Blog entries with tag “Maths”
Base conversion is the conversion between notations of number, and NOT the numbers themselves. I discuss a common mistake on methods of base conversion, and a common mistake in thinking about ‘base conversion’ in computer programs.
Lagrange’s four-square theorem is a beautiful result in number theory. However, to the best of my knowledge, I haven’t encountered it often in theoretical computer science. Today’s entry discusses two interesting stories related to this theorem.
Starting from the classic puzzles of finding patterns in a sequence, this entry explores the framework to define persuasive patterns. The framework is found to be quite self-contained in the sense that it is ‘asymptotically invariant’ to the choice of ‘language of expression’. The only short-coming of this framework is that it works only for computable sequences, yet the process of pattern discovery is incomputable.
In this entry, I discuss a pathological construction of general terms of a class of integer-valued sequences with the widely accepted concept of ‘elementary functions’. The idea here is to simply ‘concatenate’ the integers in a real number, then extract the appropriate digits for each term. It turns out that this definition characterises the elementariness very well (note that the definition is also self-referencing). The extended inspection leaves a problem open: Are all integer-valued sequences elementary? Update: The question is solved with an affirmative answer.
In this entry, I discuss a kind of widely posed exam problems for elementary calculus learners. It concerns a technique of application of (differential) mean value theorems. Speficially, a class of such problems can be solved dogmatically if the equation to prove resembles a ‘factorisable’ linear differential equation.
Let me explain the classic idea that ‘the algorithm of a crypto system should be considered and made public’ to you. Particularly, I will discuss what it means by ‘crypto system’, which tells us what information should be no secret at all.
A practical problem I encountered in 2016, which I insisted on implementing with pure CSS as long as it was possible. At first it was solved with mathematical logic tricks but later it turned out there was a much simpler solution.