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


Aug
4
comment How to Garner Mathematical Intuition
Saying this isn't well defined seems odd to me. How you go about finding proofs is also a personal matter, but no one has a problem with Polya. It's absurd to say that there aren't general guidelines and ways to think about problems that lead to better intuition. This is vitally important for math education; dismissing the idea of teaching it because it isn't well-defined is precisely the problem in the first place. Can we take a more productive approach?
Aug
3
comment I can't get satisfied with such 'so on' type logic. Is there a better way to solve it?
It is rigorous though, at least with a couple extra steps. All you have to do is show there will always be another point available to choose. Or you might be a finitist, in which case may god have mercy on your soul ;)
Aug
2
answered Guess the functional form of a graph
Aug
2
comment Areas of math that can be “gamified”?
I'm familiar with material on game design; I spent a lot of time on it in highschool and it is my real priority. A lot of my ideas in the direction of "uncover things they're intrigued about" (robotics, biology, crowd dynamics, Escher, music, fractals, social choice, etc.) would probably be used for a presentation or project instead. While I 100% agree with the perspective you're describing, my issue is mainly about finding which areas games are ideal for. I consider 'game Euclid' superior to 'presentation Euclid', and am looking for other examples in this vein.
Aug
2
asked Areas of math that can be “gamified”?
Jul
31
answered What's the importance of the trig angle formulas?
Jul
31
answered A geometric property of the graph of $y = x^2$
Jul
31
comment Why are topological spaces interesting to study?
Have you studied things like algebraic topology and cohomology yet? There are cases where you want to study things that are only dependent on how the space is connected. Even though a metric may still exist, dragging it along when it isn't "respected" by anything you're doing would only make things more difficult. Topology cleanly isolates the important features in such problems. In particular, I take some issue with point 3: the metric isn't automatically useful or relevant just because it's there.
Jul
24
comment Calculus over $\mathbb{Q}$
@RGB Wow, I've been using Cauchy sequences for a long time and that never really clicked before for some reason. I worry though that this simply means that I've asked my question poorly. While saying "point 1 is equivalent to calculus in $\mathbb{R}$" is certainly very enlightening, it somewhat serves to reinforce the point that mathematical calculus depends on $\mathbb{R}$ (more aggressively than I thought!) while "real-world calculus" functionally does not. It is this apparent gap that I really wanted to get into.
Jul
24
asked Calculus over $\mathbb{Q}$
Jul
22
comment Some theorems in euclidean geometry have incomplete proofs
@ReekMaths if the written words talk about $A,B,C,P,Q$ but only do so in abstract, without making reference to this particular diagram, then the diagram is not being used in the proof. If it says "$|CP|/|CA|=|CQ|/|CB|$, that is not using the diagram. It doesn't depend on how $P$ and $Q$ were drawn, but solely on their formal definitions.
Jul
22
comment Do groups, rings and fields have practical applications in CS? If so, what are some?
can we not do the whole "I don't need real life (sneer) applications" routine? Good for you if you don't need them, but the applications to other academic fields have always been a huge source of inspiration for mathematics and play a large part in making it so wonderfully rich. Acting like "I don't need them" $\implies$ "we should all ignore them" is just as ignorant as the reverse view.
Jul
19
answered What calculation shortcuts exist to help or speed-up mental (or paper) calculations?
Jul
19
answered The negation of a limit condition, Spivak style.
Jul
18
comment If $A+B+C+D+E = 540^\circ$ what is $\min (\cos A+\cos B+\cos C+\cos D+\cos E)$?
Are the less than and greater than inclusive? I.e., can some of the angles actually be $180^\circ$?
Jul
17
comment Is it possible to pass functions into other functions in maths?
@user18921 Other than general research into functional programming I'm not sure. I've just stumbled into/grown to realize the connection over time; I don't know the formal name for the concept. Hopefully someone who knows more can chime in.
Jul
17
answered Is it possible to pass functions into other functions in maths?
Jul
17
comment Passage not understood in a Physics formula
From a physics point of view, that is what they're doing. They're treating it like a genuine fraction and using $(a\vec{b})\cdot\vec{c}=\vec{b}\cdot(a\vec{c})$. You could justify it by setting up the Reimann sum and taking the limit in different ways, but someone probably knows a slicker method.
Jul
12
comment Why is that interior points exist only inside intervals on $\mathbb{R}$?
@GustavoBandeira If I had to hazard a guess, I'd say that your question can be read as asking if subsets of $Q$ can have interior points when taking your overall space as $Q$, while this answer depends on having your space as $R$. Which did you mean?
Jul
12
comment Examples of homeomorphisms between the real numbers and the positive real numbers?
@jkn can you include that in the question then? Looking for examples that work well with that application seems like a much more reasonabe scope.