Explain when a set is convex and why it is useful for motion planning. Why the least-square natural choice for linear regression? Why does 2ln(2) = ln(4)? How to prove if a polytope is bounded? Why does x^{x} have a minimum at \frac{1}{e}?
Currently, students are increasingly related to technology. In the case of mathematics, calculators are one of the tools of great importance and help. In addition, its use helps us to solve problems faster. Answer and Explanation: Why is it ...
Haskell is a statically typed language: all type checks happen at compile time. Static typing has the advantage that type errors don't happen at runtime. This is especially useful if a function signature is changed and this change affects many dependent parts of a project: the compiler will ...
Agreed, this reason is weak: clearly, the onus is on the interactionist to argue that they could be small, and indeed are likely to be small. But the second reason is more interesting, and returns us to the danger of assuming that physics is cumulative. Namely, the principle of the cons...
This famous dilemma about “being zero sometimes, and non-zero others” is a famous critique of calculus. It was mostly ignored since the results worked out, but in the 1800s limits were introduced to really resolve the dilemma. We learn limits today, but without understanding the nature of...
bit of calculus, which is fun. And then the full 2D question (which can be answered using some calculus, but I think it’s even more beautiful without it): if you have two random numbers between 0 and 1, what is the probability that the first non-zero digit of their ratio is a 1...
When Newton and Leibniz performed their differential calculus with “fluxions” or “monads”, they used infinitesimal numbers, and Euler and Cauchy also found them useful. Nevertheless, these numbers were viewed skeptically from the beginning. As analysis was put on a rigorous basis by the introduc...
Integration by parts is a method used in calculus to find the integral of a product of two functions. It is useful in cases where direct integration or substitution may not work, as it allows for the integration of a more complex function by breaking it down into simpler parts. ...
A large part of the polarisation here comes from the fact that many universities still teach functional programming as just an implementation of lambda calculus; therefore, if you're not interested in mathematics, functional programming is of little use to you. Having said that, universities are ...
Describe an invention which is very useful in your daily life. You should say: What it is What you use it for Is it easy to use And explain why it is very useful in your daily life. Part3 Are there inventions that have changed the world? What are the qualities of a scientist? Do...