*Question (research)

within loc compact T2 groups,

+ what makes Lie groups different to prof. groups is that they have a small neighbourhood from which every closed subgroup escapes

+ and (locally) prof. groups don't have such a neighbourhood for open subgroups

(1/x)

within loc compact T2 groups,

+ what makes Lie groups different to prof. groups is that they have a small neighbourhood from which every closed subgroup escapes

+ and (locally) prof. groups don't have such a neighbourhood for open subgroups

(1/x)

It's sad we have to require small subgroups but not for closed subgroups but for something even much stronger

open subgroups

but that also means that there is a structure in between? what is it like?

open subgroups

but that also means that there is a structure in between? what is it like?

What are the locally compact Haussdorf groups G such that for every neighbourhood U of 1_G there is a closed nontrivial subgroup H \subseteq U...

...but still there is a neighbourhood U_0 of 1_G such that every open subgroup H of G escapes U_0?

#LieGroups #TopologicalGroups

...but still there is a neighbourhood U_0 of 1_G such that every open subgroup H of G escapes U_0?

#LieGroups #TopologicalGroups

Well @Justin_Bons that is why $DAG exists 😉

Let's explore together how @Conste11ation validates data at the edge and why Metagraphs are the perfect solution for integrating AI with Blockchain

#edgecomputing #EdgeData #BigData

Ready set go 🚀

Down the #HGTP rabbit hole 👇

Let's explore together how @Conste11ation validates data at the edge and why Metagraphs are the perfect solution for integrating AI with Blockchain

#edgecomputing #EdgeData #BigData

Ready set go 🚀

Down the #HGTP rabbit hole 👇

AI is only as good as its data. With the rise of IoT devices and real-time data processing, the need for efficient and scalable edge computing solutions is paramount. Enter HGTP and Metagraphs by @Conste11ation $DAG #AI #EdgeComputing

“Academic Preparation for College: What Students Need to Know and Be Able to Do” 1983, @CollegeBoard: “In social studies, a grasp of major trends in the contemporary world such as nationalism and urbanization; the ability to recognize historical cause and effect;

a grasp of United States history in terms of the chronology and impact of political events,

development of governmental and social institutions, technological and environmental changes and changes in values.”

The significance of #mathematics in #cryptography is immense. 𝐂𝐫𝐲𝐩𝐭𝐨𝐠𝐫𝐚𝐩𝐡𝐲 involves the process of transforming messages to ensure secure communication. In this thread, we'll explore the integral role of math within cryptography & present some relevant equations (1/9)

One of the simplest examples of cryptography is the Caesar cipher, which shifts the letters of the alphabet by a fixed number. The encryption function can be written as: E(x) = (x + k) mod 26, where x is the letter's position, k is the shift, and mod is the modulo operation.(2/9)

Public-key cryptography is a more advanced technique that relies on mathematical concepts. RSA, a widely-used public-key cryptosystem, involves the generation of two large prime numbers, p and q. Their product, n = p * q, is used in encryption and decryption.(3/9)

@yessmanstu @GeraldKutney @goddeketal Military or no military,

the climate is changing fast

bc of increased carbon dioxide

in the infrared zone

of the atmosphere.

The physical properties

of carbon dioxide

include interacting

w long wave infrared energy

passing through.

FAQs here news.climate.columbia.edu/2021/02/25/car…

the climate is changing fast

bc of increased carbon dioxide

in the infrared zone

of the atmosphere.

The physical properties

of carbon dioxide

include interacting

w long wave infrared energy

passing through.

FAQs here news.climate.columbia.edu/2021/02/25/car…

@yessmanstu @GeraldKutney @goddeketal This is a similar explanation to how other molecules (with different properties) absorb different wavelengths of light (energy)

#physics #STEMeducation

Every molecule is different, and it has to do w how many electrons can move and change their orbitals

chem.libretexts.org/Bookshelves/Ph…

#physics #STEMeducation

Every molecule is different, and it has to do w how many electrons can move and change their orbitals

chem.libretexts.org/Bookshelves/Ph…

@yessmanstu @GeraldKutney @goddeketal Molecular orbital diagrams talk about where electrons likely are in any given combination of elements. chem.libretexts.org/Bookshelves/In…

For CO2 the way the electrons spin depends on how much energy the molecule has, and the levels look like this (MO diagram from flickr.com/photos/6905729…)

For CO2 the way the electrons spin depends on how much energy the molecule has, and the levels look like this (MO diagram from flickr.com/photos/6905729…)

She is Gladys West, one of the mathematians responsible for developing GPS, a technology that has changed the way we play, work, navigate, and explore our communities..

"When you're working every day, you're not thinking, 'What impact is this going to have on the world?' You're thinking, 'I've got to get this right,'" West once said in an interview with The Associated Press.

Despite suffering major stroke,heart surgery and cancer,

Despite suffering major stroke,heart surgery and cancer,

She was working for most of her life. Now at 92, she has written her memoir and going strong.

Hats off to this role model.

#funtrivia #mathematics #technologies

Hats off to this role model.

#funtrivia #mathematics #technologies

Machine Learning is hard.

I felt like quitting whenever I get baffled by the amount of information to learn.

But I followed the path to learning from Math for ML.

Here are the 5 critical reasons why you should start with Math concepts for ML

THREAD🧵 ↓

I felt like quitting whenever I get baffled by the amount of information to learn.

But I followed the path to learning from Math for ML.

Here are the 5 critical reasons why you should start with Math concepts for ML

THREAD🧵 ↓

🤔 Why Math for ML:

**********************

📌 Machine learning algorithms rely on mathematical calculations to make predictions and decisions

**********************

📌 Machine learning algorithms rely on mathematical calculations to make predictions and decisions

📌 Many machine learning techniques, such as neural networks and deep learning, are based on linear algebra and calculus

SRINIVASA RAMANUJAN: An Enigmatic Genius

By K. Srinivasa Raghava.

This December 22 marks the 135th birth anniversary of our own great mathematician Srinivasa Ramanujan-FRS and is observed as National Mathematics Day (GANIT).

1/n

By K. Srinivasa Raghava.

This December 22 marks the 135th birth anniversary of our own great mathematician Srinivasa Ramanujan-FRS and is observed as National Mathematics Day (GANIT).

1/n

The man who brought India to the World Mathematics Map is regarded as one of the greatest thinkers of the modern world without any formal education in Mathematics. Dreamt and it’s there is not always possible for a normal person without ample effort.

2/n

2/n

But the story is different for Ramanujan, a self-taught mathematician, who in his 32 years of life span on this earth has gifted his dreams to the whole world and never shied from making the effort to any extent.

3/n

3/n

Since the capital of India moved from #Calcutta (Kolkata) to #Delhi, for some reason the hatred for Mukherjees became evident. I can guess why #RajaJoykrishna was wiped out, but why his younger cousin #SirAshutoshMukherjee? If you are a student of #Mathematics, have u ever (1/n)

(2/n) been taught "Mookerji Theorems"? While Raja Joykrishna Mukherjee was the architect of #CalcuttaUniversity (I will be publishing the complete proposal he gave to Cecil Beadon) the 3 biggest financial contributors were Sir Ashutosh, Taraknath Palit and eminent barrister++

(3/n) Rashbehari Ghose.

Trivia: There is a debate whether Rashbehari Avenue is named after Rashbehari Bose of Rashbehari Ghose. Their GGG Grandson is a good friend of mine and interestingly there is rift in the family over this. Bose was from his mother's side while Ghose.....

Trivia: There is a debate whether Rashbehari Avenue is named after Rashbehari Bose of Rashbehari Ghose. Their GGG Grandson is a good friend of mine and interestingly there is rift in the family over this. Bose was from his mother's side while Ghose.....

Close your eyes, get on the time machine and imagine the period between 24th August 1808 and 1900. Elder cousin brother #RajaJoykrishnaMukherjee sets up 59 schools in 1 month in #Bengal, a record no has broken globally, sets up Indian Cultivation of Science & Calcutta (1/n)

(2/n) University that produced the greatest scholars in the world while younger brother #SirAshutoshMukherjee contribution in the field of #Mathematics led to his appointment as a Fellow of the Royal Astronomical Society and a Member of the Royal Society of Edinburgh in +++

(3/n) (at the age of 21), a Fellow of the Royal Society of Edinburgh, a Member of the Royal Asiatic Society and a Member of the Bedford Association for the Improvement of Geometrical Teaching in 1886, a Fellow of the London Physical Society in 1887+++

Raconte moi l'histoire des nombres en mathématiques en développant ton propos.

Rien sur les chiffres Arabes et les nombres Romain ?

A quoi sert la notation scientifique et pourquoi les physiciens adorent les unités ?

#OpenAI #Mathematics 2/8

Rien sur les chiffres Arabes et les nombres Romain ?

A quoi sert la notation scientifique et pourquoi les physiciens adorent les unités ?

#OpenAI #Mathematics 2/8

Raconte moi l'histoire des fonctions en mathématiques en développant ton propos.

#OpenAI #Mathematics 3/8

#OpenAI #Mathematics 3/8

How I (a #neurologist) helped a student pass in #Mathematics, which his Mathematics teacher couldn't manage

1. A 15-year old boy was brought to my clinic by his parents asking for some "pill" that would improve his interest and skill in mathematics, enabling him to pass exams

1. A 15-year old boy was brought to my clinic by his parents asking for some "pill" that would improve his interest and skill in mathematics, enabling him to pass exams

2. He was a bright class 10th kid doing well in all the subjects except in mathematics. His scores were 85-90% in other subjects, with <30% in mathematics. This appeared odd to me. On enquiry, the boy told "my mind switches off when solving complex mathematical problems".

3. The boy continued "my mind keeps on lapsing into absent-mindedness several times during exams" and "before I realize- the time is up". As per his teachers & parents, his answer sheet had many areas of ineligible scribbling. The initial part of answer would be correct though.

There are hundreds of online resources for learning how to code.

But there are much fewer online resources for math.

Maybe that's because LaTeX (the premier math writing tool) isn't good at creating them.

#QuartoPub can do both. So, is it a worthy alternative?🧵 #mathematics

But there are much fewer online resources for math.

Maybe that's because LaTeX (the premier math writing tool) isn't good at creating them.

#QuartoPub can do both. So, is it a worthy alternative?🧵 #mathematics

What is Quarto?

Short answer: It's a tool that can create many output formats all from one interface.

That means you can create classical PDF math papers as well as online math books with Quarto.

Short answer: It's a tool that can create many output formats all from one interface.

That means you can create classical PDF math papers as well as online math books with Quarto.

You may be sceptical about the online part. Maybe you have only seen math in PDF format.

But I assure you that it's a real thing. And it's powerful.

For example, every day hundreds of mathematicians on MathOverflow talk about research-level math online. mathoverflow.net

But I assure you that it's a real thing. And it's powerful.

For example, every day hundreds of mathematicians on MathOverflow talk about research-level math online. mathoverflow.net

There are hundreds of online resources for learning how to code.

But there are much fewer online resources for math.

Maybe that's because LaTeX (the premier math writing tool) isn't good at creating them.

#QuartoPub can do both. So, is it a worthy alternative?🧵 #mathematics

But there are much fewer online resources for math.

Maybe that's because LaTeX (the premier math writing tool) isn't good at creating them.

#QuartoPub can do both. So, is it a worthy alternative?🧵 #mathematics

What is Quarto?

Short answer: It's a tool that can create many output formats all from one interface.

That means you can create classical PDF math papers as well as online math books with Quarto.

Short answer: It's a tool that can create many output formats all from one interface.

That means you can create classical PDF math papers as well as online math books with Quarto.

You may be sceptical about the online part. Maybe you have only seen math in PDF format.

But I assure you that it's a real thing. And it's powerful.

For example, every day hundreds of mathematicians on MathOverflow talk about research-level math online. mathoverflow.net

But I assure you that it's a real thing. And it's powerful.

For example, every day hundreds of mathematicians on MathOverflow talk about research-level math online. mathoverflow.net

Ever wondered what a fake journal in #mathematics looks like? Follow me down the rabbit hole. I'll show you one that slipped on the slippery slope of #goldOA. #openScience #math #fakeJournal #openAccess. 👇🧵

Let me introduce you to ejpam.com/index.php/ejpa…, the European Journal of Pure and Applied Mathematics (EJPAM).

It's run by a company in Maryland, USA called "New York Business Global". This is their homepage: nybusinessglobal.com

⚡Aeroelastic Flutter⚡

The Tacoma Narrows bridge disaster of 1940 attribute the collapse of the bridge due to aeroelastic flutter.

🧵👇

The Tacoma Narrows bridge disaster of 1940 attribute the collapse of the bridge due to aeroelastic flutter.

🧵👇

1️⃣ Flutter is a dangerous phenomenon encountered in flexible structures subjected to aerodynamic forces. Flutter occurs as a result of interactions between aerodynamics, stiffness, and inertial forces on a structure.

2️⃣ In an aircraft, as the speed of the wind increases, there may be a point at which the structural damping is insufficient to damp out the motions which are increasing due to aerodynamic energy being added to the structure.

#ConradMitzenmacher-7

"A. Notation and Terminology

Throughout this paper, the phrase ›log-ratio‹ for a pair of positive real numbers refers to the ratio of their logarithms (to a common base, the choice of which cancels out)..

All logarithms without an indicated base

>

"A. Notation and Terminology

Throughout this paper, the phrase ›log-ratio‹ for a pair of positive real numbers refers to the ratio of their logarithms (to a common base, the choice of which cancels out)..

All logarithms without an indicated base

>

>are understood to be taken to the base 𝑒..

II. Review of Definitions and History

Our treatment here is based on a recent survey by Mitzenmacher [#Internet #Mathematics 1(2), 226‒251 (2004)], to which we refer the reader for more information.[ Footnote: For instance,

>

II. Review of Definitions and History

Our treatment here is based on a recent survey by Mitzenmacher [#Internet #Mathematics 1(2), 226‒251 (2004)], to which we refer the reader for more information.[ Footnote: For instance,

>

>this survey describes another argument that leads to a #PowerLaw of word frequency based on preferential attachment, originally due to Simon [Biometrika 42(3/4), 425–440 (1955)]. We do not present this argument here.]

In what follows, we let 𝑓ⱼ be the (asymptotic) fraction of>

In what follows, we let 𝑓ⱼ be the (asymptotic) fraction of>

Calculus, Pythagoras theorem, and other equations driving you crazy?

AppsHive has listed down 𝐌𝐚𝐭𝐡𝐬 𝐅𝐨𝐫𝐦𝐮𝐥𝐚 𝐀𝐩𝐩𝐬 required by beginners, intermediate and expert level mathematicians

#appshivrecommends #maths #Math #Mathematics #mathematician #apps

A thread📜

AppsHive has listed down 𝐌𝐚𝐭𝐡𝐬 𝐅𝐨𝐫𝐦𝐮𝐥𝐚 𝐀𝐩𝐩𝐬 required by beginners, intermediate and expert level mathematicians

#appshivrecommends #maths #Math #Mathematics #mathematician #apps

A thread📜

1) @symbolab

What we liked:🤩

👉Have a private tutor for every math problem step by step

👉Provide step-by-step detailed explanations

👉Has 100+ most powerful and different types of calculators to use

👉Fast calculations, shows steps, has an option to check your answer

What we liked:🤩

👉Have a private tutor for every math problem step by step

👉Provide step-by-step detailed explanations

👉Has 100+ most powerful and different types of calculators to use

👉Fast calculations, shows steps, has an option to check your answer

2) @mathway

What we liked:🤩

👉Can snap or crop and paste the photo of any math problem

👉You can choose between multiple subjects

👉Provides an instant graph of your problem

👉Provide books and the teacher video lectures

What we liked:🤩

👉Can snap or crop and paste the photo of any math problem

👉You can choose between multiple subjects

👉Provides an instant graph of your problem

👉Provide books and the teacher video lectures

⏳4592307816 Occurs at position 60 in π. It includes the ten numbers. 666 relating to 6x6x6=216. 216 relating to the diameter of the moon 2160 Miles. 351, 26th Triangular. 26 letters in the English alphabet. 60, a whole when taking about time. 22/7=3.14... 2083 the 314th prime⌛️

DRILLING SOAL PENGETAHUAN KUANTITATIF (PK) UTBK: REVIEW MATERI CAMPURAN.

📷Latsol + Video Pembahasan #BelajarEmtekaDalam2Menit📷

EDISI FINALLL MENUJU UTBK 2022. Yuk, review tipis2 materi campuran PK, pemanasan sblm UTBK!

#belajaremteka #studytwt #AMBISVERSE #mathematics

📷Latsol + Video Pembahasan #BelajarEmtekaDalam2Menit📷

EDISI FINALLL MENUJU UTBK 2022. Yuk, review tipis2 materi campuran PK, pemanasan sblm UTBK!

#belajaremteka #studytwt #AMBISVERSE #mathematics

PEMBAHASAN DRILLING SOAL PENGETAHUAN KUANTITATIF (PK) UTBK: LIMIT FUNGSI ALJABAR (TIPE SOAL UTBK 2021).

📷Disertai Video Pembahasan📷

Berisi pembahasan 10 soal limit biar makin satset ngerjain soal UTBK!

#belajaremteka #BelajarEmtekaDalam2Menit #studytwt #UTBK #mathematics

📷Disertai Video Pembahasan📷

Berisi pembahasan 10 soal limit biar makin satset ngerjain soal UTBK!

#belajaremteka #BelajarEmtekaDalam2Menit #studytwt #UTBK #mathematics

Biar paham basicnya, baca dulu pembahasan konsep limit + pembahasan soal limit PK UTBK 2021 yuuuk⬇️

Soal-soal yang dibahas di thread ini, barangkali mau kerjain sendiri duluuu sblm liat pembahasan~

DRILLING SOAL PENGETAHUAN KUANTITATIF (PK) UTBK: LIMIT FUNGSI ALJABAR (TIPE SOAL UTBK 2021).

Thread ini berisi 10 soal limit buat nguji & refresh pemahamanmu di H-2 UTBK. Gas, kerjain semuanya!

#belajaremteka #studytwt #UTBK #mathematics

Thread ini berisi 10 soal limit buat nguji & refresh pemahamanmu di H-2 UTBK. Gas, kerjain semuanya!

#belajaremteka #studytwt #UTBK #mathematics

Sebelum kerjain soal yang ada di sini, plsss baca pembahasan soal limit UTBK 2021 dulu yaa, biar bs ngerjainnya⬇️😄

Udah baca thread di atas? OK berarti kamu udh shiappp utk latsol!

🚨Petunjuk🚨

Soal nomor 1-5 saling berhubungan (nyambung).

Soal nomor 6-10 saling berhubungan (nyambung).

🚨Petunjuk🚨

Soal nomor 1-5 saling berhubungan (nyambung).

Soal nomor 6-10 saling berhubungan (nyambung).

There is a beautiful way to derive the famous Euler’s formula!

In this🧵, I’ll explain a visual, intuitive derivation. It’ll fit into a single picture at the end.

#iteachmath #MTBoS #math #maths #Mathematics

In this🧵, I’ll explain a visual, intuitive derivation. It’ll fit into a single picture at the end.

#iteachmath #MTBoS #math #maths #Mathematics

This is Thread 3 in a series, but don't worry! This thread is self-contained.

In Thread 1, we saw applications of a mass on a spring.

We solved for its future position, at time 𝑡. This led to 𝑒^(𝑖𝑡), but 𝑖 is "imaginary."

The position along the ground had to be “real,” so we sought to interpret 𝑒^(𝑖𝑡) in terms of real numbers.

We solved for its future position, at time 𝑡. This led to 𝑒^(𝑖𝑡), but 𝑖 is "imaginary."

The position along the ground had to be “real,” so we sought to interpret 𝑒^(𝑖𝑡) in terms of real numbers.

Hence the absolute need to get out of this voluntary submission system established for at least 300 years.

If you have any suggestions, put them below.

Be creative & let's brainstorm together to perhaps allow us to break these chains of oppression.

#Psychologicalreactance

⛎

If you have any suggestions, put them below.

Be creative & let's brainstorm together to perhaps allow us to break these chains of oppression.

#Psychologicalreactance

⛎

#Naturopathy

#Herbalism

#Phytotherapy

#Nutraceuticals

#AilanthusAltissima (Mill.) Swingle, 1916

False Japanese varnish, Ailante, Ailanth

« Dwarf Ailanthus is also sometimes nicknamed "the tree of hell" because of its invasive nature and the difficulty of eradicating it. »

#Herbalism

#Phytotherapy

#Nutraceuticals

#AilanthusAltissima (Mill.) Swingle, 1916

False Japanese varnish, Ailante, Ailanth

« Dwarf Ailanthus is also sometimes nicknamed "the tree of hell" because of its invasive nature and the difficulty of eradicating it. »