Why is calculus, and in particular, integral calculus, the foundation for the study of physics? In other words, why did Sir Isaac Newton develop the calculus? Why aren't math students made to memorize a definite integral table? How does music relate to math?
Why is associativity and commutativity important? Explain why are variables useful in algebra. Why does modulo not affect multiplication? why are the solutions on calculus for business economics, edition 12, barnett, gone? Why is it poor practice to divide both sides of an equation by a variable...
This post is a little bit niche, given that it’s addressed to people who may have seen the DeepMind x UCL Lecture Series on Reinforcement Learning and were wondering how the answers to the end-of-lecture questions were worked out. It took me a fair while to figure them out myself; it...
The rigorous part of limits is figuring out which functions behave well enough that simple yet accurate models can be made. Fortunately, most of the natural functions in the world (x, x2, sin, ex) behave nicely andcanbe modeled with calculus. Limits Or Infinitesimals? Logically, both approac...
“Let us agree, for the sake of convenience and epistemological honesty, that it is axiomatic (a useful definition and not a theorem) that 0º ≡ 1” *If I am interpreting you correctly*, then we may have something we can actually agree on. I agree that, for most of the situations...
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 ...
We start with an additive group, discover a ring structure, and in case we get an integral domain, our ring allows a quotient field. Now, zero is a zero divisor, hence outside the set of elements we can construct quotients for; at least not by the usual method ...
Writing out the logical form of a local conservation law in terms of quantifiers is useful because it helps to illustrate a form of robustness, in contrast to the catastrophe that Bunge fears. One knows that the negation of a conjunction is the disjunction of negations:\( \lnot (A \& B...
“I hope and believe that the above approaches will prove useful for explaining the magnetic properties of atoms and molecules and also for explaining the flow of electricity in solid bodies. There is undoubtedly a certain degree of difficulty in using a complex wave function at the moment. If...
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...