Angel "Java" Lopez en Blog

Matemáticas

Matemáticas: Enlaces, Novedades y Recursos (199)

Publicado el 1 de Agosto, 2020, 11:57

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Wear your math seatbelt, it's time for another differential geometry thread!
https://twitter.com/LucaAmb/status/1289244374996406273

How to calculate fibonnacci numbers
https://twitter.com/_julesh_/status/1289520483348688896

The Pythagorean Theorem in spherical geometry
https://twitter.com/SamuelGWalters/status/1278807718707380224

Great Woman of Mathematics: Dr. Chelsea Walton, born 1983
https://twitter.com/GWOMaths/status/1229338609741901824

Mathematics is one of few disciplines that are defined entirely by their method, not but their subject
https://twitter.com/amar_hh/status/1272550404484730881

The Perplexing Mathematics of the Napkin Ring Paradox
http://shortsleeveandtieclub.com/the-perplexing-mathematics-of-the-napkin-ring-paradox/?platform=hootsuite

Greek Vatican Manuscript 190
http://mathforum.org/geometry/wwweuclid/vatms.htm

Encontrado Nuevo Patrón en los Números Primos
https://www.gaussianos.com/encontrado-nuevo-patron-en-los-numeros-primos/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (198)

Publicado el 25 de Julio, 2020, 11:54

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The Two Forms of Mathematical Beauty
https://www.quantamagazine.org/how-is-math-beautiful-20200616/

The beauty of quaternion multiplication
https://twitter.com/johncarlosbaez/status/1285247097525026819

Computation graphs and graph computation
http://breandan.net/2020/06/30/graph-computation/?_lrsc=c44380ec-30c2-4bcb-af16-90861cd8fc50

Mathematicians Will Never Stop Proving the Prime Number Theorem
https://www.quantamagazine.org/mathematicians-will-never-stop-proving-the-prime-number-theorem-20200722/

The Tricky Math of Herd Immunity for COVID-19
https://www.quantamagazine.org/the-tricky-math-of-covid-19-herd-immunity-20200630/

A Number Theorist Who Solves the Hardest Easy Problems
https://www.quantamagazine.org/james-maynard-solves-the-hardest-easy-math-problems-20200701/

The Math of Social Distancing Is a Lesson in Geometry
https://www.quantamagazine.org/the-math-of-social-distancing-is-a-lesson-in-geometry-20200713/

Diophantine Set
https://en.wikipedia.org/wiki/Diophantine_set

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
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Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (197)

Publicado el 14 de Junio, 2020, 14:10

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We"ve been building a new tool called Penrose, which takes a big step toward automatically visualizing mathematics.
https://twitter.com/hypotext/status/1268218080993386497
https://penrose.ink/siggraph20.html

Medieval maths! This table was written around 1110 at Thorney Abbey, Cambridgeshire. It helps you multiply fractions from 1/8 to 1/2304, by integers from 1 to 10000.
https://twitter.com/Seb_Falk/status/1270999728663277569

Ranks of Elliptic Curves
https://math.berkeley.edu/~molsson/KConrad-ranks.pdf

In Mathematics, It Often Takes a Good Map to Find Answers
https://www.quantamagazine.org/in-math-it-often-takes-a-good-map-to-find-answers-20200601/

In a Single Measure, Invariants Capture the Essence of Math Objects
https://www.quantamagazine.org/math-invariants-helped-lisa-piccirillo-solve-conway-knot-problem-20200602/

The "Useless" Perspective That Transformed Mathematics
https://www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609/

Topological Logic - a rod through one hole of a double torus can pass through both with some careful stretching of the surface.
https://twitter.com/mathemaniac/status/1270680150506496003

How can you add something with period 6 and something with period 20 to create something with 7-fold symmetry?
https://twitter.com/AlgebraFact/status/1271037088180383745

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (196)

Publicado el 13 de Junio, 2020, 12:29

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Carmichael's Totient Function Conjecture
https://twitter.com/AlgebraFact/status/1264233391433625601
https://mathworld.wolfram.com/CarmichaelsTotientFunctionConjecture.html

For those who are interested in research-based solutions to stop police violence, here"s what you need to know - based on the facts and data.
https://twitter.com/samswey/status/1180655701271732224

Dot, cross, and quaternion products
https://www.johndcook.com/blog/2012/02/15/dot-cross-and-quaternion-products/

Let R be an integral domain. Then R is a field iff every finitely generated R-module is free.
https://twitter.com/AlgebraFact/status/1267834641614098433

Lenses from a Haskell Perspective
https://twitter.com/_julesh_/status/1268170429262434305

Profunctor optics, a categorical update
https://arxiv.org/abs/2001.07488

What You Needa Know about Yoneda
https://www.cs.ox.ac.uk/jeremy.gibbons/publications/proyo.pdf

Categories of Optics
https://arxiv.org/abs/1809.00738

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
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Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (195)

Publicado el 30 de Mayo, 2020, 13:18

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Triángulo y Circunferencia Circunscrita
https://www.gaussianos.com/triangulo-y-circunferencia-circunscrita/

Mathematician Measures the Repulsive Force Within Polynomials
https://www.quantamagazine.org/new-math-measures-the-repulsive-force-within-polynomials-20200514/

Isbell duality
https://twitter.com/johncarlosbaez/status/1266029338190680064

Put coplay / lens update into a state monad where the state variable is a payoff vector
https://twitter.com/_julesh_/status/1251507999606276104

Kurt Gödel Wanted to Revise Our Concept of Time
https://www.thegreatcoursesdaily.com/kurt-godel-wanted-to-revise-our-concept-of-time/

Highly composite numbers
http://wwwhomes.uni-bielefeld.de/achim/highly.html

Symbolic Mathematics Finally Yields to Neural Networks
https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/

Graduate Student Solves Decades-Old Conway Knot Problem
https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (194)

Publicado el 24 de Mayo, 2020, 11:44

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The role of voting intention in public opinion polarization
https://arxiv.org/abs/1909.07092

Mirth programming language
https://twitter.com/typeswitch/status/1249368983729471488
https://github.com/mirth-lang/mirth

Rule 110
https://en.wikipedia.org/wiki/Rule_110

The Computer Scientist Who Can"t Stop Telling Stories
https://www.quantamagazine.org/computer-scientist-donald-knuth-cant-stop-telling-stories-20200416/

Bourbaki's final perfected definition of the number 1, printed out on paper, would be 200,000 as massive as the Milky Way!
https://twitter.com/johncarlosbaez/status/1250868989414137857

Math3ma
https://www.math3ma.com/

The Mathematics of Privacy
https://becominghuman.ai/the-mathematics-of-privacy-361742827f08

Reflections on monadic lenses
http://www.cs.ox.ac.uk/jeremy.gibbons/publications/mlenses.pdf

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (193)

Publicado el 17 de Mayo, 2020, 10:02

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MIP*=RE
https://arxiv.org/abs/2001.04383

A simulation of sunflower growth
https://twitter.com/ZenoRogue/status/1247900522905886723

To Win This Numbers Game, Learn to Avoid Math Patterns
https://www.quantamagazine.org/to-win-this-numbers-game-learn-to-avoid-math-patterns-20200507/

In Star Trek Discovery we heard about the "Logic Extremists"
https://twitter.com/johncarlosbaez/status/1258475087704895488

What does "birational equivalence" mean in a cryptographic context?
https://crypto.stackexchange.com/questions/43013/what-does-birational-equivalence-mean-in-a-cryptographic-context

If you view any ellipse from just the right distance, it will *always* occupy 90 degrees
https://twitter.com/gregeganSF/status/1243318369983418368

Here"s the axioms for a group in strings
https://twitter.com/CreeepyJoe/status/1248736658612031488

Modeling Opinion Dynamics: Theoretical analysis and continuous approximation
https://arxiv.org/abs/1606.00662

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (192)

Publicado el 3 de Mayo, 2020, 14:36

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Interface Scaling in the Contact Process
https://arxiv.org/pdf/cond-mat/0003480.pdf

Radical Solutions: Evariste Galois
https://www.damninteresting.com/radical-solutions/

Explicación de teoría de colas y ejercicio resuelto
https://www.youtube.com/watch?v=t3x2KinUqAA&feature=emb_logo

Mathematical proof that rocked number theory will be published
https://www.nature.com/articles/d41586-020-00998-2

Conmutative Semigroups
https://twitter.com/johncarlosbaez/status/1246470112321953792

Quantum Natural Language Processing
https://medium.com/cambridge-quantum-computing/quantum-natural-language-processing-748d6f27b31d
https://github.com/oxford-quantum-group/discopy/blob/ab2b356bd3cad1dfb55ca6606d6c4b4181fe590c/notebooks/qnlp-experiment.ipynb

Graced With Knowledge, Mathematicians Seek to Understand
https://www.quantamagazine.org/mathematicians-grapple-with-sudden-answer-to-connes-embedding-conjecture-20200408/

Landmark Computer Science Proof Cascades Through Physics and Math
https://www.quantamagazine.org/landmark-computer-science-proof-cascades-through-physics-and-math-20200304/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (191)

Publicado el 2 de Mayo, 2020, 17:55

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Conway"s Impact on the Theory of Random Tilings
https://twitter.com/JimPropp/status/1249189041343475712

Ha muerto John Horton Conway (1937-2020) - Gaussianos
https://www.gaussianos.com/ha-muerto-john-horton-conway-1937-2020/

Math After COVID-19
https://www.quantamagazine.org/how-has-coronavirus-affected-mathematics-20200428/

Method of estimating the number of infected people
https://twitter.com/wtgowers/status/1242823142088851456

Tikzcd Editor Category Diagrams
https://tikzcd.yichuanshen.de/

Uncomputable Numbers
https://medium.com/cantors-paradise/uncomputable-numbers-ee528830d295

The Quasi-Stationary Distribution of the Subcritical Contact Process
https://twitter.com/pgroisma/status/1242941761057632257
https://arxiv.org/pdf/1908.04175.pdf

Simulation of quasi-stationary distributions on countable spaces
https://arxiv.org/abs/1206.6712

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (190)

Publicado el 25 de Abril, 2020, 16:42

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James Propp "Conway's Impact on the Theory of Random Tilings" 03 23 14
https://www.youtube.com/watch?v=e_729Ehb4vQ&feature=emb_logo

Haskell implementation of open games
https://github.com/jules-hedges/open-games-hs

Gambit: Software Tools for Game Theory
http://gambit-project.org/

The category-theoretic formulation of 1
https://twitter.com/andrejbauer/status/1253357470250123265

Linear Algebra Course
https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/

Important Formulas(Part 7) - Permutation and Combination
https://www.careerbless.com/aptitude/qa/permutations_combinations_imp7.php

Dr. Mary Cartwright, 1900-1998
https://twitter.com/GWOMaths/status/1196367452394938374

Tiling with polyominoes and combinatorial group theory
https://www.sciencedirect.com/science/article/pii/0097316590900574

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (189)

Publicado el 21 de Abril, 2020, 20:39

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John Horton Conway has died
https://twitter.com/CardColm/status/1249038195880341505

John H. Conway, 1937–2020
https://www.math.princeton.edu/news/john-h-conway-1937-2020

Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom
https://www.medrxiv.org/content/10.1101/2020.04.09.20058974v1

My PhD thesis "At the Interface of Algebra and Statistics" is now on the arXiv
https://twitter.com/math3ma/status/1249862830670729217
https://arxiv.org/abs/2004.05631
https://www.youtube.com/watch?v=wiadG3ywJIs&feature=youtu.be

John Conway Solved Mathematical Problems With His Bare Hands
https://www.quantamagazine.org/john-conway-solved-mathematical-problems-with-his-bare-hands-20200420/

Compositional game theory
https://arxiv.org/abs/1603.04641v3

Recomendando películas matemáticas
https://twitter.com/edusadeci/status/1242397128120578049

Determining the length of paper on a toilet paper roll
https://twitter.com/fermatslibrary/status/1242811233637666818

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (188)

Publicado el 18 de Abril, 2020, 11:05

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El teorema de Mills: mucho ruido y pocas nueces - Gaussianos
https://www.gaussianos.com/el-teorema-de-mills-mucho-ruido-y-pocas-nueces/

"Amazing" Math Bridge Extended Beyond Fermat"s Last Theorem
https://www.quantamagazine.org/amazing-math-bridge-extended-beyond-fermats-last-theorem-20200406/

Langlands Program
https://www.quantamagazine.org/tag/langlands-program/

The E8 lattice
https://twitter.com/johncarlosbaez/status/1241764718999506944
https://johncarlosbaez.wordpress.com/2020/03/20/from-the-octahedron-to-e8/

John Horton Conway: the world"s most charismatic mathematician
https://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-charismatic-mathematician-in-the-world?CMP=share_btn_tw

Mathematician and genius John Conway, inventor of The Game of Life has succumbed to COVID-19 today
https://twitter.com/AdiShavit/status/1249055920111452163

John Conway Reminiscences about Dr. Matrix and Bourbaki
https://blogs.scientificamerican.com/guest-blog/john-conway-reminiscences-about-dr-matrix-and-bourbaki/

Monster Group (John Conway) - Numberphile
https://www.youtube.com/watch?v=jsSeoGpiWsw&feature=emb_logo

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Notas sobre Teoría Algebraica de Números (1)

Publicado el 5 de Abril, 2020, 19:51

En estos días estuve leyendo temas de teoría algebraica de números. Algo publiqué por acá en Números Irreducibles y Primos. Hoy leo en el libro Algebraic Number Theory de Romyar Sharifi:

At its core, the ancient subject of number theory is concerned with the arithmetic of the integers. The Fundamental Theorem of Arithmetic, which states that every positive integer factors uniquely into a product of prime numbers, was contained in Euclid’s Elements, as was the infinitude of the set of prime numbers. Over the centuries, number theory grew immensely as a subject, and techniques were developed for approaching number-theoretic problems of a various natures. For instance, unique factorization may be viewed as a ring-theoretic property of Z, while Euler used analysis in his own proof that the set of primes is infinite, exhibiting the divergence of the infinite sum of the reciprocals of all primes.

Es importante conocer que la factorización única NO SIEMPRE está presente en otros anillos. Es parte de lo que la teoría algebraica de números tiene para ofrecernos.

Algebraic number theory distinguishes itself within number theory by its use of techniques
from abstract algebra to approach problems of a number-theoretic nature. It is also often considered, for this reason, as a subfield of algebra. The overriding concern of algebraic number theory is the study of the finite field extensions of Q, which are known as number fields, and their rings of integers, analogous to Z.

Curiosamente las extensions de campos comenzaron a aparecer en los trabajos para resolver los ecuaciones de grado mayor que 2. Pero si en esas extensions, definimos algo como "enteros", se nos abre la puerta a estudiar nuevos sistemas de números.

The ring of integers O of a number field F is the subring of F consisting of all roots of all
monic polynomials in Z[x]. Unlike Z, not all integer rings are UFDs, as one sees for instance
by considering the factorization of 6 in the ring Z[√−5]. However, they are what are known
as Dedekind domains, which have the particularly nice property that every nonzero ideal factors uniquely as a product of nonzero prime ideals, which are all in fact maximal. In essence, prime ideals play the role in O that prime numbers do in Z.

UFD es Unique Factorization Domain, dominio con factorización única. El caso del 6 mencionado se refiere a que 6 = 3 * 2 pero también en ese anillo Z[√−5]  el 6 es igual a (1 + √−5)(1 - √−5) y esos dos pares de factores no se dividen entre sí. Es un resultado un tanto inesperado, pero sumamente interesante.

Para recuperar la factorización única, hay que reemplazar los enteros por ideales, conjuntos de elementos de un anillo.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (187)

Publicado el 4 de Abril, 2020, 17:42

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Se obtuvo una hermosa fórmula matemática usando el número de Napie
https://twitter.com/thaiselenags/status/1237618582026059776

Sphere Point Picking
https://mathworld.wolfram.com/SpherePointPicking.html

Unpredictability, Undecidability, and Uncomputability
https://www.youtube.com/watch?v=hDpEg881BnI

Mathematics as a Team Sport
https://www.quantamagazine.org/mathematics-as-a-team-sport-20200331/

Computing A Glimpse of Randomness
https://arxiv.org/abs/nlin/0112022

Mathematicians who revealed the power of random walks win Abel prize
https://www.newscientist.com/article/2237832-mathematicians-who-revealed-the-power-of-random-walks-win-abel-prize/

"Rainbows" Are a Mathematician"s Best Friend
https://www.quantamagazine.org/rainbows-are-a-mathematicians-best-friend-20200318/?mc_cid=559347b58d&mc_eid=c608d388a6

Euler"s number via products of primes
https://twitter.com/TamasGorbe/status/1240014581394702342

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (186)

Publicado el 31 de Marzo, 2020, 11:04

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Maths, Madness and the Manhattan Project: the Eccentric Lives of Steinhaus, Banach and Ulam
https://culture.pl/en/article/maths-madness-and-the-manhattan-project-the-eccentric-lives-of-steinhaus-banach-and-ulam

"A Singular Mathematical Promenade" is a delightful book by a gifted expositor (Ghys) that beautifully showcases both the unity of mathematics
https://twitter.com/AlexKontorovich/status/1244731670487609348

A Singular Mathematical Promenade
http://ghys.perso.math.cnrs.fr/bricabrac/promenade.pdf

The Grogono Generator: an Apologia
http://users.encs.concordia.ca/~grogono/RNG/grog-gen.html

Stefan Banach
http://mathshistory.st-andrews.ac.uk/Biographies/Banach.html

Woman of the Year 1921: Emmy Noether
https://time.com/5792615/emmy-noether-100-women-of-the-year/

How Rational Math Catches Slippery Irrational Numbers
https://www.quantamagazine.org/how-rational-math-catches-slippery-irrational-numbers-20200310/

Gömböc
https://es.wikipedia.org/wiki/G%C3%B6mb%C3%B6c

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (185)

Publicado el 29 de Marzo, 2020, 12:31

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Lord Brouncker"s continued fraction for π
https://web.maths.unsw.edu.au/~mikeh/webpapers/paper168.pdf

A mathematical model for the novel coronavirus epidemic in Wuhan, China
http://www.aimspress.com/article/10.3934/mbe.2020148

Wolfe Conditions
https://en.wikipedia.org/wiki/Wolfe_conditions

Christoph and the Calendar
https://thonyc.wordpress.com/2016/02/24/christoph-and-the-calendar/

Linear Regression and Kernel Methods
http://www.numerical-tours.com/matlab/ml_2_regression/

Reproducing kernel Hilbert space
https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space

Korovkin-type Theorems and Approximation by Positive Linear Operators
https://arxiv.org/abs/1009.2601

Estructuras Algebraicas
http://www.ehu.eus/juancarlos.gorostizaga/apoyo/estruct_alg.htm

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (184)

Publicado el 28 de Marzo, 2020, 18:22

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Matemáticas online mientras dure la cuarentena
http://www.aulamagna.com.es/matematicas-online-mientras-dura-la-cuarentena/

Catriona Shearer is great at inventing geometry problems that seem impossible to solve
https://twitter.com/johncarlosbaez/status/1230520859795677184

Aryabhatta I (ca. 5th CE) was an astronomer and a mathematician and hypothesized the rotation of the earth
https://twitter.com/VatsalTrivedi18/status/1230906845839020033

Mathgen; Randomly generated mathematics research papers!
https://thatsmathematics.com/mathgen/

This past Monday marked what would have been mathematician Emmy Noether"s 138th birthday
https://twitter.com/QuantaMagazine/status/1243659920916000772

Catriona Shearer in Twitter
https://twitter.com/Cshearer41/status/1231489403761176576

Irreducible and prime elements
https://math.stackexchange.com/questions/1076517/irreducible-and-prime-elements

In algebraic topology, cohomology classes are cocycle classes. In algebraic geometry, they are Poincare duals of subvarieties. In differential geometry, they are differential forms
https://twitter.com/YuhangChen13/status/1238260647227543557

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Números Irreducibles y Primos

Publicado el 21 de Marzo, 2020, 13:02

Hoy leo en la introducción del excelente "Algebraic number theory and Fermat's last theorem", de Ian Stewart y David Tall

For organizational reasons rather than mathematical necessity, the book is divided into four parts. Part I develops the basic theory from an algebraic standpoint, introducing the ring of integers of a number field and exploring factorization within it. Quadratic and cyclotomic fields are investigated in more detail, and the Euclidean imaginary fields are classified. We then consider the notion of factorization and see how the notion of a 'prime' p can be pulled apart into two distinct ideas. The first is the concept of being 'irreducible' in the sense that p has no factors other than 1 and p. The second is what we now call 'prime': that if p is a factor of the product ab (possibly multiplied by units—invertible elements) then it must be a factor of either a or b. In this sense, a prime must be irreducible, but an irreducible need not be prime. It turns out that factorization into irreducibles is not always unique in a number field, but useful sufficient conditions for uniqueness may be found. The factorization theory of ideals in a ring of algebraic integers is more satisfactory, in that every ideal is a unique product of prime ideals. The extent to which factorization is not unique can be 'measured' by the group of ideal classes (fractional ideals modulo principal ones).

Es un tema más que interesante: uno, basado en el manejo de enteros y naturales, tiende a poner como equivalentes los conceptos de número primo y número irreducible. Pero se vió (justamente en el siglo XIX, tratando de demostrar el ultimo teorema de Fermat) que no es el caso: hay sistemas de números (anillos) donde no se cumple la equivalencia.

Ver

Irreducible and prime elements
https://math.stackexchange.com/questions/1076517/irreducible-and-prime-elements

Luego, si quieren algo más en profundidad, y cómo afecta esto a varias estructuras algebraicas:

Irreducible Elements
https://en.wikipedia.org/wiki/Irreducible_element

Any Prime is Irreducible
https://math.stackexchange.com/questions/69504/any-prime-is-irreducible

Prime implies Irreducible
https://math.stackexchange.com/questions/1149078/prime-implies-irreducible

Irreducible Elements in a Principal Ideal Domain are Prime
https://math.stackexchange.com/questions/770731/irreducible-elements-in-a-pid-are-prime

Irreducible Elements in an Unique Factorization Domain are Prime
https://math.stackexchange.com/questions/257955/irreducibles-are-prime-in-a-ufd

A principal ideal ring that is not a euclidean ring
http://www.math.buffalo.edu/~dhemmer/619F11/WilsonPaper.pdf

Ring of integers is a Principal Ideal Domain but not a Euclidean domain
https://math.stackexchange.com/questions/857971/ring-of-integers-is-a-pid-but-not-a-euclidean-domain

An example of a principal ideal domain which is not a Euclidean domain
http://www.maths.qmul.ac.uk/~raw/MTH5100/PIDnotED.pdf

En este blog, algo traté del tema cuando comenté

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (4)
http://ajlopez.zoomblog.com/archivo/2016/06/28/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (3)
http://ajlopez.zoomblog.com/archivo/2016/06/27/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (2)
http://ajlopez.zoomblog.com/archivo/2016/06/26/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra Structure and Application, de Finston y Morandi
http://ajlopez.zoomblog.com/archivo/2016/06/14/libro-Abstract-Algebra-Structure-and-A.html

En esos libros aparece más detallado la evolución del concepto, en especial, la aparición de ideales primos, que de nuevo, tuvo su origen en los intentos de demostración del ultimo teorema de Fermat, por parte de Kummer y sus números ideales, una extension para conseguir la factorización única, luego levantada por Dedekind para formar los ideales primos. Esa extension del concepto de número resultó fructífera, como se ve en los capítulos de los libros mencionados arriba.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (183)

Publicado el 23 de Febrero, 2020, 8:42

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The Category Theory Behind UMAP
https://twitter.com/johncarlosbaez/status/1226898580792737794
https://johncarlosbaez.wordpress.com/2020/02/10/the-category-theory-behind-umap/

The science checklist applied: Mathematics
https://undsci.berkeley.edu/article/mathematics

Rainbow Proof Shows Graphs Have Uniform Parts
https://www.quantamagazine.org/mathematicians-prove-ringels-graph-theory-conjecture-20200219/

Equations that changed the world
https://twitter.com/ProfFeynman/status/1227435683385663488

Every number greater than 55 is the sum of distinct primes of the form 4n+3
https://twitter.com/fermatslibrary/status/1229034200432594946

The Map of Mathematics
https://www.quantamagazine.org/the-map-of-mathematics-20200213/

The Freyd-Mitchell Embedding Theorem
https://arxiv.org/abs/1901.08591

Introduction to Clifford Algebra
https://www.av8n.com/physics/clifford-intro.htm

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas
Matemáticas: Enlaces, Novedades y Recursos (182)

Publicado el 16 de Febrero, 2020, 15:06

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Mathematical model reveals best auction strategy
https://www.newscientist.com/article/dn3678-mathematical-model-reveals-best-auction-strategy/

Why Is M-Theory the Leading Candidate for Theory of Everything?
https://www.quantamagazine.org/why-is-m-theory-the-leading-candidate-for-theory-of-everything-20171218

But what is the Fourier Transform? A visual introduction.
https://www.youtube.com/watch?v=spUNpyF58BY&feature=emb_logo

There"s something special about four-sided figures packed into circles
https://twitter.com/brilliantorg/status/1228741327984189442

Construcciones con regla y compás (III): Los polígonos regulares - Gaussianos
https://www.gaussianos.com/construcciones-con-regla-y-compas-iii-los-poligonos-regulares/

Números primos gemelos y demás familia - Gaussianos
https://www.gaussianos.com/numeros-primos-gemelos-y-demas-familia/

Great Woman of Mathematics: Katherine Johnson
https://twitter.com/GWOMaths/status/1191782750489063425

Color-Changing Material Unites the Math and Physics of Knots
https://www.quantamagazine.org/color-changing-material-unites-the-math-and-physics-of-knots-20200210/

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Por ajlopez, en: Matemáticas

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