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Engineering student at McMaster university who wants to learn math properly.


Mar
18
comment Application of Composition of Functions: Real world examples?
A function is just a process that turns one thing into another thing. Anytime you're describing something that chains processes together one after the other you're composing functions. You find a probability distribution and then want to find its average. Find a particle's position as a function of time, and then its distance from its start point. Almost any time you want to do multiple things to a function you're composing it with other functions.
Mar
5
awarded  calculus
Feb
12
comment What are the practical applications of the Taylor Series?
@Ruslan you can use the symmetries and periodicity of $\sin(x)$ to restrict your calculation to $[0,\pi/2]$. It's this range that has the maximum error of $8\%$.
Feb
1
comment Are there any other purposes for variables in math other than functions?
@tazheneryduck0 No, that doesn't make any sense. If you divide by $x$ you need to know that any results you get are only okay if $x\neq 0$, because otherwise the division wasn't allowed. But you can definitely divide by variables to find solutions to equations, it's used all the time. Your teacher seems to be confused. If $x$ is a root then $f(x)$ is what ends up being zero. That doesn't prevent you from dividing by $x$ at all.
Jan
31
answered Are there any other purposes for variables in math other than functions?
Jan
28
comment Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?
While I don't have a full answer, I would like to point out that associativity is what allows you to move your focus around when solving equations. Commutative but non-associative operations only let you switch two things around, not several in a row, so you barely gain any freedom. Associativity without commutativity is much less restricting. Also function composition is associative, (regardless of formalism; any sensible definition would be) so any algebra that can be interpreted as a collection of transformations (which is a large number of them) has to be associative.
Dec
8
awarded  Nice Answer
Dec
3
comment Explaining probability theory versus statistics
Doesn't this assume that you can't take a Bayesian approach to statistics?
Nov
30
answered Nullspace that spans $\mathbb{R}^n$?
Nov
26
comment Proof that imaginary numbers exist?
Do you mean "exist" as in "part of the 'real world'"? Or do you mean "how do you prove that you can consistently add square roots of negative numbers in a logically consistent way"?
Nov
18
revised Parametric form of a plane
deleted 3 characters in body
Nov
18
comment Parametric form of a plane
@AndyG Yes, it seems it should be. I'll update, thanks
Nov
13
awarded  Nice Question
Nov
5
comment Is math built on assumptions?
I really don't get this student's complaint, or your confusion with it. Why does "assume $x=5$" count as something more important than assumptions in any other hypothetical story? "assume we have a child in a red cape walking to grandma's house" is doing the exact same thing. It's not an assumption about one reality, but one needed to set up the story we want to tell.
Oct
23
comment Why do we consider tangent spaces and what not, when we can just use Whiteney's Embedding Theorem and do calculus in $\mathbb{R^{2m}}$?
While I suppose this is more a personal preference, working with things like tangent vector fields in $\mathbb{R}^3$ and lugging dot products etc. everywhere is more tiresome than working with an intrinsic metric. I'd imagine that situation only gets worse in the general case.
Oct
3
comment Riddle: 1 question to know if the number is 1, 2 or 3
@JohnP couldn't it be easily altered? I.e. "Is the sum of your number and a number uniformly chosen from $\{0,1\}$ greater than 2?"
Sep
21
awarded  Nice Question
Sep
10
comment mathematics behind the derivation of Lorentz transformations
@Galoisfan I said that it preserves vector operations. These are precisely the linear transformations. I suppose if you interpret 'vector operations' in a freer way then you can include affine transformations, but the question asks about the Lorentz group and not the Poincare group, so I left this out. Affine maps are simply linear map+translation anyway, so that's trivial.
Sep
9
answered mathematics behind the derivation of Lorentz transformations
Sep
6
comment Where to start?
1. What level of math have you formally studied, whether or not you feel you remember it? 2. You clearly have no issues forgetting how to add, I assume. What's the earliest point that you have trouble remembering properly?