Watch a Real Oxford University Lesson || Undergraduate Maths Tutorial

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.

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).

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

Get your Tom Rocks Maths merchandise here:

[curtisgoldthorpe]

i love this guy so much. I can just imagine him in a emo-club or concert and get's asked "what do you do?" and he's like "Im a math lecturer for oxford uni" and then the awkward silence like, is this guy serious?

truly the chad emo nerd we all need in our lives.

[willosborne]

Thanks so much again for having me on! Really appreciate all of Tom's help this year. It turned out that lots of concepts from this session came up in our actual exam, so I think it was one of my better papers! -Will

[RCSmiths]

I love the transparency to how you guys articulate math. Education, knowledge, and the applications of that knowledge is so important. Cheers guys

[Bengolstar]

Man this channel is fantastic, really! As a med student I’ve lost my love for maths but this channel has brought it back for me!! Thank you so much man! Please keep up this type of content it really is one of a kind !

[Mystery_Biscuits]

Man I miss complex analysis. That whole area of maths I really enjoyed in my degree. Especially the course I took on integral transform methods. Learning that I could apply contour integration to find inverse Laplace transforms of arbitrary functions instead of having to rely on a lookup table was a really cool thing to learn.

[arrjay]

This is a great perspective on how lessons are taught and most importantly how complex problems are broken down to get to the outcome

[Roadtoplat]

So exited love Toms teaching style and personality, to quote the late and great Tina turner he’s “simply the best”.

[judahsharonb]

You are the best math tutor I have ever seen. You just make the subject more interesting. Watching your videos motivates me to delve deeper into the subject. You truly rock math!!! Keep going. I really hope to make my way into Oxford's too...to learn from great teachers like you. And on an informal and personal note, your tattoos and hairstyle are just amazing. -Lots of love from a grade 12 student..:) Thanks a lot Tom

[markburton]

I studied some of this recently as part of my open university maths degree. Very interesting video

[GaborRevesz_kittenhuffer]

2:10 2(b)(i)... nice counterexample! ...but! with f(x)=x+1/x you cannot simply let X = [ε, ∞) for arbitrarily small ε>0, because for x, y inside (0, 1/√2) you won't satisfy d(f(x), f(y)) < d(x, y). you can quickly see this if you sketch a graph of f. wherever |f'|>1 two sufficiently close points will get dilated (un-contacted) under f. so you did well by choosing X = [1, ∞).

[adayah]

In 3(a) instead of solving the system of equations for (ux, vx) you could notice that its determinant equals u^2 + v^2 which is non-zero. The pair (vy, -ux) also satisfies this system (because of the other pair of equations), so (ux, vx) = (vy, -ux) because the solution to such a system is unique.

As a side note, although implicit differentiation allows to elegantly avoid tedious computations, it creates a little gap in the solution - you never proved that u and v are differentiable w.r.t. x and y.

[bumblebee]

I remember studying maths at GCSE level and that was hard. I would often leave the classroom with black ink and highlighter on my forehead.

[thomasmuntzer]

is there a tutor for every two students? no wonder people do so good there.

[muhammadharoon]

Even though I am done with AS( Advanced subsidiary) level but still I don’t even understand a thing in this video. Btw, sir really enjoying your videos.

[spacetime]

I found seeing 3 different personalities in the students interesting tbh, to how 3 different people express understanding or mathematical thinking is interesting.

[JamesJoyce]

I was hoping one of them was going to say "dam - I prepped Jane Eyre - this isn't English?"

[minyare]

My dream is to study mmath at Oxford uni 🇬🇧🤲 and this video motivated me thank u so much xx

[bobovv]

That was great. Good luck in the exams guys. If you do another such video, maybe a slightly less complicated topic would have broader appeal...something from 1st semester 2nd year perhaps.

[ribaldc]

Tutorial Oxforf: one teacher, 2 Students. Tutorial german university (Albertus Magnus University Cologne): one Teacher 20 and more students It's a little different, i think.

[justin]

Studying at Oxford University is every nerd's dream.