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Flashcards 2021-12-01 What is the Weierstrass substitution?? The substitution $t = \tan\frac{x}{2}$ used to evaluate integrals. What do you substitute for $\text{d}x$ in the Weierstrass substitution?? $$ \text{d}x = \frac{2}{1 + t^2} \text{d}t $$ Why is the Weierstrass substitution useful?? Because it turns complicated integration of trig functions into a rational function. What technique would you use for evaluating $$\int^{\pi/2}_{pi/3} \frac{1}{1 + \sin x - \cos x} \text{d}x$$?? The Weierstrass substitution. $$\int \csc (x) \text{d}x$$ Can you make the Weierstrass substitution?

Flashcards 2021-12-01 What do Kepler’s laws describe?? The motion of orbits. What is Kepler’s First Law?? All of the planets move in elliptical orbits with the sun at one focus. What is Kepler’s Second Law?? The radius vector sweeps out equal areas in equal times. What is the “radius vector” for Kepler’s Second Law?? The imaginary line between the sun and the planet. Which of Kepler’s laws does this show?? Kepler’s second law. What is Kepler’s Third Law?

This is a list of all the miscellaneous content on the site: [[Favourite Media]]B Last updated: 2021-11-29 Backlinks [[How to get around]]M Metadata date: 2021-11-30 07:54 tags: - '@?public' - '@?safe-to-post-online' - '@?misc' title: Miscellaneous

Advanced Problems in Mathematics is a series of books designed to help students work through STEP exam material. Like with [[UKMT Questions]]N and [[MAT Questions]]N, the idea is not to use flashcards to memorise the answers to questions but to help spot common patterns in order to help with problem solving. [[APM - Q2 - Finding a general result]]N Backlinks [[Misc Notes]]N Metadata date: 2021-11-30 07:44 tags: - '@?

[[MAT - Paper 2013 - Q1G]]N [[MAT - Paper 2011 - Q1I]]N [[MAT - Paper 2016 - Q2]]N [[MAT - Paper 2011 - Q1E]]N [[MAT - Paper 2015 - Q1J]]N [[MAT - Paper 2014 - Q5]]N [[MAT - Paper 2011 - Q1G]]N [[MAT - Paper 2011 - Q3]]N [[MAT - Paper 2013 - Q1C]]N [[MAT - Paper 2007 - Q1D]]N [[MAT - Paper 2018 - Q6]]N [[MAT - Paper 2019 - Q1F]]N [[MAT - Paper 2020 - Q2]]N [[MAT - Paper 2013 - Q1I]]N [[MAT - Paper 2018 - Q1B]]N [[MAT - Paper 2011 - Q5]]N [[MAT - Paper 2012 - Q1G]]N [[MAT - Paper 2016 - Q1H]]N [[MAT - Specimen Paper 1 - Q1H]]N [[MAT - Paper 2008 - Q1C]]N [[MAT - Paper 2017 - Q1I]]N [[MAT - Paper 2012 - Q3]]N [[MAT - Paper 2014 - Q3]]N [[MAT - Paper 2013 - Q1F]]N [[MAT - Paper 2018 - Q3]]N [[MAT - Paper 2010 - Q3]]N [[MAT - Paper 2018 - Q5]]N [[MAT - Paper 2016 - Q1I]]N [[MAT - Paper 2019 - Q2]]N [[MAT - Paper 2015 - Q2]]N [[MAT - Paper 2010 - Q6]]N [[MAT - Paper 2014 - Q1D]]N [[MAT - Paper 2012 - Q2]]N [[MAT - Paper 2008 - Q2]]N [[MAT - Paper 2019 - Q1H]]N [[MAT - Paper 2019 - Q3]]N [[MAT - Paper 2014 - Q1E]]N [[MAT - Paper 2018 - Q1J]]N [[MAT - Paper 2009 - Q5]]N [[MAT - Paper 2012 - Q1J]]N [[MAT - Paper 2009 - Q3]]N [[MAT - Paper 2014 - Q1J]]N [[MAT - Paper 2018 - Q2]]N [[MAT - Paper 2011 - Q1C]]N [[MAT - Paper 2013 - Q1H]]N [[MAT - Paper 2016 - Q5]]N [[MAT - Paper 2016 - Q3]]N [[MAT - Paper 2018 - Q1H]]N [[MAT - Paper 2012 - Q5]]N [[MAT - Paper 2017 - Q3]]N [[MAT - Paper 2017 - Q2]]N [[MAT - Paper 2010 - Q7]]N [[MAT - Paper 2018 - Q1G]]N [[MAT - Paper 2016 - Q1E]]N [[MAT - Paper 2018 - Q1F]]N [[MAT - Paper 2010 - Q5]]N [[MAT - Paper 2007 - Q1F]]N [[MAT - Paper 2011 - Q2]]N [[MAT - Paper 2015 - Q1B]]N [[MAT - Paper 2016 - Q6]]N Backlinks [[APM Questions]]N [[Misc Notes]]N Metadata date: 2021-11-29 12:01 tags: - '@?

[[UKMT Senior Maths Challenge - 2020 - Q14]]?? [[UKMT Senior Maths Challenge - 2019 - Q6]]?? [[UKMT Senior Maths Challenge - 2019 - Q16]]?? [[UKMT Senior Maths Challenge - 2019 - Q1]]?? [[UKMT Senior Maths Challenge - 2019 - Q14]]?? [[UKMT Senior Maths Challenge - 2019 - Q4]]?? Backlinks [[APM Questions]]N [[Misc Notes]]N Metadata date: 2021-11-29 11:56 tags: - '@?

These are miscellaneous notes I’ve made on things like textbooks, blog posts and mathematics. For book notes, see [[Book Notes]]N. Textbooks [[AI: A Modern Approach]]N Articles/Essays [[Article - Augmenting Long-term Memory]]N [[Article - Gwern LSD Microdosing RCT]]N [[100 Tips for a Better Life]]N [[Replacing Guilt]]N [[Meditations on Moloch]]N [[How can we develop transformative tools for thought?]]N [[Game Theory As A Dark Art]]N Mathematics For specific questions, I make notes in:

These are notes on books I’ve read, along with a rating and some extra random thoughts about them. Each one starts with a really stupid caveman explanation of the book, which I thought was funny a while ago but hurt to read a bit now. Notes on other things like textbooks, extra maths and articles can be found in [[Misc Notes]]N. Some of the notes contain flashcards, which are denoted by headings ending with two question marks, ?

These are my notes for studying Maths, Further Maths, Computing and Physics at A-level. These notes weren’t written with anyone else in mind, so if they do not make a whole lot of sense or seem strange you might be lacking the context that I had at the time of writing them. There’s also a lot of spelling mistakes (see the Further Maths ‘matricies’ topic for example). For a list of all the notes for each subject, see:

Man has existential crisis about who he is and what the mind is. Notes My notes aren’t great for the first two sections, as I hadn’t started highlighting. I. A Sense of Self Borges and I Borges and I, by Jorge Luis Borges Autobiographical essay about the conflict between the self and the persona. People think about themselves differently to how they act. Which is the true “you”, the one out there in the world or the one in your thoughts?

Flashcards 2021-11-26 How could you formulate the travelling salesperson problem in terms of Hamiltonian cycles?? Finding the shortest Hamiltonian cycle on a graph. For small graphs, how can you solve the travelling salesperson problem?? Try every Hamiltonian cycle. What is the nearest neighbour algorithm used for?? Finding a Hamiltonian cycle that can be used as an upper bound for the TSP. What are the 4 steps of the nearest neighbour algorithm?? Choose any start vertex Go to the nearest vertex that hasn’t been included Repeat 2 until all vertices have been included Return directly to the start vertex What would be the first step in using the nearest neighbour algorithm on this distance matrix?

Flashcards 2021-11-25 How would you write the probability that $B$ occurs, given that $A$ has already occurred?? $$ P(B|A) $$ What is true about $P(A|B)$ for independent events?? $$ P(A|B) = P(A|B') = P(A) $$ How would you calculate $P(A | B)$?? $$ \frac{0.15}{0.15 + 0.25} $$ How would you calculate $P(A | A \cup B)$?? $$ \frac{0.15}{0.4 + 0.15 + 0.25} $$ How would you calculate $P(A' | B')$?? $$ \frac{0.2}{1-0.15-0.25} $$ Why do you have to be careful dealing with conditional probabilities involving things like “given $B'$”?