All Questions

I want to give to my students instructions/advises for drawing (directed) graphs (with few nodes, less than 15) in draft mode (before drawing final one on the official test paper). But I really have ...

After explaining some basic trigonometry to my kid, such as $\sin (\alpha+\beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$, Law of sines, Law of cosines, I wonder if there are some ...

This question came up while teaching ~16 year olds binary numbers. Why do place values increase to the left and not the other way round?

For Lang's Undergraduate Algebra and Undergraduate Analysis, I cannot find any weekly problem sets online. I've found that doing every problem in every section takes far too long, and without problem ...

What are some good answers to questions eg. "why do we need to study square roots"? Of course the answer depends highly on who is asking. For the scope of my question, I have a student in ...

Do any textbooks or (somewhat?) standard curricula introduce logarithms and their applications in arithmetic without assuming the students know any algebra? (I do not mean just the use of logarithms ...

In the textbook I am using to teach mathematics to high school students I found the following illustration about composition of functions. I do not agree with this illustration. For me $g$ is the ...

Q: What is a succinct, clear and purely algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? Here I am aiming for high-school students (in the U.S.). I have a purely ...

I get this question a lot from new students who are taking their first proof-based math class. They are struggling because they don't have that fluency with proofs, to begin with. They don't know ...

I am teaching a Calculus class with around 30 students. The classroom is about 100 m^2. So far I have been using myopenmath.com to assign homework problems to my students. Now I would like to deliver ...

Two students in my game development course would like, as a final project, to develop a video game for teaching mathematics. In contrast to the many other games for teaching maths, which focus mainly ...

To most people, a torus is a donut-like shape. Topologists like to describe the torus differently: you start with a square, and "identify opposite sides". We can imagine gluing together one ...

Are differential equations considered calculus and included in a calculus class or is it its own class? Also, if it is its own class then what calculus classes does it come after?

This seems like such a niche trick to teach students when factoring polynomials. Like, the polynomials I've seen textbooks ask students to factor by grouping seem so cherry picked that I can't imagine ...

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!

I'm currently working on some precalculus packages for students who need review. For inspiration, I'm looking at some prealgebra books and I'm wondering why isolating for $x$ is taught before ...

Do students learn implicit equations (such as $x^2+y^2-r^2 = 0$) and parametric equations (e.g., $x=a t^2,\;y= 2 a t$) in a first course in algebra, which in the US would be early high school, maybe ...

I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...

I am supposed to hold tutorial sessions for an undergraduate course in calculus. But the software provided by the university is not good at all. I saw the question suggesting to use Ziteborad but it ...

What is the clearest way to indicate various operations along the following lines: $f(x) = 3x$: The function $f$ multiplies its input by 3. $g(x) = x-5$: The function $g$ decreases its input by 5. $h(...

Long ago, when I was the student, I encountered a bunch of stories that we were asked to illustrate with graphs. I seem to remember that it was a set of around 10 examples. One involved some two ...

What are the estimated hours for teaching AP Calculus AB for students aiming for a 5? Similar question, how many hours of practice will the student need to put it. Some Clarifications based on ...

I am teaching Calculus III this semester and a student signed up for this course after completed Calculus I and II in a different institution. I quickly realised that this student does not understand ...

I've been thinking a bit of this comment and the following one: "(Look at all the complaints we get about kids who can't combine fractions!)" "Because it is not about you. Not about ...

In this weird pandemic school year, I'm doubly interested in technology integration to help my virtual (high school) students as much as my in-person students. I've been particularly eager to get ...

Years ago as a college freshman I was taking my first calculus course. Another freshman skipped it because he had calculus in Advanced Placement in high school. I mentioned we were learning the limit ...

I am teaching Calculus (one and also several variables). I would like to create questions in which students would watch a short video and then answer a question related to the content of the video. In ...

For the following linear differential equation $$a_ny^{(n)}+\cdots+a_1y'+a_0y=Q(x),$$ most books teach the method of undetermined coefficients, variation of parameters and Laplace transforms. ...

I'm taking a discrete math course. The textbook we use is such a pain to read because the amount of material is very overwhelming. For example, chapter 1 alone is 115 pages. And every subsection, 1.1-...

The dimension theorem (the rank-nullity theorem) can be explained in many ways. I consider it as a consequence of the first isomorphism theorem/splitting lemma. When I teach undergrad matrix-theoretic ...

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...

I am working with a college student who was placed into a pre-college level math class. She's in a unit that covers a lot of unit conversions (simple ones, like 5 km = ___ miles or 3 yards = ___ cm ). ...

I'm working on converting a course to make it free to the students, and I'm considering using Ximera. What I haven't found online is documentation for/information on tips and best practices for ...

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...

When casually discussing with my 13 yo child about probabilities, he told me there is a 50% chance to win at the lottery To what I said no, there is a 1 chance over 90 million (I roughly estimated ...

Suppose one were writing a book aimed at high-school students (and their teachers), where "high-school" in the US means grades 9,10,11,12 (where college/university starts at 13). The book is ...

Today I came across the inclusion-exclusion principle for the first time. I believe I have understood it, however when I tried solving some questions on it, I got severely stuck. I couldn't solve any ...

Currently a 5th year PhD student, and I've been fighting tooth and nail to teach one of our junior-year honors sections in undergraduate algebra next fall (desperately hopeful we'll be able to return ...

The following "chain rule" is in my multivariable calculus course: If $f$ depends on $x$ and $y$, but $x$ and $y$ depend on $t$, then $\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{d ...

I'm currently self studying a Linear Algebra text book due to the fact that I forgot the vast majority of it since I took the course 10 years ago. My general strategy is to take every single example, ...

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...

My two main ones are Electrostatic force field $\mathbf{E}\left(\mathbf{r}\right)=\frac{Q}{4\pi\epsilon_0 \left|\left|\mathbf{r}\right|\right|^3}\mathbf{r}$ and Gravitational force field, $\mathbf{F}\...

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...

Symmetry is an important concept in mathematics and it has a built-in aesthetic appeal. The following shows how different types of symmetry relate to one another. Start with the equation $f(x) = -x^2 ...

The question What are some good mathematical applications to present in an abstract algebra course? asks about mathematical applications of abstract algebra. What are some applications of abstract ...

My instinct is often that there should be some technical word for the common class of equations and inequalities. That is: statements that connect two numerical expressions, with a relational operator ...

I am looking a good,stable and cheap graphics tablet for online math educations that you use to use and love to use. I gotto prepare remote videos.

(Repost from MO, where the question will eventually be closed.) This question is related to lectures I have to make concerning differential calculus in one variable, but the students are quite ...

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he ...