Posts

Harry Potter is a wizard. Pretty good! Had been meaning to read for a while. Backlinks [[Harry Potter and the Chamber of Secrets]]N [[Book Notes]]N Metadata date: 2022-01-17 19:27 finished: true rating: 7 tags: - '@?book' - '@?public' - '@?safe-to-post-online' title: Harry Potter and the Philosopher's Stone

See also: [[My Experience with the Online Imperial Admissions Process]]B . I’m writing this post because I had a lot of questions about the specifics of the Oxford online interview and admissions process, but didn’t really find much super-concrete information. For some context, I made my UCAS application on October 11th 2021 to the following universities: Oxford, Mathematics and Computer Science Imperial, Mathematics and Computer Science UCL, Mathematics and Computer Science Southampton, Computer Science with Artificial Intelligence Bristol, Mathematics and Computer Science I have now received an A*AA offer from Oxford, which I’m really happy about.

Like Superman, but from a more rational Lex Luthor’s perspective. This was pretty good! It’s free to read online, listen to as a podcast or download an EPUB version (which is what I did). I read this after being recommended it on the [[Bit of a Tangent]]?? podcast, specifically episode 22 and the story is about Lex Luthor trying to grapple with Superman, who he considers an existential risk. Backlinks [[Book Notes]]N Metadata date: 2022-01-08 15:52 finished: true rating: 7 tags: - '@?

. Thoughts? Some of this reads like a “get rich quick” book page 126 Notes What is Optionality?? Optionality = the right, but not the obligation to take action. Optionality lets you explore freely, you have agency. From this definition, it seems pretty similar to the idea of slack which is defined by Zvi Mowshowitz as “the absence of binding constraints on behaviour”. Optionality lets you explore freely. Good options have an asymmetry between the cost and the potential benefit.

See Also [[Maths - Numerical Methods]]S Try out an interactive visualisation of Euler’s method here: Euler’s method. Flashcards 2021-12-08 How could you summarise Euler’s method for solving first-order differential equations?? Start with some point on the curve and then follow the direction of the curve. If a gradient is given by $\frac{\text{d}y}{\text{d}x}$, how much would you increase the $y$-coordinate for a step size of $h$?? $$ y_1 = y_0 + \frac{\text{d}y}{\text{d}x} h $$

Flashcards 2021-12-08 What is gravitational potential?? The energy transferred per unit mass to move an object from infinity to a point. What is the gravitational potential at infinity?? $$ 0\text{J}\text{kg}^{-1} $$ Why is gravitational potential always negative?? Because you’re having to do the opposite of what gravity wants you to do. What is gravitational potential energy?? The energy transferred to move an object from infinity to a point. What does the graph of $V$ against $r$ look like for gravitational potential?

This a list of my projects, i.e. things I’ve spent time working on in the past. They’re loosely sorted by how exciting I think they are. For the most part, all of the code is available on my GitHub and my GitLab. On projects that you can try out right now in the browser, you can either click the link in the text or just click on the image. aqa++ go-albatross sergeant eulers 3d-noughts-and-crosses cal8 life gofu** go-lmc stacked timetable Works in Progress human-synthesizer map epq Older Projects punk function-mirror genetic-tea store-destruct genocides zombies corporate-jargon-generator midi-to-sonic-pi bad-video-calculator CodePen Quite Boring jump jbook spotify-song-cleaner aqa++

Flashcards 2021-12-06 What speed must a satellite be going at to orbit a planet at radius $r$?? $$ \sqrt{\frac{GM}{r}} $$ What three things must be true for a geostationary satellite?? It must be in an orbit above the Earth’s equator. It must rotate in the same direction as the Earth’s rotation. It must have an orbital period of 24 hours. What is true about a polar orbit?? It passes over a planet’s poles.

These are a few blog posts that I hope people might find interesting. A lot of them are a work in progress, or don’t exist at all. For brief explanations of things I’ve worked on in the past, see [[Projects]]B . Blog posts with a “⚠️” are either a work in progress, and posts with a “✍️” haven’t even been started yet. 2022 Jan: [[A Dangerous Way of Taking Derivatives]]B Feb: [[Can you ever draw in 3D noughts and crosses?

See Also [[Further Maths - L'Hôpital's Rule]]S [[Further Maths - Taylor Series]]S Flashcards 2021-12-05 How would you rewrite $$\lim_{x \to \infty} \frac{2-3x}{1+x}$$ in order to evaluate it without L’Hôpital’s rule?? $$ \frac{\lim_{x \to \infty} 2 - 3x}{\lim_{x \to \infty} 1 + x} $$ How could you evaluate $$\lim_{x \to \pi/2} (x-\frac{\pi}{2})\tan x$$ using a Taylor series?? Approximate $\cot x$ around $\pi/2$ What must you make sure to do when evaluating a limit with a Taylor series?

Flashcards 2021-12-05 In what form can you express $a\sin x \pm b\cos x$?? $$ R\sin(x \pm \alpha) $$ In what form can you express $a\cos x \pm b\sin x$?? $$ R\cos(x \mp \alpha) $$ You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $R$?? $$ R = \sqrt{a^2 + b^2} $$ You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $\alpha$?

See Also [[Further Maths - Maclaurin Series]]S [[Further Maths - Limits]]S Flashcards 2021-12-01 What is the Maclaurin series a special case of?? The Taylor series. What is the formula for the Taylor series about $x = a$?? $$ f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + … $$ When is the Taylor series valid for $x = a$?? When $f^{(n)}(a)$ exists and is finite for all natural numbers and for values of $x$ for which the infinite series converges.