Digital audio myth debunked here with evidence in physics mathematics and chemistry. The chemical makeup of the vinyl record has influence on the physics and the mathematics of what your stylus and cardridge (moving magnet / moving coil) will pickup.

Be amazed at the fact that the signal remains smooth when going through AD DA conversion all the way up to the Nyquist frequency

Watch, listen and learn

https://www.youtube.com/watch?v=cD7YFUYLpDc

#Digital #physics #mathematics #Lineair #Algebra #chemistry #Analog #Signal #Audio #Vinyl #PA #Studio #Sound #Noise #Ratio #effects #faders #Yamaha #Behringer #Mackie #Focusrite #Nyquist

Testing inputs changes results, but these negatives still confuse me.

#math #algebra #learning

Drats! I've just seen a job posting for tutoring that requires algebra and Mandarin.

I knew I should have kept up my Mandarin. 😭

(I'm joking. Even at my best, I was intermediate in Mandarin. i had enough of it to get around Taiwan but not nearly enough to deal with tutoring math in that language.)

#Mandarin #algebra #tutoring

When abstract algebra morphs into ass crack algebra...

#algebra #AssCrack #ass

Introduction to Hp Spaces (Cambridge Tracts in Mathematics, Series Number 115) 2nd Edition by Paul Koosis (PDF)
Author: Paul Koosis
File Type: PDF
Download at https://sci-books.com/introduction-to-hp-spaces-cambridge-tracts-in-mathematics-series-number-115-2nd-edition-0521056810/
#Algebra, #PaulKoosis

I'm doing a review of basic #algebra, and was looking for something in #python #matplotlib to plot intervals on the number line. Didn't find anything, so I wrote this.

https://chesterjankowski.com/blog/plotting-intervals-on-the-number-line/

From Classical to Modern Algebraic Geometry: Corrado Segre's Mastership and Legacy (Trends in the History of Science) by Gianfranco Casnati (PDF)
Author: Gianfranco Casnati
File Type: PDF
Download at https://sci-books.com/from-classical-to-modern-algebraic-geometry-corrado-segres-mastership-and-legacy-trends-in-the-history-of-science-3319329928/
#Algebra, #GianfrancoCasnati

Introduction to Linear Algebra (5th Edition) 5th Edition by Lee W. Johnson (PDF)
Author: Lee W. Johnson
File Type: PDF
Download at https://sci-books.com/introduction-to-linear-algebra-5th-edition-5th-edition-0201658593/
#Algebra, #LeeW.Johnson

Basic Algebraic Geometry 1: Varieties in Projective Space 3rd Edition by Igor R. Shafarevich (PDF)
Author: Igor R. Shafarevich
File Type: PDF
Download at https://sci-books.com/basic-algebraic-geometry-1-varieties-in-projective-space-3rd-edition-b00edemdhm/
#Algebra, #IgorR.Shafarevich

Problems and Proofs in Numbers and Algebra 2015th Edition by Richard S. Millman (PDF)
Author: Richard S. Millman
File Type: PDF
Download at https://sci-books.com/problems-and-proofs-in-numbers-and-algebra-2015th-edition-331914426x/
#Algebra, #RichardS.Millman

TIL about M87 the Super Massive Black Hole in the Messier87 Galaxy

One internet article states its distance at 55x10⁶ light-years away. It spins at 860 x 10⁶ km/h!

Quotes from Wikipedia differ a bit

The black hole's mass = (6.5 ± 0.2stat ± 0.7sys) × 109 M☉.[76]

This is one of the highest known masses for such an object. A rotating disk of ionized gas surrounds the black hole, and is roughly perpendicular to the relativistic jet. The disk rotates at velocities of up to roughly 1,000 km/s (2,200,000 mph) or 1⁄300 the speed of light,[77]
^Z

#Nasa #Space #Astronomy #BlackHole #Physics #chemistry #telescope #mathematics #calculus #Linear #Algebra

https://en.wikipedia.org/wiki/Messier_87#Supermassive_black_hole_M87*?wprov=sfla1

An awsome galactic image captured by passionate astronomers

Brief: SDSO 1 is a new class of planetary nebula within our galaxy.

Read more on the page

#Nasa #Space #Astronomy #picture #of #the #Day #Physics #chemistry #telescope #mathematics #calculus #Linear #Algebra

https://apod.nasa.gov/apod/ap250804.html

Sirius in its Binary Dance with Sirius B are the brightest in the night sky. It's a gorgeous view of awsome galactic power watching this Blue Star. You can't see Sirius B with the eyes due to the difference in emitted Light. If you look in Canis Major you can see Sirius. To see both together you need a telescope.

Sirius is just 2.64 parsec away {very close}

Space is magnífico

#Nasa #Space #Astronomy #Physics #chemistry #telescope #mathematics #calculus #Linear #Algebra

https://en.wikipedia.org/wiki/Sirius?wprov=sfla1

I received and rejected my first plenary talk invitation recently. It was for the 2026 BLAST conference in Waco, Texas. Since I am transgender, it doesn't seem wise to visit Texas for any length of time. I told the conference organizers as much, and that I am disinclined to go anywhere I'm a second-class citizen.

As you can see at https://math.colorado.edu/blast/ I was one of the organizers for last year's BLAST meeting in Boulder, Colorado. I knew that the next two meetings would be in Texas and Indiana and passed along the same concerns (not just about trans people, but about women's safety) which I had already expressed to my fellow organizers in 2025. I got a polite response, but it's still tough to keep missing the next steps in my career progression because of things like this.

#math #academia #research #logic #algebra #topology #Texas #Colorado #Indiana #trans #transgender #feminism

#Mathematics #GroupTheory #Algebra #TheoreticalComputerScience

In my study (a while ago) I learned about Σ Algebras (theoretical computer science).
Then later, I learnt in math there are σ Algebras, which seems sort of the same thing.
Today I'm curious about group theory, and groups are also sort of the same thing.

Can anyone tell me what's the difference? Between Σ Algebras, σ Algebras, and groups?

I've always found it cool that if you double the smaller acute angle in a 3-4-5 triangle you get the larger acute angle in a 7-24-25 right triangle. You can see this as a consequence of the double angle formula for sine. If \( \alpha \) is the smaller acute angle in a 3-4-5 triangle, then

\[ \sin (2\alpha) = 2\sin\alpha\cos\alpha=2\frac{3}{5}\frac{4}{5}=\frac{24}{25}\]

In fact, if the sine and cosine of an angle are both rational, then so will be the sine and cosine of twice that angle. This gives a way to turn Pythagorean triples into new Pythagorean triples!

For example, suppose \( \alpha \) is an acute angle in a right triangle with \(a^2 + b^2 = c^2 \). Then

\[ \sin 2\alpha = \frac{2ab}{c^2} \]
\[ \cos 2 \alpha = \frac{a^2-b^2}{c^2} \]

By the Pythagorean identity

\[ \left(\frac{2ab}{c^2} \right)^2 + \left(\frac{a^2-b^2}{c^2} \right)^2 = 1\]

And so

\[ \left(2ab \right)^2 + \left(a^2-b^2 \right)^2 = \left(c^2\right)^2\]
which of course also follows directly from algebra.

For example, using this process

\[ (3,4,5) \mapsto (7,24,25) \mapsto(336,527,625)\]

#Math #MathEd #Mathematics #NumberTheory #Algebra #Geometry

An Introduction to Homological Algebra (Universitext) 2nd Edition by Joseph J. Rotman (PDF)
Author: Joseph J. Rotman
File Type: PDF
Download at https://sci-books.com/an-introduction-to-homological-algebra-universitext-2nd-edition-b00fb132s0/
#Algebra, #JosephJ.Rotman

Cohomological Methods in Homotopy Theory: Barcelona Conference on Algebraic Topology, Bellatera, Spain, June 4–10, 1998 (Progress in Mathematics, 196) 2001st Edition by Jaume Aguade (PDF)
Author: Jaume Aguade
File Type: PDF
Download at https://sci-books.com/cohomological-methods-in-homotopy-theory-barcelona-conference-on-algebraic-topology-bellatera-spain-june-4-10-1998-progress-in-mathematics-196-2001st-edition-3764365889/
#Algebra, #JaumeAguade

Arithmetic Duality Theorems by J. S. Milne (PDF)
Author: J. S. Milne
File Type: PDF
Download at https://sci-books.com/arithmetic-duality-theorems-141964274x/
#Algebra, #J.S.Milne

Boost your math skills with Beginning and Intermediate Algebra (6th Edition) by K. Elayn Martin-Gay. This eBook offers clear explanations, targeted exercises, and real-world applications. Perfect for self-study or class use.

ISBN: 978-0135837917
Note: eBook is a scanned PDF, no access codes included.

#Algebra #MathLearning #eBook  https://textbooks.dad/product/beginning-and-intermediate-al...
https://textbooks.dad/product/beginning-and-intermediate-algebra-6th-edition-ebook/?fsp_sid=4365