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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245 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
2
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1answer
368 views

What textbook should I get to self-learn Calculus? [duplicate]

I did not have the option to take calculus during high school. I would like to pick up this subject during my free time. I am a software engineer. I would like to improve my understanding of maths. ...
2
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2answers
172 views

At what education level is this “simple” problem adequate?

Given the following problem: Alice, Bob and Carl stand on a straight line. Alice is one rod away from Bob. Dana stands one rod away from both Bob and Carl. Carl is as far from Alice as Alice ...
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1answer
64 views

Any comprehensive material to revise the mathematics

I left school long back and so my mathematics knowledge also fades out. I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations. I tried ...
2
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1answer
1k views

Complex division: polar form vs complex conjugate

The original problem In an electricity course which I volunteered to help with, the students solve circuits using phasors. Using phasors requires a good knowledge of complex numbers arithmetics, ...
2
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1answer
355 views

any Math game for kids?

I need to plan a "game" for kids about 10-11 years old that involves mathematics and some physical activity or game. It must be short-time and not very difficult because it's a stage of a big game. ...
2
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1answer
597 views

General definition of growth in mathematics

From high school math one knows "linear growth", "exponential growth", "logistic growth", "bounded growth" etc., but is there a common accepted general definition of "growth" which covers the special ...
2
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2answers
387 views

Good math software [closed]

I have finally decided to go more deep into math and cs, so to do that I will need proper tool, math tool. Could you please tell me what's the best open source math tool on the web today, since as far ...
2
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1answer
117 views

weakly locally one-to-one?

Is there any standard name for this concept that is weaker than local one-to-one-ness? In some open neighborhood of $x_0$ there is no point $x\ne x_0$ such that $f(x)=f(x_0)$. Or, if you like: In ...
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3answers
327 views

I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources ...
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0answers
52 views

Where to start with Euler and Ramanujan?

What are the specific qualifications for directly studying Euler and Ramanujan's works.Is Hardy's "A Course in Pure Mathematics" a good start?
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0answers
24 views

Which FOL consequence relation is better (to teach)?

Backstory: I had problems of accepting Mendelson's rule of Generalization (it's $(A(x) \vdash \forall x, A(x)$). Surfing around the net, I found this post which explained the situation for me: ...
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42 views

Methods for solving for partial fraction coefficients.

When I present partial fraction decomposition, there are typically two approaches to solve for the coefficients of the fractions: Clear the fractions, multiply out the products, and equate ...
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0answers
31 views

E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
2
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1answer
54 views

Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
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0answers
60 views

Increased Math Productivity on Mobile Devices [closed]

I have been answering questions on Math.SE for a (relatively) short time now, and I have found that answering questions on my Android phone is somewhat of a nightmare. I end up commenting much of the ...
2
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2answers
42 views

Proving of this trigonometric identity

$$\frac{\cot \beta}{\csc \beta - 1} + \frac{\cot \beta}{\csc \beta + 1} = 2 \sec \beta$$ What I've done: $$\frac{\frac{\cos \beta}{\sin \beta}} {\frac{1}{\sin \beta} +1} + \frac{\frac{\cos ...
2
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0answers
53 views

What makes a good mathematical poster? [closed]

During my second year of university I have done some assignments and some papers, but this is my first time I have to make a mathematical poster. What could make my poster stand up. So up to now I ...
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0answers
25 views

What is a point to give the Abel's Test for product series convergence a place in introductory textbooks?

One of the hypotheses of the Abel's test for product series convergence is stronger than the corresponding Dirichlet's test; that is, the former imposes the convergence of one of the series and the ...
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0answers
52 views

What to do when finding “complex” result by accident?

This happened a couple of times today. While working on some problems, you find unexpected relationship between objects, which are not obvious to find directly. For example today I found out that ...
2
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0answers
29 views

Powerful pictures or plain proceedings?

After tutoring someone about polynomial manipulation, my mind went back to this equivalence: $(a+b)\times (c+d)=ac+ad+bc+bd$ I realized that, while it can be memorized as it is, it has a very simple ...
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0answers
39 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
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0answers
52 views

Circular Logic and Continuity

So, I was doing a Calculus problem a few minutes ago and just recalled something that my real analysis professor said during a lecture years ago... To provide context, take the function $f$ defined ...
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54 views

Is the precise definition of a limit worth covering in Calc 1?

I'm teaching calc 1 this semester and am trying to decide if I should cover the precise definition of a limit. My first impression was that I should. It helped me to gain a deeper understanding of ...
2
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1answer
72 views

How To Prove Irrational Square Roots and Inequalities In Courant's Calculus Book? [closed]

Here's the proofs questions in a screenshot The first questions ask about proving the irrationality of non perfect squares. Numbers 3,5, and 6 ask for inequality proofs. I find it daunting that the ...
2
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1answer
82 views

Alternative proof that base angles of an isosceles triangle are equal

The "classic textbook proof" of equality of base angles of an isosceles triangles which I studied in my school days is as follows: Let $\Delta ABC$ be a triangle with $AB = AC$ and let $D$ be the mid ...
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2answers
153 views

What do we mean by 'defining a function'?

First I will start by quote from Wikipedia about function's defining methods : There are many other ways of defining functions. Examples include piecewise definitions, induction or recursion, ...
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0answers
37 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 ...
2
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0answers
89 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 ...
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0answers
24 views

Learning Logic and Metric Spaces

I want to learn how to manipulate metric spaces. I have been reading this book about metric spaces. ...
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3answers
125 views

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
33 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
75 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" ...
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0answers
42 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
260 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 $B$ ...
2
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0answers
87 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
159 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
64 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
65 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 ...
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0answers
66 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
117 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 ...
2
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2answers
136 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? ...
2
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0answers
61 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
88 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 ...
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0answers
143 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
65 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 ...
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0answers
150 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
73 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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2answers
335 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 ...