Experience an Oxford University Math Class with Dr. Tom Crawford 📚

Real-life recording of a tutorial at the University of Oxford with mathematician Dr Tom Crawford. The lesson goes over a past exam paper as part of a revision tutorial covering the second year undergraduate Metric Spaces and Complex Analysis course.

The exam covered in the tutorial is from the second year undergraduate course in Metric Spaces and Complex Analysis. More information on the course can be found here: https://courses.maths.ox.ac.uk/course/view.php?id=1045

Students would be expected to answer 4 out of 6 questions in a 3-hour closed book exam at the end of the year. The course is consists of 32 hours of lectures and 8 hours of tutorials.

Topics covered in the video include: compact sets, continuous functions, complete metric spaces, Contraction Mapping Theorem, multifunctions, Cauchy-Riemann equations, complex logarithm, Weierstrass M-test, contour integrals, indentation lemma, Residue Theorem, Cauchy's Integral Formula, conformal maps, and stereographic projection.

For a question by question breakdown please see below.

Q2. Metric Spaces, Compact Sets, Contraction Mapping Theorem
Q3. Holomorphic Functions, Cauchy-Riemann Equations, Weierstrass M-test
Q4. Contour Integration, Residue Theorem, Laurent's Theorem
Q5. Cauchy Integral Formula
Q6. Stereographic Projection, Conformal Maps

Filmed at St Edmund Hall, University of Oxford.

Thanks to Luke and Will for taking part (both current second year undergraduate maths students).

Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow in Mathematics at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford

For more maths content check out Tom's website https://tomrocksmaths.com/

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