# Course - Complex Analysis MT23

> Source: https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/ · Updated: 2025-09-30 · Tags: uni, course

> Builds on the content taught in [Course - Metric Spaces MT23](https://ollybritton.com/notes/uni/part-a/mt23/metric-spaces/) and generalises the study of real analysis in Prelims ([Course - Analysis MT22](https://ollybritton.com/notes/uni/prelims/mt22/analysis-i/), [Course - Analysis II HT23](https://ollybritton.com/notes/uni/prelims/ht23/analysis-ii/) and [Course - Analysis III TT23](https://ollybritton.com/notes/uni/prelims/tt23/analysis-iii/)) to the complex numbers, which turns out to be simpler than real analysis (sort of).
> <br>
> Proves some remarkable theorems related to functions which are complex differentiable: 
> <br>
> - [Notes - Complex Analysis MT23, Cauchy's integral formula](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/cauchys-integral-formula/)
> - [Notes - Complex Analysis MT23, Casorati-Weierstrass theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/casorati-weierstrass-theorem/)
> - [Notes - Complex Analysis MT23, Liouville's theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/liouvilles-theorem/)
> - [Notes - Complex Analysis MT23, Residue theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/residue-theorem/)

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=65)
- [Lecture Notes](https://courses.maths.ox.ac.uk/pluginfile.php/31198/mod_resource/content/1/complex.pdf)
- [Panopto for 2020](https://ox.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx#folderID=%22d260f7b7-b2bb-4680-8031-ad8b0141409b%22)
- Sister course: [Course - Metric Spaces MT23](https://ollybritton.com/notes/uni/part-a/mt23/metric-spaces/)
- Other courses this term: [Courses MT23](https://ollybritton.com/notes/uni/part-a/mt23/)

### Notes
- [Notes - Complex Analysis MT23, Analytic functions](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/analytic-functions/)
- [Notes - Complex Analysis MT23, Argument principle](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/argument-principle/)
- [Notes - Complex Analysis MT23, Casorati-Weierstrass theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/casorati-weierstrass-theorem/)
- [Notes - Complex Analysis MT23, Cauchy's integral formula](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/cauchys-integral-formula/)
- [Notes - Complex Analysis MT23, Cauchy's theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/cauchys-theorem/)
- [Notes - Complex Analysis MT23, Complex differentiability](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/complex-differentiability/)
- [Notes - Complex Analysis MT23, Complex integration](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/complex-integration/)
- [Notes - Complex Analysis MT23, Conformal maps](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/conformal-maps/)
- [Notes - Complex Analysis MT23, Dirichlet problem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/dirichlet-problem/)
- [Notes - Complex Analysis MT23, Domains](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/domains/)
- [Notes - Complex Analysis MT23, Extended complex plane](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/extended-complex-plane/)
- [Notes - Complex Analysis MT23, Geometry](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/geometry/)
- [Notes - Complex Analysis MT23, Homotopies](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/homotopies/)
- [Notes - Complex Analysis MT23, Identity theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/identity-theorem/)
- [Notes - Complex Analysis MT23, Integral examples](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/integral-examples/)
- [Notes - Complex Analysis MT23, Jordan's lemma](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/jordans-lemma/)
- [Notes - Complex Analysis MT23, Laurent series](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/laurent-series/)
- [Notes - Complex Analysis MT23, Liouville's theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/liouvilles-theorem/)
- [Notes - Complex Analysis MT23, Logarithms](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/logarithms/)
- [Notes - Complex Analysis MT23, Misc](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/misc/)
- [Notes - Complex Analysis MT23, Möbius maps](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/mobius-maps/)
- [Notes - Complex Analysis MT23, Morera's theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/moreras-theorem/)
- [Notes - Complex Analysis MT23, Multifunctions and branch cuts](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/multifunctions-and-branch-cuts/)
- [Notes - Complex Analysis MT23, Open mapping theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/open-mapping-theorem/)
- [Notes - Complex Analysis MT23, Paths and curves](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/paths-and-curves/)
- [Notes - Complex Analysis MT23, Power series](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/power-series/)
- [Notes - Complex Analysis MT23, Residue theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/residue-theorem/)
- [Notes - Complex Analysis MT23, Riemann's removeable singularity theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/riemanns-removeable-singularity-theorem/)
- [Notes - Complex Analysis MT23, Rouché's theorem](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/rouches-theorem/)
- [Notes - Complex Analysis MT23, Winding numbers](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/winding-numbers/)
- [Notes - Complex Analysis MT23, Zeroes, singularities and poles](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/notes/zeroes-singularities-and-poles/)

### Lectures
- [Lecture - Complex Analysis MT23, I](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/lectures/i/)
- [Lecture - Complex Analysis MT23, II](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/lectures/ii/)
- [Lecture - Complex Analysis MT23, III](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/lectures/iii/)
- [Lecture - Complex Analysis MT23, IV](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/lectures/iv/)
- [Lecture - Complex Analysis MT23, V](https://ollybritton.com/notes/uni/part-a/mt23/complex-analysis/lectures/v/)
- ...started watching lecture videos, which may or may not have been a mistake...

### Problem Sheets
- ...continuing on from [Course - Metric Spaces MT23](https://ollybritton.com/notes/uni/part-a/mt23/metric-spaces/).
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/94000/mod_assign/introattachment/0/A2-2023-sheet4.pdf)
- [Sheet 5](https://courses.maths.ox.ac.uk/pluginfile.php/94001/mod_assign/introattachment/0/Sheet%205.pdf)
- [Sheet 6](https://courses.maths.ox.ac.uk/pluginfile.php/94002/mod_assign/introattachment/0/sheet%206.pdf)
- [Sheet 7](https://courses.maths.ox.ac.uk/pluginfile.php/94003/mod_assign/introattachment/0/sheet%207.pdf)
- [Sheet 8](https://courses.maths.ox.ac.uk/pluginfile.php/94004/mod_assign/introattachment/0/sheet%208.pdf)

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