Lecturer: Aleksander Doan

Teaching assistant: Brad Wilson

Syllabus: https://www.ucl.ac.uk/maths/sites/maths/files/math0017.pdf

Course materials: Lecture notes and quizzes on Moodle, homework on Crowdmark

Drop-in sessions: Friday 17:30 on zoom, link on Moodle

Stop by and ask questions. If there are no questions, I will go through homework solutions.

Final mark: 90% Exam, 10% Coursework

Homework: 4-5 problems a week, submit 2-3 of them each worth 10 points

Two Moodle quizzes (each worth 30 points, in those weeks no compulsory homework)

References

Lectures based on lecture notes by Megan Griffin-Pickering, available on Moodle. My own notes from lectures will be uploaded to Moodle as the term progresses. Other good resources are

• Terence Tao’s lecture notes
• R L Schilling Measures, Integrals and Martingales
• R G Bartle, The elements of integration and Lebesgue measure

Lectures will be recorded and available on Lecturecast, but the recording quality is not always good and they might be available with a delay, so regular participation is strongly recommended.

Prerequisites

The following topics will be crucial for being able to understand lectures in this course. You can find them in any analysis textbook (such as this one) or your lecture notes from Analysis 1 and 2.

• Set theory: countable and uncountable sets, power set, functions between sets (injective, surjective, bijective), cardinality, basic operations on sets (union, intersection, difference, complement)
• Analysis: limits and series of numbers and functions, pointwise and uniform convergence, Cauchy sequences, continuous and differentiable functions, infimum and supremum, liminf and liminf, Euclidean distance, open and closed sets, open neighborhood of a point, bounded and compact sets (in terms of coverings and in terms of sequences)