eka-mark

I teach people math.

[eka-mark]

Teaching an intro to robotics for the past month or so has been very interesting. I think I'll integrate some of this material into my usual classical mechanics and multivariable calculus courses. Small manipulator robots with just a few links make for some great exercises and examples.

[eka-mark]

There is no functor from the category of finite sets and functions to itself that maps n-element sets to F(n)-element sets, where F(n) is the nth Fibonacci number.

[eka-mark]

Where to Find the Colors Your Screen Can’t Show You

An atlas of the vibrance of the real world

Green traffic lights are a beautiful indescribable turquoise, the most intense turquoise you’ve ever seen. You’ll feel crazy once you see it, and want to run around telling everyone. Green traffic lights not only aren’t green, but they’re also exquisitely beautiful.

[eka-mark]

Hi, Mark.

I'm Joe from Nigeria. I'm looking to get into math tutoring myself. I love math a lot. I have a degree in computer engineering and the parts of my degree that I really enjoyed were the courses that were math dependent and involved lots of problem solving. Courses like Engineering maths, Control Engineering, digital electronics, power electronics etc. I tutored in the University but I was only ever paid once for it. I have experience from my service year(in Nigeria, you get deployed to a state that's not your state of residence where you get posted to an organisation after a three weeks camp and then you serve the country for a whole year) where I taught several subjects like math, computer science, basic science etc.

Do you have any advice for someone starting out like me who's wants to tutor online?

Thanks in advance, Mark. 🙏🏾

I can only offer very generic advice without knowing more (which I'll do below), but I'd be happy to chat with you about this if you book a free consultation with me on my website.

Focus on helping students with whatever they say their goals are, try to make sure they actually master material before moving on (even if this means covering less material), make it easy for them to pay you, and encourage successful students to recommend you to people they know.

[eka-mark]

[A]lmost every teacher has experienced telling a student a certain mathematical fact ... only to have them demonstrate on a test that they have not learned it. Such experiences suggest that it is not enough for students simply to be told information if we want to produce deep and meaningful learning.

What Does Active Learning Mean For Mathematicians?

Benjamin Braun, Priscilla Bremser, Art M. Duval, Elise Lockwood, and Diana White

[eka-mark]

This week, I get to show somebody one of my favorite math book figures, illustrating Liouville's theorem in Hamiltonian mechanics:

[soballoonist]

hey op, what book is this?

[eka-mark]

(x)

[eka-mark]

It's awfully considerate of nonempty finite sets to have an equal number of odd-sized and even-sized subsets.

(Hint: apply the binomial theorem to (-1+1)^n.)

[eka-mark]

Looks like I'll be tutoring a highschool student over the summer. I told them to blink twice if their parents are making them do this against their will.

[eka-mark]

This week, I get to show somebody one of my favorite math book figures, illustrating Liouville's theorem in Hamiltonian mechanics:

[eka-mark]

One can display infinitely many pairs of nonisomorphic simple groups having the same finite order, but the classification of the finite simple groups shows that there do not exist three nonisomorphic simple groups of the same order.

Joseph J. Rotman, An Introduction to the Theory of Groups

[eka-mark]

“Despite being one of the most familiar and widely recognized natural phenomena, lightning remains relatively poorly understood. Even the most basic questions of how lightning is initiated inside thunderclouds and how it then propagates for many tens of kilometers have only begun to be addressed.”

— Joseph Dwyer & Martin Uman, The physics of lightning (2014)

[eka-mark]

I'd like to reiterate this because of the recent Quanta article on this subject.

[tpwrtrmnky]

Like. Look. Listen. I have taught introductory quantum physics at a university level, and I need you all to incorporate this into your trans advocacy: There are situations where you need to make a decision to prioritize being comprehensible to your target audience above being The Most Unassailably Correct.

[eka-mark]

I also teach quantum physics sometimes. I'd love to hear about the compromises of this nature that you've found useful, if you'd like to expand on this! Do you have in mind things like ignoring the subtleties of the spectral theory of unbounded operators on Hilbert space, in favor of a more "everything is just linear algebra" approach, for example?

[eka-mark]

My former students keep recommending me to their friends by saying I'm a better math tutor than any LLM. :)

[eka-mark]

How cool is it that a category object in the category of groups is the same thing as a group object in the category of categories (or even in category of groupoids)? There's just no obvious reason why swapping the words "groups" and "categories" should lead to equivalent definitions. I guess this is one of those cases in which category theory validating all the things you would want to be true.

I've been reading this short expository article, which explains the relationships between these and crossed modules, all of which are apparently incarnations of (strict?) 2-groups. I don't understand crossed modules at all yet, but I'm looking forward to working out for myself what the smallest finite strict 2-groups are, concretely. Maybe later this year I'll be able to read Baez & Lauda's notes on 2-groups.

It's crazy that category theorists use the term "2-group", though, since that has long meant something totally different in group theory: a 2-group in the original sense is a group whose elements all have order a power of 2, which is a completely unrelated concept.

[eka-mark]

Happy Euler Day to all who celebrate!

[eka-mark]

In honor of the equinox, here's a simple derivation of an accurate formula for the position of the Sun in the sky (at a given date and latitude): https://arxiv.org/abs/1208.1043. It makes for a nice supplement to a classical mechanics course.

[eka-mark]

Accurate reckoning. The entrance into the knowledge of all existing things and all obscure secrets.

opening lines of the Rhind Mathematical Papyrus, c. 1550 BC

(source for this translation)