#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.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: 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)?

#Math #Algebra #GroupTheory

algebra final tmrw 😤 watch me cook

#algebra #abstractalgebra #grouptheory

Một lập trình viên đã tối ưu tốc độ thư viện đường cong Elliptic, chỉ sử dụng lý thuyết nhóm thuần túy trong toán học, mà không cần đến lập trình cấp thấp (assembly) hay tăng tốc GPU (CUDA). Đây là một thành tựu đáng chú ý trong việc cải thiện hiệu suất mật mã.
#EllipticCurve #Cryptography #GroupTheory #Optimization #Math #Programming #ĐườngCongElliptic #MậtMãHọc #LýThuyếtNhóm #TốiƯu #ToánHọc #LậpTrình

https://www.reddit.com/r/programming/comments/1nyrnmt/if_youre_so_smart_then_why_are_you_poor

Evariste #Galois - #GroupTheory #QuantaMagazine #Maths #Mathematics

#GaloisGroups and the #Symmetries of #Polynomials
By Allison Whitten

https://t.co/sNKYd7wOdM

Petra Cini, composer and pianist, gave a special #nikhef theory seminar on musical representations: violence, purity and mathematics

#MusicalMetaphors #GroupTheory #SO3