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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3answers
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Good math books to get on with my education? [closed]

im looking for a set of good math books. Since i live in norway im going through the norwegian school system, where i choose to go whats called a electrical line. Im not gonna go to deep into the ...
2
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0answers
31 views

Determine the set of points $M$ of affix of $z\in\mathbb{C}$

Determine the set of points $M$ of affix of $z\in\mathbb{C}$ such that there exists at least one real $t$ satisfying $z^2=t(t-i)$ My attempt: We look for the form $z=x+yi$ and we want there is a ...
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0answers
74 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
2
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0answers
38 views

Ratio Question (Primary School)

Now, there are 6 students who are sharing 4 desks at the library. While 4 of them are using the desks, the other 2 students have to wait and watch. If they have to use the desk for the same amount of ...
2
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1answer
228 views

Solve a problem using vectors

The purpose of this problem is to use vectors to show that the medians of a triangle all meet at a point. First, I have to show that $P$ (see the picture below) must lie two-thirds of the way from $B$ ...
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0answers
85 views

On which occasions will the intelligent layperson fail to recognize a mathematics problem?

Suppose an intelligent lay person is ignorant of mathematics and believes all the crap taught in classrooms to the effect that mathematics consists of believing dogmas, obeying instructions, and ...
2
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1answer
155 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering ...
2
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1answer
60 views

A basis in the $k$-th exterior power of a vector field

Definition: Let $\mathbb R^n$ be the $n$-dimensional real vector space. An exterior $k$-form call any skew-symmetric tensor on $\mathbb R^n$ of rank $k$. Denote the set of exterior $k$-forms by $E^k$. ...
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0answers
64 views

Instructive video content for High School kids?

I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
2
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0answers
62 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
2
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0answers
104 views

Pen-and-paper educational games

I'm teaching maths at the 8-16 year level, one-on-one tuition. What are some good pen-and-paper maths games I can play with these kids? Googling "math games" just gets me a load of interactive ...
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2answers
133 views

$f(x)=\sin(43x)+\cos(2x)$ is periodic function?

$f(x)=\sin(43x)+\cos(2x)$ is periodic function. I got the period of $\sin(43x)$ is $\frac{2\pi/}{43}$ and period of $\cos(2x)$ is $\pi$. Then the period of $f(x)$ is $2\pi$. Am I right? Any comment? ...
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0answers
60 views

Is there a name to refers to anything that is a point, line, plane, etc?

I'm teaching my juniors in high school some beginning linear algebra, but I find there is some vocabulary I am missing. I want to say that points, lines, and planes are all related, but is there a ...
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0answers
86 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
2
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0answers
141 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
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0answers
63 views

What is a sound curriculum for exponent rules in freshman algebra in high school?

We all know the the rules of exponents covered in freshman algebra. The question is, what is the best way to approach these topics as most 9th graders struggle in this area? I work as an after school ...
2
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1answer
75 views

Storytelling and Applied Narrative as a Teaching Tool

Is anyone integrating storytelling or applied narrative as a technique/methodology to help teach undergraduate mathematics-based course work? If so, how are you using it and from which sources are you ...
2
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0answers
146 views

Convention on the order of scalar multiplication (Multiplier vs multiplicand)

Is there a convention on the order of scalar multiplication? I know there were questions before mine, but I would like to know if such distinction is culturally dependent. This came from a news in ...
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0answers
71 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
2
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0answers
294 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
2
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0answers
204 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...
2
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0answers
609 views

The NES mathematics accreditation test

I have to take the NES mathematics test to get accreditation as a High School teacher to become highly qualified to teach mathematics. I have a PhD in physics so I thought that I wouldn't have to ...
2
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1answer
110 views

Visual proof ot the distributive property in $\mathbb{Z}$

Is there a intuitive/visual (not formal) "proof" that the distributive property holds in $\mathbb{Z}$? For the natural numbers $\mathbb{N}$ I know something like this: There are two ways to get ...
2
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0answers
137 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 ...
2
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0answers
146 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 ...
2
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0answers
121 views

What's the acceptance of rational trigonometry in current mathematics courses?

I've been reading about Wildberger's rational trigonometry and I'm willing to learn it. I'm wondering if it's usage is accepted in undergraduate mathematics courses. It seems there's a redefinition on ...
2
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4answers
513 views

Resources for learning mathematics for intelligent people?

Could people recommend resources to help my wife learn more complicated mathematics? She had a really terrible maths education, and while she essentially OK with every day maths she keeps wanting to ...
2
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0answers
78 views

What's the definition of a random number?

What sequence of numbers can I call as random number? What's the right way of getting $n$ random numbers? Are the numbers generated by "dice", too known as random numbers? Can a machine (computer), ...
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0answers
75 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 ...
2
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0answers
360 views

These unknown uniformly differentiable functions

Let $f$ be defined on $[a,b]$ and there uniformly differentiable ($\,$the $\delta$ in the definition of derivative is independent of the point). Given $\epsilon>0$, choose a partition $P \, : \, ...
2
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0answers
115 views

What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...
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0answers
82 views

Proving two Dedekind cuts represent the same number.

Hey guys I have a quiz soon and I really dont know how to prove this question. I tried my best but it is not working. Please help out with anything or hints. Let $(A'_1, A'_2)$ be a Dedekind cut of ...
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1answer
94 views

What does brace below the equation mean?

An example of what I am trying to understand is found on this page, at Eq. 3. There are two braces under the equation... What is the definition of the brace(s) and how does it relate to Sp(t) and ...
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0answers
60 views

Where can I get “computer based math” education as defined by Conrad Wolfram?

Textbooks, courses, and other resources would be helpful. http://www.computerbasedmath.org/
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0answers
94 views

Where read recent developments in Math presented in a way that is easy to understand?

I posted a similar question a few months ago, but I don't think people understood my question. I often find articles such as this which discuss exciting developments in science. I have a great ...
2
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0answers
205 views

MathJax (or something like it) as a classroom “blackboard”

At the risk of possible overlap with this (9-month-old) question Chatting about mathematics (with real-time LaTeX rendering) what is the best desktop application now for running MathJax in the ...
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2answers
604 views

How to get better at algebraic manipulations?

I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to ...
2
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0answers
125 views

References on the equivalence of different definitions of integrability

While writing a chapter of a book about mathematical analysis, I decided to compare some definitions of integrability that are usually taught to sophomore students, in Italy. I briefly collect four ...
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0answers
255 views

Motivating questions for some topics in undergraduate calculus

Being a grad student I'm going to teach a whole class for the first time the coming summer and I'm looking for some motivational problems which I could use to introduce different topics. In other ...
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0answers
248 views

Am I graduate if I take my bachelor degree in Italy?

I don't know if it is appropriate to ask here such a question since it doesn't involve a specific mathematical problem, but I think such information will be useful for many people like me... My real ...
2
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1answer
523 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
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4answers
831 views

Solved to be 7 after arithmetic

I recently made a blunder while trying to explain a question asked to me in an interview, The question was Think of $X$ Add $X$ to itself ($X+X = y$) Times the result by $3$ ($y\times 3 = z$) ...
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2answers
491 views

Can any function represent something in the real world?

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function ...
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2answers
327 views

Why it is always circle to represent a Set?

When we draw a Venn diagram, we use circle to represent a Set. We can use any closed plane figure but most of the time it is a circle. Why? are there any specialty about that?
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4answers
417 views

Help for Mathematics High school

I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new ...
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3answers
131 views

How to show $\Bbb R$ is Archimedean?

Suppose $X$ is a real number such that $X > 0$. We want to show there exists and $n \in \mathbb{N}$ such that $X \geq \frac{1}{n} $. MY attempt: If $X < \frac{1}{n} \; \; \; \forall n $ then $X ...
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5answers
739 views

Good discrete mathematics notes?

Good morning, Do you know of a good resource for discrete mathematics notes, lectures and/or videos? I found the classes + notes given to be lacking at my university... Topics covered thus far: ...
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5answers
79 views

How to prove $\sin3θ=3\sinθ-4\sin^3θ$

I was solving an A Level past paper (November 2014 P32) when I stumbled upon this question. It first asks us to expand $\sin(2θ+θ)$ which is easy using the identity $\sin(A+B)=\sin A\cos B+\cos A\sin ...
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4answers
209 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 ...
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2answers
111 views

Let $\{a_n\}_{n=1}^\infty$ be an infinite sequence. Does there exist an infinite series whose partial sums is $\{a_n\}_{n=1}^\infty$?

Definition: By an Infinite Sequence of real numbers, we shall mean any real valued function whose domain is the set of all positive integers. Definition: By an Infinite Series of real numbers, we ...