For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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3
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2answers
150 views

Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
28
votes
6answers
2k views

Cool mathematics I can show to calculus students.

I am a TA for theoretical linear algebra and calculus course this semester. This is an advanced course for strong freshmen. Every discussion section I am trying to show my students (give them as a ...
3
votes
5answers
415 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
2
votes
1answer
137 views

What does one need to teach Mathematics in American schools with a BSc Mathematics degree?

I'm graduating with a math degree next year (BSc Maths - more theoretical than applied) from an African university, and am going to the US next year to visit a friend for a few months. However, I'd ...
4
votes
1answer
352 views

Workshop on Pascal's Triangle for Middle School Students

We're going to hold a three-hour math workshop for some middle school students. It'll about the Pascal's triangle. Well, we can ask the students to find patterns in the triangle, or try to prove some ...
5
votes
6answers
420 views

“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
2
votes
0answers
132 views

Variation on the Sobolev space $H^1_0$

Let $\Omega\subset\mathbb{R}^n$ be a bounded open set, let $$ C^1_0(\overline\Omega) = \{u\in C^1(\Omega)\cap C(\overline\Omega):u|_{\partial\Omega}=0\}, $$ and let $C^1_c(\Omega)$ be the space of ...
9
votes
1answer
401 views

Where can I find the 1960s New Math syllabus?

I've been looking everywhere for even a short summary of the content of the 1960s New Mathematics Math education reform in the US but I cannot ;-; Does anyone know?
0
votes
1answer
149 views

Lattice Squares; Basic Interesting Facts and Problems

I'm going to write an article in an educational magazine for middle school students, about the game Square It. The purpose of the game is to make lattice squares: I want to introduce the game, and ...
9
votes
3answers
2k views

how to explain prime numbers to children

My little cousin (12year) asked me about how emails are encrypted and I want to answers her in such a way she understands it. This is diffuct, but I am happy with teaching the definition of a prime ...
1
vote
3answers
969 views

A round table probability question

Hi guys I am writing my P exam for the second time and I remembered two question that confused me when writing the exam. I asked my prof. but it confused him as well. For simplicity I will ask one ...
0
votes
2answers
111 views

Finding the variance of x,y by discrete distribution

I am writing my P exam for actuaries. I have the solution manual but I ran into this question, which confused me. I understood the solution but it did differently in how I wouldve tackled the problem. ...
88
votes
23answers
7k views

Why is there no “remainder” in multiplication

With division, you can have a remainder (such as $5/2=2$ remainder $1$). Now my six year old son has asked me "Why is there no remainder with multiplication"? The obvious answer is "because it ...
3
votes
2answers
875 views

What is the distance between the line and plane if it is parallel?

So far, I've gotten that the line is parallel to the plane $x = 2 + t$, $y = -3 + 2t$, $z = 1 + 4t$ With the vector of that being $U$ is $(1,2,4)$ and the plane $2y-z = 1$ with the vector $V$ being ...
4
votes
2answers
163 views

Can abstract nonsense be helpful here?

Here a question for those among you, who teach Homotopics/Algebraic Topology at university. I encountered some questions that were in my view quite easier to solve in category hTop instead of Top ...
12
votes
6answers
1k views

Am I just bad at math? [closed]

I currently pursuing a degree in computer science. When I started back 4 years ago, I took a test to see how I would place into certain subjects. My math scores were absolutely horrible. I started ...
0
votes
1answer
221 views

teaching inverse functions using ideas of codomain and onto functions

I am looking for some resources (books, Web sites, etc.) for teaching calculus students about inverse functions, using the ideas of codomain and onto functions (as well as one-to-one functions, of ...
3
votes
1answer
57 views

Proofs as games?

A long time ago (but I can't remember when), I was introduced to the (pedagogical) concept of writing a proof as giving a winning strategy for a game. Basically, given a statement $\forall x\exists y ...
23
votes
11answers
2k views

Puzzles or short exercises illustrating mathematical problem solving to freshman students

At high school, the solution method to almost all mathematical exercises is to apply some technique or algorithm you have learned before. At the university, the situation is fundamentally different. ...
3
votes
5answers
141 views

Motivation for Studying Combinatorics (Middle School Version!)

I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real ...
3
votes
0answers
118 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 ...
2
votes
1answer
42 views

Identify the derivative of a distribution

When someone wants to identify the derivative of a distribution $T\in \mathcal{D}'(\mathbb{R})$, we usually write, for $\varphi\in\mathcal{D}(\mathbb{R})$ , $$<T',\varphi> = -<T,\varphi'> ...
7
votes
4answers
388 views

A Handwaving Proof of a Specific Existence and Uniqueness Theorem

My problem is as follows: Given the second order homogeneous linear differential equation with constant coefficients $$a\frac{d^2y}{dx^2}+b\frac{dy}{dx}+c\,y(x)=0,$$ is there a good heuristic ...
0
votes
1answer
124 views

Combinatorial Game Theory Prerequisites

I am planning to self-study Combinatorial Game Theory. I have gathered some useful references from here. Reference for combinatorial game theory. I plan to make a study about a local combinatorial ...
1
vote
1answer
84 views

Finding dimensions of functions

Hey guys I need help showing if a function is a vector space or not. I believe we show is addition and multipication holds. but I don't know. Also how do I find out dimensions of such functions. The ...
1
vote
2answers
109 views

Explanation of math statement

This symbols are used to describe left recursion : $A\to B\,\alpha\,|\,C$$B\to A\,\beta\,|\,D,$ It is taken from : http://en.wikipedia.org/wiki/Left_recursion How can these symbols be ...
4
votes
0answers
177 views

What is tensor, really?

How can one understands the definition of tensor from the purely formal point of view? To what abstract structure this concept can be generalized?
0
votes
1answer
45 views

Solving a partial differential equation help

this is my differential equation course. I got back into school after a couple of years. This is just the start of this course and I am having difficulties in one of these practice problems. This is ...
2
votes
0answers
133 views

Is my general approach to proofs acceptable? A general topology example.

Proving: $A$ is closed iff $A = \bar{A}$. "To the right": If $A$ is closed, $ A = \bar A$ If $A$ is closed this means that it contains all of its own accumulation points. And we would find that its ...
4
votes
3answers
156 views

abstract algebra example book

It's very exciting when you can use the theory to solve "lower level" problems. For example, I'm looking forward to understanding why the quintic equation is not solvable. In the undergraduate ...
1
vote
0answers
35 views

The role of a uniqueness theorem for IVPs in a lower-division ODEs class

Please tell me your thoughts about this, and if you agree or disagree. I'll describe my current viewpoint, which is subject to change. Note that I've never taught a lower-division ODEs course. It ...
4
votes
2answers
195 views

What is the most motivating way to introduce modular arithmetic?

What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?
0
votes
1answer
75 views

Rates of Change Question with Mixed Units

I have come across the following question in a past exam paper of a module that I will be teaching this semester. The volume $V$ of m$^3$ of earth removed from a pit after $t$ hours is given by ...
6
votes
1answer
116 views

Books/Articles/Journals about pedagogy and the experience of teaching

I'm going to be a teaching assistant and I'm currently looking for books/reviewed articles/journals written by mathematicians or people who taught mathematics (at a university level) about pedagogy ...
1
vote
0answers
72 views

College math competitions ranking

I am searching for math competitions for college students. Of course I am familiar with Putnam, but I am looking for a lower ranking competition. Either US-national or regional (South/Texas). I tried ...
0
votes
1answer
408 views

Probability and perfect squares [duplicate]

An integer $n$ is randomly chosen from $1$ to $k^2$, where $k$ is an integer. What is the probability that $n$ is a perfect square? I know I have to first figure out the probability of getting a ...
0
votes
1answer
274 views

Write the functions with the given domain and range

Domain $\mathbb{R}$, range the set of reals $\geq k$ where $k$ is a given constant. Domain = $\{ x \mid x \in \mathbb{R} \}$. How would I write the range?
6
votes
3answers
1k views

Teaching the concept of a function.

I am doing a class for at risk high school math students on the concept of a function. I have seen all the Internet lesson plans and different differentiated instruction plans. The idea of a ...
3
votes
1answer
567 views

About game theory for high school students

I am a mathematician with a background in analysis who is teaching at a local high school in his spare time. There is some room for extra curricular math subjects and I want to use it for game ...
2
votes
1answer
166 views

Where can I find Putnam competition questions and solutions online?

Math people: Until recently, at least, there existed at least one Web page containing complete Putnam competition problems and solutions from the past twenty years or so. In retrospect, I see that I ...
0
votes
1answer
57 views

Where are the resources on the prime number theorem?

I am looking for resources which explain the prime number theorem to 18 year old students. I am not seeking a proof of the result but something which will have an impact and motivate a student to ...
46
votes
13answers
16k views

Interesting math-facts that are visually attractive

To give a talk to 17-18 years old (who have a knack for mathematics) about how interesting mathematics (and more specifically pure mathematics) can be, I wanted to use nice facts accompanied by nice ...
4
votes
4answers
478 views

How to Make an Introductory Class in Set Theory and Logic Exciting

I am teaching a "proof techniques" class for sophomore math majors. We start out defining sets and what you can do with them (intersection, union, cartesian product, etc.). We then move on to ...
0
votes
1answer
40 views

Realizability in mathematics

What does it mean in mathematics when someone says "it is realizable"? If someone could give me a general and intuitive explanation I would appreciate it. Thank you!
0
votes
1answer
735 views

Any way to solve math problems faster?

Is there a faster way to solve math problems? I'm talking about proving theorems, proving certain properties of a function, etc. The way I do it is I write out the problem and all relevant definitions ...
1
vote
2answers
130 views

How is how $O(\log n)$ is a subset of $O(n^b)$?

This is an excerpt from a textbook I am reading: A number of useful shortcuts can be applied when using asymptotic notation. First: $O(n^{c_1}) \subset O(n^{c_2})$ for any $c_1 < ...
0
votes
3answers
164 views

Euler's Constant - How is the value obtained?

$e$ - Euler's constant $e = \lim_{n\to\infty}(1 + \frac1n)^n \approx 2.71828$ I'm wondering how 2.71828 is obtained from that.
2
votes
1answer
147 views

What is a Math Learning Graph?

I went through may topics on learning maths effectively, learning math at later years (I am 30, so I read it to get motivated) One thing I missed is a natural flow of topics that one must learn to ...
3
votes
5answers
358 views

General misconception about $\sqrt x$

I noticed a large portion of general public (who knows what square root is) has a different concept regarding the surd of a positive number, $\sqrt\cdot$, or the principal square root function. It ...
2
votes
1answer
83 views

Where can I get all mathematician's birth day and death day?

Did anyone do some some similar statistic thing? wiki's page is too few. mathematician in wiki For example, I want to know which day/ month that most mathematicians be born or died.