Important new study of college #calculus instruction https://www.science.org/doi/10.1126/science.ade9803

we’ll, okay, I have some issues with how multiplications are defined in (this presentation of) smooth infinitesimal analysis, leading to the field of infinitesimals (instead of the “usual” field of reals).

I think Bell’s approach here may be too brief, and he could do more to distinguish the category theoretic definition from the traditional Dedekind definition.

Of course, he’s trying to keep the resulting calculus familiar and digestible, and not overwhelm the reader with topos needed to generate viable axioms for SIA.

My concern is that if I have to relearn the foundations before reassuring myself that the calculus is well-defined—and only with “nice” functions representable by Taylor series—then that’s a big challenge 🥲

#calculus #analysis #CategoryTheory

#mathematics #math #maths #mathstodon #mathématiques #calculus #calcul
Les mathématiques auraient pu être aussi simples ?!🙄
(vous pouvez prouver vous-mêmes que ce n'est pas une règle de calcul correcte, très facilement ... )

#mathematics #maths #mathématiques #mathstodon #calculus
On me pose cette question (pour me saborder ma sieste!😉):
Que vaut cette expression ?

6 2 + 5 x 3 6 + -

Répondez en mode CW + n'hésitez pas à BOOSTER.

#mathematics #maths #mathématiques #mathstodon #calculus
On me pose cette question :
Que vaut cette expression ?

6 2 + 5 x 3 6 + -

Répondez en mode CW + n'hésitez pas à BOOSTER.

meditative https://youtu.be/XfWgfZ5V2qI #math #calculus

0^0 | Hacker News

"P6] Existence of a multiplicative identity: a * 1 = 1 * a = a ; 1 /= 0.

- [P7] Existence of multiplicative inverses: a * a^(-1) = a^(-1) * a = 1, for a /= 0.

These are taken from page 9 of Spivak's Calculus, 3rd edition. He goes on to build the foundations of all of calculus from rules like these"
https://news.ycombinator.com/item?id=7519827#:~:text=P6%5D%20Existence%20of,rules%20like%20these
#calculus

I feel like @cosmician is turning to the dark side of Math which is lambda calculus.

#math #mathematics #lambda #calculus #lambda_calculus

UA: Всім привіт! Чи може мені хтось порекомендувати крутий ЮТуб-канал по математиці як 3blue1brown? Дякую наперед ☺️

EN: Hi all! Would someone recommend me a really cool #YouTube channel about #maths like 3blue1brown? Thanks in advance ☺️

#mathematics #algebra #geometry #calculus #математика #алгебра #геометрія

For example: I had a #calculus (2H) tutor at one point who would have us solve Very Cartesian Integration Problems™ using polar coordinate transforms (@futurebird may appreciate this). It was absolutely the wrong thing to do if you actually wanted to solve the problem quickly, but it broke the mindset about there being a "right" way to solve it and developed confidence and mastery with polar transformations (because if you can do it on a y = -ax + b line you can _definitely_ do it on a curve).

@cosmology Write 't' for time and rewrite the statements:

(1) 'Time can go backwards (with respect to itself)'

as

'dt/dt < 0 is possible'

and (2) 'Time can slow down (with respect to itself)'

as

'dt/dt < 1 is possible'.

But dt/dt = 1 #Calculus

dt/dt cannot be < 0 or < 1

** #Time cannot go backwards or slow down with respect to itself! **

The cognitive confusion in vaguer statements is in the (usually unstated) second variable; dt/dt' < 0 and dt/dt' < 1 are possible only if t' != t .

Finished my syllabi today for my 3 classes. I'm teaching #algebra2, Precalculus, and AP #Calculus. I'm hoping I am not out of my depth. Though I believe it will be easier than the Algebra 1 classes I had last year, as those were all Freshmen and this year should be mostly Seniors. At least I feel a little bit better having gotten an idea of my classroom procedures and how they are changing from last year.

#teaching #teacher #education #backtoschool

Maybe calculus could help us understand this paradox?

#Calculus #YouTube #Jokes

[PT] O calculo matricial necessário para entender o Deep Learning;
[EN] The #Matrix #Calculus You Need For #Deep #Learning,

https://explained.ai/matrix-calculus/

The book *Grading for Growth* by @dccmath and @RobertTalbert is now available! Read about it and find the link to order on their Substack: https://gradingforgrowth.com/p/grading-for-growth-the-book-is-now

My calculus class appears as a case study in chapter 5 (“Standards-Based Grading”) as a fairly straightforward example. Of course I’ve made a few changes in the system even since I did this interview 😉 but I think it still stands as a good reference for anyone considering an SBG or other alternative grading system.

Check it out!

#Grading #GradingForGrowth #Teaching #AlternativeGrading #StandardsBasedGrading #SBG #Calculus

It's going to be interesting teaching concavity as a topic in AP Precalculus this year. To help my students remember the difference between concave up and concave down, I decided to make some fun new posters for my classroom!

Concave Up like a CUP
Concave Down like a FROWN

https://mathequalslove.net/concavity-posters/

#mtbos #iteachmath #classroommath #mathed #APPrecalculus #calculus #APCalculus

Something new I think I'll try with my calculus class this coming year is tasking them with developing a rigorous definition of the relation

\[ a \approx b\]

and determining which properties (reflexive, symmetric, addition, etc) this relation has.

I think this could help both with their understanding of \( \epsilon - \delta\) proofs and the concept of linearization (i.e. \(f(x + h) \approx f(x) + h f'(x)\)).

#Math #MathEd #Calculus

Just wanted to share a little milestone on my journey. This morning I got the results for the first module in my Pure #Mathematics BSc degree from the #openuniversity. I've been working hard on that for most of the past year and I really proud that I was awarded a distinction grade.

#Mathematics and other technical topics don't come easily to me so I'm very happy with the result. There's a lot of effort / struggle / time spent behind it. Happy to have had some good role models and encouragement along the way. Looking forward to the next two modules which start formally in October! We get to dive into #linearalgebra and #calculus. Exciting! 🤓

A Curious Family of Integrals that Always Give \(\pi\)!

I wonder if it is possible to characterize \(\frac{P(x)}{Q(x)}\) such that by inspection we can say: this is \(n\pi\). Travis has commented that the denominator has a special Galois group. Does anybody know who can answer this question at MathSE:
https://math.stackexchange.com/questions/4736889/a-curious-family-of-integrals-that-give-pi?noredirect=1#comment10046166_4736889

#math #calculus #integral #rationalfunctions #pi

Now an integral involving the silver ratio: https://geometriadominicana.blogspot.com/2023/07/an-integral-involving-golden-ratio.html?fbclid=IwAR0Q8aVBR9naL5DIMFhgsV2t-HsaCAQGDKkGRnKVvnpHIlyewuALpWIhrQo&m=1
#math #calculus #integral #trigonometry #silverratio