#group-theory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #group-theory, aggregated by home.social.
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Groups, Fields, and Galois: Part 1 | UCLA Extension
Dr. Michael Miller, a retired researcher at RAND, has been teaching upper level undergraduate/graduate level math courses for fun at UCLA Extension for over 50 years. This fall he'll be introducing the areas of groups, fields, and Galois theory from abstract algebra to those interested in abstract math: Groups, Fields, and Galois: Part 1. His intention is to do a follow-on class on Galois theory in the Winter which will use this class as a foundation. If you're in the Los Angeles area his […]https://boffosocko.com/2026/08/13/groups-fields-and-galois-part-1-ucla-extension/
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MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
MVspa_ Stochastic processes
Стохастические процессы, Випадкові процеси
#Stochastic processes
#Стохастическиепроцессы, #Випадковіпроцеси
t.me/scilib_yura15cbx/230MVsa Statistics and applications
Статистика та додатки, Статистика и приложения
#Statistics
t.me/scilib_yura15cbx/229EM_ Mechanics of elastic materials
Механіка пружних матеріалів, Механика упругих материалов
t.me/scilib_yura15cbx/228MPd_ Dynamical systems
Динамические системы, Динамічні системи
#Dynamical systems
t.me/scilib_yura15cbx/227MNw_ Wavelets, signal processing
Вейвлети, обробка сигналів, Вейвлеты, обработка сигналов
#Wavelets, #signal processing
t.me/scilib_yura15cbx/226MNs_ Simulations of physics
Физические симуляции
t.me/scilib_yura15cbx/225MNl_ Numerical linear algebra
Числова лінійна алгебра, Численная линейная алгебра
t.me/scilib_yura15cbx/224MNf_ Finite elements
Конечные элементы, Скінченні елементи
t.me/scilib_yura15cbx/223MNd_ Numerical calculus
t.me/scilib_yura15cbx/222MDgt_ General topology
#topology
Общая топология, Загальна топологія
t.me/scilib_yura15cbx/221MDdg_ Differential geometry
Диференціальна геометрія, Дифференциальная геометрия
t.me/scilib_yura15cbx/220MDat_ Algebraic and differential topology
Алгебраическая и дифференциальная топология, Алгебраїчна та диференціальна топологія
t.me/scilib_yura15cbx/219MCv_ Variational calculus
Варіаційне числення, Вариационное исчисление
t.me/scilib_yura15cbx/218MCta_ Tensor calculus, forms
Тензорное исчисление, формы, Тензорне числення, форми
t.me/scilib_yura15cbx/217MCsf_ Special functions
Спеціальні функції, Специальные функции
t.me/scilib_yura15cbx/216MCf_ Functional analysis
Функциональный анализ, Функціональний аналіз
t.me/scilib_yura15cbx/215MCet_ Elementary calculus textbooks
Підручники з елементарного числення, Учебники по элементарному исчислению
t.me/scilib_yura15cbx/214MCde_ Differential equations
Дифференциальные уравнения, Диференціальні рівняння
#Differential equations
t.me/scilib_yura15cbx/213MCcf_ Continued fractions
Суцільні дроби, Непрерывные дроби
t.me/scilib_yura15cbx/212MCc_ Complex variable
Комплексная переменная, Комплексна змінна
t.me/scilib_yura15cbx/211MCat_ Advanced calculus
t.me/scilib_yura15cbx/210Asymptotics, perturbations
Асимптотика, збурення,
Асимптотика, возмущения
#Asymptotics, #perturbations
#Асимптотика, #збурення,
#Асимптотика, #возмущения
t.me/scilib_yura15cbx/209Group theory, Теория групп, Теорія груп
#Group theory, #Теориягрупп, #Теоріягруп
t.me/scilib_yura15cbx/208Algebra textbooks,
Підручники з алгебри,
Учебники по алгебре
t.me/scilib_yura15cbx/207Set theory,
Теория множеств, Теорія множин
#Set theory,
#Теория множеств,
t.me/scilib_yura15cbx/206Representation theory
Теорія репрезентації, Теория представлений
t.me/scilib_yura15cbx/205Quantum groups
#Quantum groups
Квантовые группы, Квантові групи
t.me/scilib_yura15cbx/204Mathematical logic
#Mathematical logic
Математична логіка, Математическая логика
t.me/scilib_yura15cbx/203Linear algebra
#Linear algebra
Линейная алгебра, Лінійна алгебра
t.me/scilib_yura15cbx/202Homology, Гомологія, Гомология
#Homology, #Гомологія, #Гомология
t.me/scilib_yura15cbx/201Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Algebraic geometry
#Algebraic geometry
Алгебраическая геометрия, Алгебраїчна геометрія
t.me/scilib_yura15cbx/200Finite groups
Скінченні групи, Конечные группы
t.me/scilib_yura15cbx/199Differential algebra
#Differential algebra
Дифференциальная алгебра, Диференціальна алгебра
t.me/scilib_yura15cbx/198Category theory
Теорія категорій, Теория категорий -
#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?
-
#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?
-
Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.
\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]
The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.
The riff and rote for 2026 are shown in the next two Figures.
Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.pngRote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotescc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.
\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]
The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.
The riff and rote for 2026 are shown in the next two Figures.
Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.pngRote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotescc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
A section of a group G is a quotient of a subgroup, viz. K normal in H subgroup of G, the section is H/K.
Does anyone know if there is a more-or-less standard terminology not just for the section-up-to-isomorphism-of-the-group-H/K, but for the "instantiated" or maybe "concrete" section, e.g. the pair (K,H)?
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A section of a group G is a quotient of a subgroup, viz. K normal in H subgroup of G, the section is H/K.
Does anyone know if there is a more-or-less standard terminology not just for the section-up-to-isomorphism-of-the-group-H/K, but for the "instantiated" or maybe "concrete" section, e.g. the pair (K,H)?
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algebra final tmrw 😤 watch me cook
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Quanta Magazine really has nicely in-depth yet approachable writing on #mathematics, in this case an introduction to Lie groups #GroupTheory https://www.quantamagazine.org/what-are-lie-groups-20251203/
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Quanta Magazine really has nicely in-depth yet approachable writing on #mathematics, in this case an introduction to Lie groups #GroupTheory https://www.quantamagazine.org/what-are-lie-groups-20251203/
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Some time ago for practicing #haskell I implemented a well know algorithm for combining multiplets https://github.com/mdrslmr/MultipletCombiner . This algorithm from #grouptheory is used in #particlephysics and other #physics topics. The code is probably pretty useless since the results are anyway textbook standards. But I found it was a nice exercise. I'm sure the code can be improved a lot easily.
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Why are normal subgroups called "normal?" Most subgroups are not normal, which seemingly makes the name incorrect.
But in an Abelian group, all subgroups are normal. Abelian groups were the first groups to be studied by white European men, and they are the easiest for humans to work with.
Therefore, normal subgroups are called normal because they are the subgroups which pose the least challenge to the incumbent power structures.
#GroupTheory #NormalSubgroup -
Why are normal subgroups called "normal?" Most subgroups are not normal, which seemingly makes the name incorrect.
But in an Abelian group, all subgroups are normal. Abelian groups were the first groups to be studied by white European men, and they are the easiest for humans to work with.
Therefore, normal subgroups are called normal because they are the subgroups which pose the least challenge to the incumbent power structures.
#GroupTheory #NormalSubgroup -
Drafted a 3rd inquiry activity for D3 and D4 play with flips and rotations.
I am hoping it's not to dry. I'll read through it again tomorrow.
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Drafted a 3rd inquiry activity for D3 and D4 play with flips and rotations.
I am hoping it's not to dry. I'll read through it again tomorrow.
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#DocMadhattan: The Abel Prize 2025: Masaki Kashiwara
https://docmadhattan.hashnode.dev/the-abel-prize-2025-masaki-kashiwara
Masaki Kashiwara wins the 2025 Abel Prize for groundbreaking work in algebraic analysis, D-modules theory, and crystal bases in representation theory
#mathematics #physics #AbelPrize #MasakiKashiwara #grouptheory #quantumgroups
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Me: If you're a student in my class you will do group presentations, meaning that you will organize into a subset of the class, stand in front of the room, and talk about math to the rest of the class.
Also me: Let's talk about group presentations, a completely abstract algebraic concept that have absolutely nothing to do with standing in front of the room talking about your work.
Also also me: Okay, time for group presentations about group presentations.
#Algebra #ITeachMath #GroupTheory #GroupPresentation -
Me: If you're a student in my class you will do group presentations, meaning that you will organize into a subset of the class, stand in front of the room, and talk about math to the rest of the class.
Also me: Let's talk about group presentations, a completely abstract algebraic concept that have absolutely nothing to do with standing in front of the room talking about your work.
Also also me: Okay, time for group presentations about group presentations.
#Algebra #ITeachMath #GroupTheory #GroupPresentation -
New 📚 Release! Introduction to Group Theory: An Activity-Based Approach by Joe Fox #books #ebooks #math #grouptheory
This book is an introduction to group theory suitable for an introductory course in abstract algebra. Much of the content is delegated to a series of activities that are meant to be worked through by the students with the help of the instructor.
Find it on Leanpub!
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New 📚 Release! Introduction to Group Theory: An Activity-Based Approach by Joe Fox #books #ebooks #math #grouptheory
This book is an introduction to group theory suitable for an introductory course in abstract algebra. Much of the content is delegated to a series of activities that are meant to be worked through by the students with the help of the instructor.
Find it on Leanpub!
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Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \text{Then} ~ 2025
= 81 \cdot 25
= 3^4 5^2 \)\( = {p_2}^4 {p_3}^2
= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]
The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.
Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.pngRote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \text{Then} ~ 2025
= 81 \cdot 25
= 3^4 5^2 \)\( = {p_2}^4 {p_3}^2
= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]
The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.
Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.pngRote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.pngReference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes -
A shop called "Wreath Products" that sells mathematical puzzle toys, mobiles (like for baby cribs or art)...and, sure, also decorative wreaths.
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A shop called "Wreath Products" that sells mathematical puzzle toys, mobiles (like for baby cribs or art)...and, sure, also decorative wreaths.
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Sat Dec 7, 2024 on zoom & in-person
Session in memory of Richard Parker at the annual Nikolaus conference at Aachen (on group & representation theory). Main speakers:
Gerhard Hiß
Gabriele Nebe
Colva Roney-Dougal -
Sat Dec 7, 2024 on zoom & in-person
Session in memory of Richard Parker at the annual Nikolaus conference at Aachen (on group & representation theory). Main speakers:
Gerhard Hiß
Gabriele Nebe
Colva Roney-Dougal -
Source : Youtube / Timothy Nguyen
https://www.youtube.com/watch?v=jQLOGT7pM94
#mathematics #maths #math #GroupTheory #Youtube -
@gilesgardam Adding hashtags like #GroupTheory #Algebra will help people find this post (more important on mastodon than some other microblogging platforms, b/c "there is no algorithm here", or rather, the timeline is only chronological based on follows & searches)
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@j2kun So addition and negation, when operating on the 𝑛-bit integers, generate the dihedral group (https://en.wikipedia.org/wiki/Dihedral_group) that expresses the symmetries of a \(2^{n-1}\)-gon.
I didn't think of this before. 😃
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Here's a tip for beginners in #AbstractAlgebra, #GroupTheory or #NumberTheory.
Sometimes it's useful to think in terms of the divisibility ordering instead of the usual ordering where 0 ≤ 1 ≤ 2 ≤ …. Divisibility gives a partial ordering on the natural numbers where we say that n ≤ m if n divides m. Or we can extend this order to all integers, in which case n and -n become equivalent in this order because they divide each other.
The main difference is that this isn't a total order. For example 7 doesn't divide 8 and 8 doesn't divide 7. The other difference is that while 0 is the least natural number in the usual ordering, it's the *greatest* number in the divisibility ordering, because everything divides 0!
Thinking this way makes several definitions make more sense:
1. The least common multiple of 12 and 10 is 60, even though 0 is also a common multiple of 12 and 10. This is because 0 is greater than 60.
2. If an element of a group never becomes the identity when you repeatedly multiply it by itself, then we say it has order 0. This is because the order of an element is the least power of the element that equals the identity, under the divisibility ordering.
3. Likewise we say that a ring has characteristic 0 if 1 + … + 1 is never 0. Again we can use the divisibility ordering to say that the characteristic is the least integer for which adding together that number of 1s gives 0.
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I wrote a blog post on how to work out the injectivity radii of the unitary groups. If you like getting results in differential geometry and group theory with (mostly) just linear algebra, this one's for you! https://sethaxen.com/blog/2023/02/the-injectivity-radii-of-the-unitary-groups/
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How will the ability to do comparison or modulo efficiently in Finite Cyclic Groups break Elliptic Curve Cryptography?
https://crypto.stackexchange.com/questions/103944/how-will-the-ability-to-do-comparison-or-modulo-efficiently-in-finite-cyclic-gro
#ellipticcurves #grouptheory -
Anyone know anything about solving a 7x7x7 Rubik's cube?
I've got three centres down and I am looking for a hint (and just a hint!) if this is on the right track.
If I should be doing something else, I would appreciate a gentle nudge in another directions.
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Very good introduction to abstract algebra. Just one remark: why don't such guides cover categories?
https://www.youtube.com/watch?v=IP7nW_hKB7I&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6
