All Questions

I want to try making some calculation-less questions about vector calculus identities that are solely based upon picture diagrams of vector fields, or fields that could be sketched out by hand. The ...

Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...

As an undergrad student of applied mathematics, I have something to say that make's me ashamed of myself. I suck at proving things in mathematics and i know that if I don't get better in doing this ...

I try to comprehend a step on an integral. The calculation follows: $\int\limits_{0}^{t} \mid \exp{(At)} \mid dt$ I wonder, in complex case, that $\mid \exp(\cdot)\mid$ do not coincide with $\exp(\...

If you could build an ideal online homework platform for mathematics, what combination of features should it have in order to be effective at levels from high school through undergraduate, and why? ...

If $x= a\tan^2y+ b\sec^2y$ the find $x+a/x-b$.

I am tutoring a student preparing to take Calculus 1 at a university. This student hasn't taken precalculus for a year, so I have been drilling him on definitions, rules, and theorems from a college ...

I teach in a regional university. In my department, students take their "proof course" (a course that sole focus on writing proofs) in the third or even fourth year. All the courses before ...

The Art of Mathematics by Sung-Dae Hong is the standard high-school mathematics textbook in South Korea. The series gets new editions and reprints since 1966. Wikipedia has a page for it. Had it ever ...

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...

I feel it may be a good idea to introduce some related open problems in a calculus course. Surely I am not expecting my students to solve any one of them, though I cannot say it is absolutely ...

Many of us our coming off our first semester of required-online classes; and at some of our institutions we are preparing for what is most likely a required-online semester in the fall. (That is: The ...

Once, when I Was doing calculus 2, someone challenged me to calculate and prove the Gaussian integral, with a few hints, and a few days, I managed to. It was a great feeling to solve a “deep” multi ...

[I originally posted this is the Mathematics Stack Exchange and was told to post it here instead] This might seem like an odd topic for this forum, but I'm losing my mind. I am about eight months away ...

I am a college instructor who's just had an outbreak of academic dishonesty connected to students posting take-home exam problems on a platform called Chegg. Chegg collects a membership fee from ...

Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...

Now that everyone has had the experience of teaching math in an online/remote/synchronous/asynchronous format, and looking forward to more of this in the Summer and Fall terms, how do we change our ...

I am a student, in my last year of school(17 years old) When I was about 13 years old I fell into the calculus trap by starting off learning trigonometry on my own, when I was supposed to factor ...

I am a student from CS background. I have been following "Discrete Mathematics and its Applications" by Kenneth Rosen, though it is a good book, but it does not cover group theory. I would like to ...

I would like to construct a good worksheet for my students. I am thinking of creating an instruction that will cover all problems related to identity equations. Here is how I initially constructed ...

Recently, there is an idea sparkling out from my mind due to the COVID-19 outbreak. In the past, we typically attend a course, complete homework and assignment, then finish the semester with a final ...

It's hard to be more descriptive with the title without making it excessively long. What I'm wondering is this: what is the "right attitude" or "right psychology" when confronted with a mathematical ...

I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...

We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The ...

I am currently reading Spivak Calculus on Manifolds and Munkres Analysis on Manifolds. I am looking for a more advanced text, especially on vector fields as they relate to the great conserved fields ...

After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...

(1) When do students in Canada learn about the four triangle centres (centers), circumcenter, incenter, orthocenter, and centroid? In the USA (more precisely, Indiana), the math curriculums are by ...

How do I refresh advanced math I learned at a graduate level? I once was able to do the full solution of a particle in a parabolic well and other advanced math, however 20 years later I'm struggling ...

An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (...

I am UK-based but I guess this issue currently affects all maths educators and has probably been addressed by those how have been delivering courses through online channels for the past few years. ...

Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...

I'm taking integral calculus at the moment. I was understanding everything quite well until we started learning about finding volume of a solid of revolution. I understand the concept, but practicing ...

I am trying to compile a document of preparation questions to use in mock interviews with students applying to study Maths at top UK Universities. I have many questions already, but it is always ...

I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes. I understand at every level one ...

I tutor a 16 year old girl. As far as I can tell, she has average talent and interest in math. However, her knowledge of math is that of a 10 year old or even below. She knows the basic operations on ...

I am looking for 3d-math animation software that is specifically meant for Visualization: That is geometry-based software that can aid in making visualizations as in https://www.youtube.com/watch?v=...

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...

The New Math curriculum built math eduction on set theory. Have there been any attempts to do something similar with category theory? I was fortunate to grow up in a relatively enlightened ...

I hope this is the right place for posting this, but if not, please let me know! I recently took a second class in Python programming which, toward the end, also taught a little bit of SQL. As it ...

My job is starting to have me delve into categories that require things like regression analyses on data sets, essentially i'm being introduced to "Data Science" type material. Coming from a computer ...

In his book "Surely you're joking Mr. Feynman", Richard Feynman relates the following story. As he was supervising a group of calculators for Manhattan project, he at some point gave them a lecture on ...

I hope the essence of the question is clear from the title. There are obvious advantages to making the linear map the central notion of a linear algebra course: the notion can be illustrated with ...

This r/math post spurred this question. To concretize the meaning of "ace", assume success means earning professorial tenure at a Top 100 world university. your liked stronger branch doesn't exactly ...

I recently taught an introduction to real analysis. I assigned a (covid-induced) take-home final, which included the question: Define the set S by $$ \bigcup_{n=1}^\infty \left\{ \frac{a}{2^n}\...

We all know the (apparently verified1) anecdote recounting George Dantzig arriving late to a lecture (by Jerzy Neyman), and later solving two open problems written on the board, mistaking them for ...

I typically will write my own slides for a course, and then may make a screen recorded video of me talking over the slides. Now I'm planning on doing a screen recording over slides the publisher has ...

In the UK, calculus taught in secondary school focuses mainly on computation of derivatives and integrals and solving simple differential equations. There is a small amount of discussion about limits ...

I am looking for some examples of when proof by contradiction is used in a problem with more than one case. In all the elementary examples, there are only two options (eg rational/irrational, ...