32

Under the laws in most countries, a work such as a book is automatically copyrighted as soon as it is written down. Putting the copyright notice in the book isn't what makes it copyrighted. The notice just makes it easier to sue for copyright violation, because it's harder for the person who copied to claim they didn't know the work was copyrighted. For this ...


30

I would say the standard implementations of the Rational Root Theorem (make a huge list for the sake of making the huge list) indeed feel like a complete waste of time. However, the theorem can sometimes combine nicely with technology tools. I'll provide an example of this. Consider the following algebra puzzle: Solve for $x$: $7x^3 -39x^2+52x+30 = 0$. If ...


12

I think an important learning outcome of this part of high school Algebra 2 (theory of polynomials) is developing mathematical capacity to juggle several disparate abstract tools all at once, similar to how in calculus, one uses first derivative test, second derivative test, concavity, asymptotes, intercepts, end behavior, etc., all at once, in some ...


11

Agreed...it's one of the less useful parts of high school algebra. But not because "you could use a computer"--you could say that about almost everything. And then we get some of the same people who push the "use a computer" who are surprised when their kids flounder because of lack of manipulational ability in calculus. ;) The reason ...


11

Let $x = \sqrt 2 + \sqrt 7$ prove that $x$ is irrational. \begin{align} x - \sqrt 2 &= \sqrt 7 \\ x^2 - 2\sqrt 2x + 2 &= 7 \\ x^2 -5 &= 2\sqrt 2x \\ x^4 -10x^2 +25 &= 8x^2 \\ x^4 -18x^2 + 25 &= 0 \end{align} So $\sqrt 2 + \sqrt 7$ is a root of $x^4 -18x^2 + 25$. According to RRT, if $x$ is rational, then $x = \pm 1$ or $x=...


10

The RRT is not taught in isolation. It is taught as a collection of tools for (partially) factoring polynomials. It should be taught with Descartes' rule of signs and some form of polynomial division. It is direct preparation for understanding the proof of Eisenstein's criterion for irreducibility. The "shadow" of that application is via Gauss's ...


8

I believe Overleaf would be your best bet. I am currently taking a class right now where the lecturer writes up the contents of the lecture using overleaf and it's very feasible. Even though you don't want to wait around for it compile, Overleaf renders documents pretty fast, and can render without you needing to press the command to do so. I'd say there's ...


8

I do think that having an introduction and primer to LaTeX in the course of a college math/computing degree is appropriate and beneficial. For example, I work this into my discrete math course, and require that weekly submissions to the Discussions board be in that format (the Blackboard LMS supports LaTeX entry). My community-college students often have ...


7

I would reluctantly agree that it's not a particularly powerful tool if you have electronics at your disposal. But I might double down and say that you should be teaching synthetic substitution as well so that students can factor cubic and quartic polynomials without their calculators. About a year ago, I went down a YouTube rabbit hole of watching videos ...


6

No. There is a sort of magical thinking implicit here that something needs to stay, be different between computers and people. At the end of the day, we are "meat" computers. And the computers themselves are getting more and more sophisticated in doing things that were hard for them previously. But the existence of a soul (whether or not true) ...


4

Theorem: For every integer $m$, the polynomial $x^3 - mx^2 - (m+1)x - 1$ is irreducible among polynomials with rational coefficients. Proof: This polynomial has degree $3$, so if it is a product of lower-degree polynomials, the decomposition is (linear)(quadratic) or (linear)(linear)(linear). Either way, there is a linear factor and thus a rational root ($...


4

Copyright is related to works, not ideas or facts. To quote the Oxford Learners Dictionaries: if a person or an organization holds the copyright on a piece of writing, music, etc., they are the only people who have the legal right to publish, broadcast, perform it, etc., and other people must ask their permission to use it or any part of it The important ...


4

Have you checked out Math Open Reference? The site has animations that demonstrate how to do the constructions, in the style that you indicated. It won't let students DO the construction online; instead it shows them the steps necessary to do the construction. It also includes printable worksheets for them to practice doing it by hand as well as providing an ...


4

This looks promising but it is not free: mathspad.co.uk.       You can experiment with the tools without creating (or paying for) an account:      


4

You might find jupyter notebooks useful, especially if you use either the Sympy or Sage computer algebra systems. These notebooks allow you to enter mathjax enabled markdown on the fly; which can also be generated as the output of sage and sympy. For example, sympy shows a live example session on their site: Graphs are also straightforward, and can be quick ...


3

My recommendation for a usable, inexpensive drawing tablet would be the XP-Pen StarG40. It's what I've been using this year (in conjunction with Blackboard/Collaborate) and costs about $40 as of this writing. It's the lowest-cost tablet I've seen, and it works reasonably well (there are encoding issues in Collaborate that make it always a bit jittery, but it'...


3

3 blue 1 brown has an outstanding video on Fourier series: https://www.youtube.com/watch?v=r6sGWTCMz2k Thinking of a periodic complex valued map as a parametric curve in the complex plane, and thinking of the complex exponentials as "clocks" running at different speeds, the problem becomes: how do we draw anything using a bunch of revolving clocks ...


3

You can of course keep using iPad. One way to do this is to start a zoom meeting with your students and share your iPad screen. Then you can write in a note taking app such as GoodNotes. The draw back of this method for me is that sometimes I want to show some Mathematica generated 3d models. You can use Wolfram Player on iPad. But then you can not edit the ...


3

I really think this questions gets to a bigger issue. This is part of a general problem with our approach to math education. The point of high school math class, from any practical standpoint, is not to teach students things that they will constantly be using all the time (or even ever). Empirically this is verified in myriad examples, not just the rational ...


3

(feel free to change to comment): If you are going to ADD something, then you need to make an argument over what to cut. Or say camels have it easy and can carry more straw (they don't, but at least adresse the issue). I see this mental lapse all the time. Life is an optimization/choice problem. Not an "add" problem. By the way, starting to ...


3

At the University where I'm teaching, there is such a course mandatory for all students (not only in math, but also physicists, chemists and computed scientists) and recommended in the first year of studies. It's a 1 credit course (meaning the it "officially" assumes about 25 hours of work), and it's offered online - the student is supposed to read ...


3

It is true that $\LaTeX$ is a language, but I lived through the transition from WordPerfect and WordStar to Microsoft Word, and I lived through the transition from troff to $\LaTeX$. Already Overleaf, MathJax and other similar software developments are lowering the TeX entrance-threshold. In the future, $\LaTeX$ will likely move "under the hood" as ...


2

One clear objection to teaching Latex to all undergrads that would be raised in a faculty meeting would be: Latex indeed is pervasive in mathematical and theoretical physics publications (it is not that common in experimental physics, I don't know about engineering), but the majority of undergrads will not stay in academia, but will enter the job market once ...


2

I use a 16" Wacom Cintiq Pro. The advantage that the Cintiq line has over the Intuos line is that the Cintiqs act as secondary displays. There are a number of reasons why I consider this to be a huge selling point. I can see what I am writing. That is, as I write, I see writing appear "on the page" under the pen. This is in contrast to ...


2

In an attempt to answer your question: Are the PISA data detailed enough to measure effects by such AI based approaches in mathematics? I found three things that point to the answer being no. I dug through the 2018 PISA School Questionnaire, which is administered to school principals, and found no question on AI that would allow the data to be parsed in ...


2

I have used Microsoft OneNote 2016 (plus screensharing software) for online tutorial sessions in number theory during the past year. It has worked very well and I will continue to use it. You can enter plain text just like in Microsoft Word and switch to Math mode by pressing a shortcut (["Alt" + "+"] in my case (German), but it might ...


2

I use Lyx as my LaTeX "word processor", and it's really good at real-time interpretation. You can build your statements using a GUI sort of like Microsoft Equations back in the day or you can just type straight LaTeX. The creators insist that it isn't WYSIWYG, but the distinction between WYS on the screen and WYG out of a printer is insignificant ...


2

I think it is not a good idea to oblige students to take a course on latex. Students do need to learn to write, and they can be taught to use latex as part of being taught to write, if need be, but the basics of latex are easily learned independently, and students need to learn to learn things independently. What might not be obvious to students is that it ...


1

I think https://www.robocompass.com/ fits the bill... if you are ok with something code-driven, which for me is just an amazing bonus for my students and for exposition. So, the way in which robocompass deviates from rusty compass is directly related to a major potential benefit. Worth a look, anyway!


1

I worked with Jim Fowler and Bart Snapp on Ximera as a graduate student. It is still (to my knowledge) primarily being maintained by Jim Fowler. I would recommend contacting him at his Ohio State email address. I am not sure if this is the case, but one design issue we ran into with randomization is how frequently edge cases come up, and the wide ...


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