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IB Maths Tripos

0.74MB. 0 audio & 954 images. Updated 2019-05-31.
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Decks for the IB Maths Tripos: All courses except Electromagnetism, Fluids and Optimisation Made by Neel Nanda. If you find this useful, I'd love to hear about it! And please message me with any errata. Disclaimer: These were entirely written to make sense to me, and according to how I think about maths. I hope they're useful! But some proportion are unlikely to make much sense to other people. To use these, there are Android (free), iOS (paid) apps, or you can download desktop software here https://apps.ankiweb.net/, you can't add shared decks directly through the website Categorised into subdecks by course, and into different note types: Define is definitions Recall is formulae/equation/fact recall Prove is bookwork, stating & proving theorems Archetype is the algorithm for a typical exam question Intuition is a mix of tricks, useful mindsets and high level understanding (note:[name of category] should sort for those) In descending order of how useful I expect them to be as flash cards and ascending order of how interesting I expect it to be to see another perspective on the course! Make a filtered deck if you want to do all the courses in a random order Complex Analysis v Methods was a bit of a fudge, if you're doing just one course sort by tag:CA or tag:CM (will be a bit of irrelevant stuff in methods)

Sample (from 578 notes)

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Question How to solve DEs with Laplace transforms? (ODEs vs PDEs, how to use bcs?)
Back Transform wrt one variable, gets out an eqn if ODE, an ODE if PDE, each easy to solve.Bcs hopefully fall out of transform, if not then use the limit tricks to use them to constrain form of solution
Extra Note that the reason this works is that we're converting to an eigenbasis, and in an eigenbasis each component is independent, we can consider each independently
Tags CM
Definition Connected Component
Back Largest connected superset of a point x, ie union of all connected sets containing x. NOTE: Unrelated to closed and open with regards to the entire space, only care about connectedness of the subset, eg [$][0,1)[/$] would be included
Extra Subtlety, to show it works must show that it's non empty because {x} works
Tags MTS
Question How to solve Laplace on the disk?
Back 1. Use FS to get bcs as [$]f(\theta)=\sum f_n e^{in\theta}[/$]2. [$]\phi(z, \bar z)=f_0+\sum (f_n z^n+f_{-n} \bar z^n)[/$]
Extra [$]z,\bar z[/$] is a natural change of variables because Laplacian becomes nice
Tags Methods

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on 1564343150
Good for me to learn about courses i did not go to
on 1559165828
\forall \epsilon, | Neeliness - Cleanliness | < \epsilon

I don't think decks like this can be used "as is", though they certainly make a great base when creating your own deck.
on 1558374483
Neel = god