All Questions
3,355 questions
-1 votes
0 answers
67 views
Would there be purpose of goal of setting equations? [closed]
If there is a equation denoted like so, $${\displaystyle x^{5}-3x+1=0}$$ Negelecting the meaning of this equation or solving it, would there be historical background equations were adopted or could ...
- 19
16 votes
3 answers
2k views
What's the easiest way to help a high schooler understand how to avoid the trap of extraneous and missing solutions?
There are many traps that involve inequalities and equations that I feel like I have internalized by myself, but my high school son really struggles to understand. Is there some simple rules that can ...
- 1,916
0 votes
1 answer
164 views
Polynomial GCD convention for over $\Bbb Z$ vs. over $\Bbb Q$
This year, I have been assigned to teach a very particular second-year class of 14/15-year-old students, of an high secondary school. In an entrance test, when you want to calculate the $\operatorname{...
- 8,896
7 votes
0 answers
102 views
Teaching a differential equations course to Physics majors
Next semester (over a 6-month period), I will be teaching the course “MAT203: Linear Algebra and Ordinary Differential Equations” for physics majors (they already have some basics in linear algebra). ...
- 2,750
-1 votes
2 answers
179 views
Prove $0.6\dot{1}\dot{2} = \frac{101}{165}$ [closed]
For those who wants a bit background, this is a proof question for international GCSE paper, for students aged 14-16. This is what the candidate has written. Obviously, it is NOT the usual method we ...
- 274
2 votes
1 answer
61 views
De Finetti diagram applied to random based genetic phenomena - projections and geometry
I am preparing a class that studies De Finetti diagrams, in the context of random based genetic phenomena. The below De Finetti diagram shows genotypes frequencies ($p(AA), p(aa)$ and $p(Aa)$) and ...
- 1,369
0 votes
2 answers
92 views
Distinguishing between the two definitions of "quotient" in arithmetic [closed]
I am trying to explain to an 8-year-old girl the difference between two versions of division in arithmetic. For example, \begin{equation*} \frac{11}{4} = 2.75 \end{equation*} and we say that $2.75$ is ...
- 111
5 votes
0 answers
192 views
Mathematics courses by Tom Lehrer [closed]
The (now late) Tom Lehrer was well known to be trained as a mathematician. As also well known and explained on his wikipedia page and all his obituaries, he taught mathematics throughout his life in ...
- 187
4 votes
0 answers
240 views
What should I do if I can't do many exercises when self studying?
I'm currently self-studying functional analysis. My general approach is to read each chapter, make sure I understand all the definitions, and carefully follow every proof. I usually manage this part ...
- 969
25 votes
13 answers
3k views
Simple rules that generate complexity
I'm planning a low-level classroom presentation on the theme of "simple rules that generate complexity". Any ideas? The one I already have is Pascal's triangle mod 2 (i.e., with entries in $\...
0 votes
0 answers
96 views
How many distinct odd numbers $abcdefghi$ made from $1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9$, such that $d+e+f=10$?
How many distinct odd numbers $abcdefghi$ made from $1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9$, such that $d+e+f=10$? Note that $abcdefghi$ each letter represents a digit, not as a multiplication of ...
- 2,491
1 vote
2 answers
245 views
A structured map of mathematics? [closed]
This question is a bit of a deviation from the usual questions on MSE. It's a question about mathematics itself. In my understanding, the way most of us learn mathematics under the traditional ...
- 312
0 votes
1 answer
117 views
Distributing brackets when working with factorials
I've recently been asked why $$(n-r)!\ne (n-r)\Big(n-[r-1]\Big)!=(n-r)\Big(n-r+1\Big)!\tag{a}$$ I gave a simple example to show $(\mathrm{a})$ for the case that $n=5, r=3$; The LHS of $(\mathrm{a})$ ...
- 561
0 votes
1 answer
75 views
Optimal Worker Allocation Problem: Minimizing Completion Time with Unidirectional Movement and Unknown Worker Speeds
Hello fellow mathematics enthusiasts, As a university student, I've been exploring an optimization problem with potential applications in manufacturing and workflow management: Consider a workflow ...
5 votes
0 answers
103 views
A pedagogical proof of Schur's lemma in the infinite-dimensional case?
PRELIMINARIES. Let $H$ be a complex Hilbert space. Denote $B(H)$ the space of bounded operators of $H$ into itself and $GL(H)$ the group of invertible elements of $B(H)$. We say that $H$ is a ...
- 34.9k