Section outline

    • Questions on the Complex Analysis part of the course. Please feel free to post questions/answers/corrections to the notes.


    • The first example sheet, covering material from Chapters 1, 2 and 3 of the Metric Spaces notes. 

    • The second example sheet, covering material from Chapters 4, 5 and 6 of the Metric Spaces notes.

    • The third example sheet, covering material from Chapters 7, 8 and 9 of the Metric Spaces notes.

    • The fourth example sheet, the first one covering the complex analysis parts of the course (sections 1,2 and 3 of the notes)

    • Branch cuts, Integration along paths, Winding Numbers, Cauchy's Theorem, sections 4-7.1 of the notes


    • Cauchy's integral formulae, Liouville's Theorem, Identity Theorem, Morera's Theorem, Isolated singularities, Laurent series, sec. 7.2-9 from the notes.



    • The argument principle, open mapping theorem, residue calculus, Jordan's lemma, sec. 10-11.3 of the notes


    • Summation of infinite series, keyhole contours, conformal transformations, Dirichlet's problem, sec 11.4-12 of the notes



    • These are the notes for the first third of the course, on metric spaces. They are relevant to the first three exercise sheets.

    • These are the notes for the second part of the course- relevant for problem sheets 4-8.

    • These are notes from R. Earl who taught the course in the past. 

    • Slides for week 5 Lectures (updated/corrected)

    • Slides for week 6 Lectures

    •  Slides for week 8 Lectures (updated/corrected)