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.

learn more… | top users | synonyms (3)

0
votes
2answers
164 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. ...
92
votes
23answers
8k 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
2k 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
179 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
276 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
68 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 ...
25
votes
11answers
3k 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
174 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 ...
6
votes
1answer
211 views

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

Background. Let $x$ denote an arbitrary real number. Then $x^n$ can be defined for each $n \in \mathbb{N}$ as follows: $$x^n = \underbrace{x \times \cdots \times x}_n$$ If $x$ is furthermore ...
2
votes
1answer
44 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
451 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
141 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
91 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
114 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
202 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
48 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 ...
3
votes
0answers
148 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
161 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
289 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
80 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
125 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
74 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
624 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
472 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
2k 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
715 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 ...
3
votes
1answer
189 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
61 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 ...
49
votes
13answers
23k 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
690 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
43 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!
-2
votes
1answer
858 views

Any way to solve math problems faster? [closed]

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
155 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
188 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
161 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
388 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
88 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.
3
votes
2answers
450 views

Did Euler have a trick? [closed]

Did Euler have a trick for discovering things? Some sort of general method he could apply to mathematical objects he came across to see if they yielded any new truths? Did he just ask the right ...
8
votes
3answers
892 views

What is the probability that GCD of $(a,b)$ is $b$?

My question is quite simple. I have been googling a lot lately trying to find a solution to this: Given a sequence of n integers $[1,2,...,n]$. If we pick two numbers randomly from the set say, a and ...
3
votes
0answers
154 views

Where to start?

I want to learn Mathematics but I don't know where to start. Sometimes I really get frustrated as I am a Software Engineering graduate (currently working) and I feel like I don't know anything about ...
5
votes
9answers
758 views

Ceiling and floor functions

What are some real life application of ceiling and floor functions? Googling this shows some trivial applications.
2
votes
3answers
208 views

Learning times tables?

I have some weird gaps in my learning, I can do lambda calculus and some basic category theory, but I do not know how to do some of the most basic of arithmetic. (I am in my mid 20s) Seeing this gap ...
6
votes
2answers
186 views

Is it a problem being unable to understand a mathematical definition without examples?

I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning ...
9
votes
4answers
766 views

Middle school number theory

Find at least three numbers that satisfy all three conditions: (1) there is a remainder of $1$ when the number is divided by $2$; (2) there is a remainder of $2$ when the number is divided by $3$; ...
2
votes
2answers
20k views

Why are prime numbers important in real life? [duplicate]

What practical use are prime numbers? Why do we emphasise the teaching of prime numbers?
4
votes
7answers
2k views

New & interesting uses of Differential equations for undergraduates? [closed]

I'm teaching an elementary DE's module to some engineering students. Now, every book out there, and every set of online notes, trots out two things: DE's are super-important, vital, can't live ...
4
votes
5answers
1k views

How to know that irrational numbers never repeat?

How would you respond to a middle school student that says: “How do they know that irrational numbers NEVER repeat? I mean, there are only 10 possible digits, so they must eventually start repeating. ...
1
vote
0answers
62 views

Metalanguage on mathematics

I've heard that in the first class of my degree are teaching concepts like metalanguage. What does it mean. Could you give some examples? I've searched on google that metalanguage means representing ...