MATH0057 Probability and Statistics (or other courses on probability) is also recommended.
Timetable

Alternative credit options

There are no alternative credit options available for this module.

Description

The module introduces the probabilistic method, a powerful approach with many applications in combinatorics. The basic idea behind the method is that to prove that a combinatorial object with certain properties exists, it suffices to show that a random construction produces such an object with positive probability. The main topics covered in the module are the following: the basic method, linearity of expectation, alterations, the second moment, large deviations and the local lemma. Each of these topics will be presented along with applications in several different areas in combinatorics. The course will cover additional topics that will vary from year to year, including correlation inequalities, martingales, and various more intricate applications of aforementioned methods.

Module deliveries for 2024/25 academic year

Intended teaching term: Term 2 听听听 Undergraduate (FHEQ Level 7)

Teaching and assessment

Mode of study: In Person
Methods of assessment: 90% Exam

10% Coursework
Mark scheme: Numeric Marks

Other information

Number of students on module in previous year: 7
Module leader: Dr Frederick Illingworth
Who to contact for more information: math.ugteaching@ucl.ac.uk

Last updated

This module description was last updated on 19th August 2024.

听

Useful links

Sustainability

For a list of modules related to climate change as well as social and environmental sustainability at 果冻影院, type 'climate' or 'sustainability' into the search. Visit Sustainable 果冻影院 for information on extra-curricular activity on sustainability.

Important information

The catalogue has been updated with key information about the modules that will run during the 2024/25 academic session. Current and prospective students can browse through the catalogue to consider possible module choices for the coming year.

Please note,听information in the catalogue is听subject to change as teaching and assessment arrangements for 2024/25 may need to be adjusted in line with the University's Feedback and Assessment principles and operating model.

Centrally managed exam durations will be provided on students' individual exam timetables. Arrangements for locally managed timed assessments and in-class activity will be confirmed by the teaching department for the module.

听