Mathematics education consists in the practice of teaching and learning mathematics, along with the associated research. Research in mathematics education concerns the tools, methods and approaches that facilitate the practice of mathematics or the study of this practice.

learn more… | top users | synonyms (1)

0
votes
5answers
153 views

New idea to prove that 4 divides $5^n-1$

I was working for various method to solve this :$n\in \mathbb N \to \; 4|(5^{n}-1)$ my try was : 1st :$$n=1 \to 4|5^1-1\\n \geq 2 \to 5^n=25,125,625,3125,...\\ n\geq 2 \to ...
2
votes
1answer
75 views

Difficult to read about different subjects simultaneously, should I leave one for now? [on hold]

I learn math by reading books. Usually I read 3 books (about 3 different subjects) simultaneously and switch focus every couple of days. The books i'm studying right now are Rudin's functional ...
7
votes
5answers
402 views

New idea to solve this equation

I was teaching $\left \lfloor x \right \rfloor$ function properties and equation . I solved this equation in my class . My works are show below. Some students ask me for new Idea...,and now I am ...
1
vote
1answer
27 views

Probability of 2 students being chosen the both have under 100 books at home

Suppose we select two students at random from the class of fifteen. What is the probability that both students chosen have less then 100 books at home? Data provided is the amount of books each ...
13
votes
5answers
2k views

When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right ...
1
vote
0answers
36 views

A harder long division puzzle than the first; what should “Algebra I” solution look like?

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine: ...
6
votes
3answers
90 views

“Long-division puzzles” can help middle-grade-level students become actual problem solvers, but what should solution look like?

This is my first post. I hope it's acceptable. EDIT Since there are people to whom such notation is foreign, I will point out that the problem represents KRRAEE / KMS, where PEI is the quotient and ...
7
votes
8answers
835 views

Most natural intro to Complex Numbers [closed]

This is a soft question but I'm willing to ask. There are few ways to introduce the field of complex numbers, but if You had the opportunity to write an elementary textbook, what would be the most ...
3
votes
1answer
116 views

Students and Real Analysis

I am currently working on a project investigating why students tend to struggle when they first encounter Real Analysis and what can be done to improve the situation. I would be very grateful if any ...
0
votes
0answers
40 views

The $\epsilon$-$\delta$ definition of a limit of a linear vs a non linear function

I am teaching elementary analysis and introducing the concept of $\epsilon$-$\delta$ definition of the limit to first time learners. For example, we take $\displaystyle\lim_{x \to 2} (2x - 1) = 3$, ...
19
votes
8answers
2k views

How do authors make their problems/exercises for their math books? [closed]

I want to be a math professor one day, but I'm wondering how to make my own original problems to give them to my students. I think that it is a responsibility of the professor to create original and ...
0
votes
0answers
39 views

Math wheel from 1917 question [duplicate]

http://www.washingtonpost.com/news/morning-mix/wp/2015/06/06/eerie-chalkboard-drawings-frozen-in-time-for-100-years-discovered-in-oklahoma-school/ I hope this came out like it was on the webpage. It ...
8
votes
0answers
76 views

How to explain the topic of Fourier transform interactively? [closed]

This is a soft question . In the walk-in for the lectureship, I have decided to give demo lecture on the topic of Fourier transform. The principal of the institution ask me to take lecture ...
0
votes
1answer
39 views

Prove lines being parallel within a traiangle

Here is the problem: The only condition given is $DF//BC$, is it possible to prove that $GH//BC$? Please verify it. Any help will be appreciated.
1
vote
1answer
24 views

Extract sum of coefficients in a binomial expression

I have two questions: (1) Given $(1-x+x^2)^{3n}=c_0 + c_1 x + \dots +c_{6n} x^{6n}$, find $c_0+c_1+ \dots +c_n$. I manage to find $c_0+c_1+ \dots +c_{6n}$ by putting $x=1$ but I do not know how to ...
0
votes
1answer
59 views

Learning math by analyzing/proving theorems?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
2
votes
0answers
27 views

How should the topic of frequency domain be taught?

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics, Digital Signal and image Processing. Some of concepts which are very ...
160
votes
14answers
10k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
2
votes
0answers
38 views

how to teach steady state in queueing - if at all? [closed]

I am teaching an undergraduate course in Operations Research to business students (they are not: maths students). I want to check, if and how teaching the steady state makes any sense. As in the ...
0
votes
1answer
21 views

Algorithm for finding Complex Eigenvectors?

I'm wondering if there's a fairly easy algorithm by which one can, by hand, find eigenvectors corresponding to complex eigenvalues for small matrices. Of course, one can always row reduce, but it can ...
1
vote
2answers
148 views

Why study Lowest Common Multiple - LCM

What is the most motivating way to introduce LCM of two integers on a first elementary number theory course? I am looking for real life examples of LCM which have an impact. I want to be able to ...
5
votes
1answer
120 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
2
votes
0answers
82 views

Argument for the zero vector not being defined as an eigenvector

Two days ago, my lecturer of Advanced Numerical Methods gave a review on the topic about eigenvalues and eigenvectors. Just as the lecturer presented the definition of eigenvalues and eigenvectors, a ...
1
vote
1answer
74 views

Understanding and teaching the concept of derivative

I need to prepare an introductory lecture about derivatives and the concept of differentiation to a class of people with a general mathematical background (who have also studied calculus a few years ...
1
vote
5answers
148 views

Why do counits go that way?

Imagine you want to motivate for an audience the definition of an adjunction in terms of unit and counit. So you can say: Often two functors $\mathcal{C} \begin{array}{c} \stackrel{\large ...
1
vote
0answers
74 views

Ideas for math problem solving class for undergraduate students in university

In our university there is a huge gap between two group of students. a group of them came from Math Olympiad competitions and have a very strong background from high school but others, they have just ...
7
votes
3answers
165 views

Algebraic number theory topics for undergrads

What are some interesting topics or problems in algebraic number theory which could be presented to students in a first undergraduate algebra course (which covers some elementary number theory, ...
3
votes
0answers
114 views

Examples of categories which appear naturally without objects

Regarding the morphisms-only-definition of a category (which is equivalent to the usual one dealing with objects and morphisms), I would like to ask: Which examples of categories in practice appear ...
2
votes
8answers
356 views

A pedagogical proof that 9's can be ignored when calculating digital roots

I was asked by an elementary school teacher for a proof that you can ignore all 9's when calculating the digital root of a number. For instance, when calculating the digital root of 7593329, you ...
11
votes
1answer
152 views

Has the age at which we teach Mathematics changed over the last two centuries?

My experience of learning Advanced Trigonometry and Calculus is that it was done to 17 and 18 year olds (School Curriculum in Australia). I assumed that it was similar in the UK, US and Europe. In ...
2
votes
3answers
96 views

Teaching cardinality

I would like to give a class of 60 minutes to my undergraduate students about cardinality. I would like to begin with the definition of cardinality and end with one or two good application of this ...
3
votes
4answers
143 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
0
votes
1answer
40 views

Find functions with ''smart'' tangents.

This is a didactic question. Given a differentiable function $y=f(x) \;, x,y \in \mathbb{R}$, I want to construct an exercise in which we have to find a straight line that passes through a point ...
3
votes
1answer
90 views

Two categories sharing the same objects and morphisms

Is there a natural example of two categories $\mathcal{C}$, $\mathcal{C}'$ which have the same class of objects and the same class of morphisms, including source and target maps, but different ...
1
vote
2answers
77 views

Abstract/formal interest of rings

I am about to introduce first year undergrads to the concept of rings, after spending some time looking at groups; and I would like to give them more than a practical motivation (the most usual rings ...
4
votes
2answers
102 views

Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S

This is a very easy fact we use in Group Theory, But somehow, I wondered that whether there may be another way (other than Lagrange's Theorem) to prove that the order of an element divides the order ...
2
votes
2answers
62 views

Necessity of algebraic symbolism

We solve different problems algebraically .For example,if we add $20$ with a number and the sum is $42$.What is the value of the number.To solve we denote the number as $x$ and write like this ...
0
votes
1answer
121 views

How to explain this question to a 6 year old

My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has ...
5
votes
4answers
123 views

Explaining that $1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1)$

I have a few students that are having trouble understanding that $$1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1),$$ specifically that $$\frac{1 \cdot 3 \cdot 5 \dotsm ...
1
vote
4answers
86 views

What is not the second derivative of a parametric equation?

1142004    Consider the parametric equations $x=f(t)$ and $y=g(t)$. To "find" $\frac{d^2y}{dx^2}$, there are three ways to go: (1) the correct one, that is, ...
6
votes
1answer
138 views

Help with diagram chasing

Given the diagram $\require{AMScd}$ \begin{CD} 0 @>>> A @>f>> B @>g>> C @>>> 0 \\ @. @V\alpha VV \#@V\beta V V\# @VV\gamma V @. \\ 0 @>>> {A'} ...
2
votes
0answers
70 views

A good way to explain $\varepsilon$-$\delta$ for chemistry / biology students?

I feel like I have a pretty good way to talk about $\varepsilon$-$\delta$ to physics and engineering students (and possibly students in comp sci). But I am not very sure what I can do for chemistry ...
1
vote
1answer
106 views

Why are Fourier series important?

Are there any real life applications of Fourier series? Are there examples of Fourier series which have an impact on students learning this topic. I have found the normal suspects of examples in this ...
3
votes
1answer
37 views

Find a set of minimal natural axioms, from which we construct $\mathbb{Z}$.

I am interested in this question for teaching two very different kind of students. The first (less important to me) is students in their first year in the university. I wish to construct ...
1
vote
0answers
73 views

Intuition behind the link between coding theory and group theory

I am trying to find an easy link between group theory and coding theory. The usual path that most of the texts follow is that they present introductory material on groups, fields, rings, etc., and ...
1
vote
0answers
38 views

Proper usage for term, addend, factor, multiplicand, expression, formula

The definitions and usage of the following words seem to vary, depending on the source text: term addend factor multiplicand expression formula The words are being used in the context of ...
-5
votes
3answers
91 views

Why does the author prefer function names after arguments?

As you can see above, the author prefers to write functions after elements, which is contrary to the century old practice of writing arguments after the functions. I wonder why he does that? Is ...
3
votes
2answers
395 views

An example of a great explanation or freely accessible article on a math concept [closed]

Question: Give an example of a great explanation or freely accessible article on a math concept (suitable at the undergraduate or lower level), and explain why you think it is great. Possible ...
108
votes
44answers
13k views

What's your favorite proof accessible to a general audience? [closed]

What math statement with proof do you find most beautiful and elegant, where such is accessible to a general audience, meaning you could state, prove, and explain it to a general audience in ...
94
votes
11answers
6k views

Is there a domain “larger” than (i.e., a supserset of) the complex number domain?

I've been teaching my 10yo son some (for me, anyway) pretty advanced mathematics recently and he stumped me with a question. The background is this. In the domain of natural numbers, addition and ...