Questions related to the teaching and learning of mathematics.

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9
votes
5answers
168 views

The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
8
votes
2answers
168 views

Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
7
votes
4answers
560 views

Learning math: still paper and pen

Is it, from an educational perspective, still sound advice to recommend people to use paper/a notebook (of the traditional sort, not the device) and pen/pencil? I wonder if computers are a ...
6
votes
2answers
79 views

Information on crucial results concealed as exercises or neglected in a textbook

First, where can students find lists, information, or resources on the crucial results, inequalities, theorems, etc... which a textbook might not explictly feature or even bring up at all? Second, ...
6
votes
3answers
590 views

How to fill gaps in my math knowledge?

Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge. As I think many people who explore math ...
5
votes
1answer
103 views

When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
5
votes
1answer
512 views

Quickest way to understand Kruskal's Tree Theorem

I came across the Kruskal Tree Theorem the other day and thought it looked pretty interesting (especially the stronger finite form due to Friedman). I'm currently a first year mathematics ...
5
votes
1answer
390 views

Is it ever really Pi Time?

Walking with my son at 3:14pm the other day, I mentioned to him, "Hey, it's Pi Time". My son knows 35 digits of $\pi$ (don't ask), and knows that it's transcendental. He replied, "is it exactly ...
3
votes
2answers
159 views

What's the right moment to learn Set Theory?

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra ...
3
votes
0answers
102 views

Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?

Let $x$ denote an arbitrary real number. Then $x^n$ makes sense for arbitrary $n \in \mathbb{N},$ via the obvious recursive definition. We can extend this definition by asserting that if $x$ is ...
3
votes
1answer
195 views

Functions that generate “easy” matrices of full rank

While explaining how to invert matrices I once used this ill-fated example $A=\begin{pmatrix} 1&2&3\\4&5&6 \\7&8&9 \end{pmatrix}$ which can not be inverted ($\det(A)=0$). That ...
3
votes
5answers
283 views

how to explain that Prob[heads, tails] = 2 * Prob[heads, heads] to a student?

I throw two coins (simultaneously). A student (very much a beginner in both math and probability theory) thought that the following 3 outcomes are equally likely: "two heads", "two tails", "a head and ...
2
votes
0answers
64 views

Looking for online matlab-based differential equations course/text.

I am looking for an online ODE course that would be matlab/project-oriented. A full online text/course in the spirit of this linear algebra text is preferred. I know about the following CODEE and ...
1
vote
2answers
69 views

Do users of RTL languages adopt an LTR standard for mathematics (in the same way they often do when using LTR words or phrases in RTL text)?

Non-mathematician here. There is a discussion on this forum titled "Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong?" I found it ...
1
vote
2answers
420 views

GRE Probability question

How many 3-digit positive integers are odd and do not contain the digit 5 ? My attempt: 100-999 3 -digit integers, 900/2=450 odd numbers. Now how to calculate odd numbers which do not contain digit 5 ...
0
votes
2answers
92 views

linear congruence questions

A: For the two systems of linear congruences, one system has integer solutions while the other does not. For the system with integer solutions, write down 2 of them whose difference is less than 192. ...
0
votes
5answers
930 views

Explain why perpendicular lines have negative reciprocal slopes

I am not sure how to explain this. I just know they have negative reciprocals because one one line will have a positive slope while the other negative.
0
votes
0answers
72 views

Are any authors experimenting with including (formally meaningless) aids to human understanding in their mathematical writing?

Are any authors experimenting with including (formally meaningless) aids to human understanding in their mathematical writing? For instance, there's at least five ways to understand a function, ...
0
votes
1answer
234 views

What are the prerequisite for understanding complex analysis?

Which should I complete first before complex analysis? I am following Visual Complex Analysis by Tristan Needham. Is there any easier book?
0
votes
1answer
77 views

How would I take multiple single bit binary numbers and convert it into a single binary array number?

So lets say I have these: 101010101001 Now lets also say I didn't count them you should count binary, lets say I counted that number at 6 because their are 6 1s and the 0s don't count. Now how would ...
0
votes
3answers
160 views

Looking for a simple problem for math demonstration

I'm holding a 3-5 minute speech next week on mathematical problem solving, and how it makes me happy, to 15-20 non-mathematicians. As a part of it, I had thought about demonstrating two problems, but ...
-3
votes
1answer
269 views

Proving By Subsets [closed]

I am currently trying to learn about conducting proofs by using subsets. In my textbook, there is an example on this very matter; however, the seem to do something that is in contradiction with what ...
-11
votes
1answer
119 views

1+2+3+4+… = -1/12 [duplicate]

I was browsing through Youtube and I saw this really cool thing.. but it seems really counter-intuitive could someone please explain to me why: 1+2+3+4+..... = -1/12? Here's the link to the guy's ...