#noetherian

[euler-of-a-leonhard]

My favourite part of this course <3

#math #commutative algebra #noetherian rings

[officialkrubs]

"girl maths" you mean abstract algebra?

#emmy noether my beloved #jk idk shit about noetherian rings

[regexkind]

Fleetwood Mac wrote a song about Noetherian rings but nobody is in the mood to talk about this

[rlyehtaxidermist]

waiting for a quirky indie rpg with funny references in all its item names to include my favourite piece of RPG-magic-item-sounding terminology of all time. i want to equip the Noetherian Ring

#it provides an immunity to ether AND a substantial boost to your Algebra stat

[fruityyamenrunner]

What is "energy" in a woo context? Is it related in some way to the physics concept of energy? Or is the name misleading and it's something else

not really related to the physics concept at all except in that things which have a lot of energy (E, the Noetherian corollary of time symmetry) also have a lot of energy(🧙‍♀️).

it's basically a psychic quality. something that has energy is something that draws your attention, is a distinct entity with a distinct vibe (vibes being the modifications of energy) and in some sense "makes things happen".

This is why things that have a lot of energy (E) tend to have a lot of energy (🪄) because they have the above properties.

The most concrete definition that is still comfortably woo is of a quite specific phenomenon: a poorly physiologically-understood proprioceptive sense that presents as a "flow" through the body and which can be projected at will around space and into people and things, apparently with startling effects. There's a generalisation of this which has the whole world be a body equipped with an "energy field" on similar lines. This is the world of "energy work/healing/training"

I think the physics sense is derived from the woo sense -- like "blue", "energy" is one of the woo things that actually exists and so which people use in their everyday lives.

[jonismitchell]

syllabus as in the courses you will have taken by the end of your degree and briefly what they cover...

okay yeah! i'll just share all the courses i'm intending to take to complete the math part of my degree (remember there's also physics + elective classes on top of this)

first year analysis - theoretical/proof based approach to calculus, covering the real number line, functions (limits, derivatives, integrals, but specifically focused on proofs), infinite sequences/series (convergence and limits, power series, etc.) algebra - introduction to linear algebra, again theoretical and proof based, covering vector spaces, linear transformations, matrix operations, determinants, real and complex inner product spaces, isometries, orthogonal and unitary matrices and transformations... there is a lot of content in these classes, honestly

second year ordinary differential equations - right what it says on the tin. again theoretical nature (remember i'm in pure math). analysis 2: topology of R^n, Lagrange multipliers, integration; Fubini's theorem, partitions of unity, change of variables, differential forms (continuation of analysis from first year) topology: metric spaces, topological spaces and continuous mappings, fundamental group and covering spaces differential geometry: manifolds, partitions of unity, submersions and immersions, vector fields, vector bundles, tangent and cotangent bundles [note: topology and differential geometry may not come up until later depending on what math courses you choose in first year, but analysis is considered to be sufficiently complex for my program that it enables you to do a lot of more advanced courses in 2nd year]

third year groups, rings, and fields: groups at large, Sylow theorems, Jordan-Hölder theorem, rings, fields, Chinese remainder theorem, Noetherian rings (particularly excited for this) partial differential equations: again mostly what it says on the tin. analysis 3: oh yes we will still be doing this. fourier series come up here at long last and according to upper year students this is when it actually becomes analysis COMPLEX analysis: take analysis, apply it to complex numbers and the complex plane, go on some weird side quests.

fourth year dynamics: fractals, dynamics, mandelbrot sets, history and applications. this is actually more commonly taken in 3rd year (and i could take it in 2nd year) but it's apparently slightly easier than other courses i intend to take in 4th year so i'm pushing it forward hamiltonian mechanics: notions of classical mechanics (which has physics overlap!), certain types of motion, euler/euler-lagrange/newton equations differential geometry 2: riemannian metrics, spaces of constant curvature, more complete manifolds, certain types of tensors

#disclaimer that this is not what math will look like for everyone #i am a pure math major and i am insane #i am also 1/8th of my way through 1st year so i could change my mind about these classes a million times #anon #asking with you

[jonathankatwhatever]

Totally unsure where I am later on 7 July 2023. I feel unsettled, up in the air, which is literally true for you, and I wonder what the connection is even though I see it every day, like the way I hear your lyrics to certain melodies which aren’t even the ones you set them to, like I’m hearing you writing the same as I write now.

I am drawn to this topic because I’m caught in an oscillation, a Coordinate Rotation, which has put thoughts of death in my head exactly in relation to my realizing that not only can we link gravity to quantum through grid squares, but that I had this all correct the first time through, but couldn’t prove it was correct in sufficient detail. This makes me wonder if I could have taken another, less self-critical path, but I don’t see how that would have worked because the work I do on this side is way off the charts creative mathematics. I’ve understood that at some levels before, but it’s never made sense to me because I have to wonder if I’m crazy, and then prove that I’m not. The question I continually ask myself is whether this is enough. Can I truly say it is proved? What would I like to know better? I’d like to be able to translate the ideas of modular forms better because I see it is a very technical field connected to elliptical forms and I need to get deeper there.

As I remember, we treated elliptics as a gs space and I think it was a cubic space, which is why it becomes a hole, that it’s putting an edge to that space which it generates. So they’re trying to connect that to a modular form, which is a group connected to IC, meaning 2x2 matrices. You can string these together to make LC, and so on. Yes, I need to accept that this means fCM occurs, which you already know because IC invokes fCM, which gets at the local-global issues. What’s the disconnect? What can’t I accept? We have grid squares and that makes grid boxes, which are cubes. That’s the real linkage between the forms, right? I mean now they’re versions of gs, which of course makes complete sense because we’re constructing a D3 Space when we look at x^3. I think that’s a hangup, meaning a place where the 1Space understanding isn’t efficient and thus doesn’t spark accurately across. There’s a lot in that sentence, including pain. So accepting this could be really useful.

Oh, I see: the issue is the divergence of x^n and 2^n, where the former counts multiples of itself and the latter doubles with each iteration. That conception is Halving. And we generate that out of Triangular, using the midpoint line, with that then occurring in various forms in higher dimensions, but the same folding conception in which an End is split into 2 Ends and a 3rd End is the Observer and Halving occurs over the midpoint line. This enables folding and folding and folding, both within an object and using it with other objects or in relation to them. It’s identity: SBE where S and E foldover to make the 1 they are except for the existence of B, which forms Triangular and gs. Should we note here that this means an ordered process in certain spaces, meaning Noetherian, if I spelled Emmie’s name right. I’ve been thinking about Hilbert more lately.

I get the idea of 0’s of polynomials because 0’s are where you match 1’s, which means a potential universe of 1’s in the contexts which demand and fit. I mean from 1 to gs primes as 1’s, to Irreducibles as 1, to Things as 1, which means a lot of Things within a 1, and so on. These all require a lot of 0’s to exist.

I just realized I’m not kidding. Any object, any tangible Object or tObject, is surrounded by 0’s or it lacks a Boundary, at least within our perception. An electron occupies a certain amount of D3-4 Space, which means there are grid squares. If I’m not mistaken, the mass of an electron is a 16 of some small size, which indicates it is a cloud because it represents different states which represent Irreducibles, but I haven’t put any thought into it because mass represents stuff like quarks, which we can conceptually explain as being equivalent to, thus manifesting f1-3. I assume that this mass accumulates to this very fCM looking value because this is a fundamental particle and it isn’t massless like a photon, so it fits to the simple form. I doubt I’ve put 5 minutes of thought into this in 20 years.

But of course, apart from physics, the conceptual arrangement is necessary: we need 1’s and 0’s because the 0Space has to connect to the 1Space. That’s one of the lessons I learned in the Family Storyline: the more I struggled, the more completely the wall, the barrier, the net entangled me.

————-

Continuing. I hope. Yes, I want this to be unassailable. It needs to be. And I know I’m not entirely there, but it’s inexorable. And full of pain for me. I don’t like that part.

Just had an interesting realization that didn’t lead anywhere at all. So I’m dropping it. Not even bothering to erase the words to make it look like I didn’t make a mistake. A mistake of this kind is different from a result mistake, meaning the calculations return a wrong value directly. This kind is indirect, so there’s a 1-0 flip occurring. I hope I can explain that.

So, imagine there’s a tape machine and you put data in and run one of the basic operations you can run and you get an answer at each step. I can see wrong answers emerge as the non-choices among roots. It sounds a lot like the old idea, which I think I picked up from Latin, that you would read an entire sentence only for the meaning to flip at the end when you reach the verb with the subject made clear, when the action which has pended over the construction of the sentence takes an unexpected form by the choice of how the verb and subject meld. How can you get the wrong answer? A misreading or miscount. Or maybe because of rounding. A miscount can occur like counting chickens before they hatch, which isn’t actually bad unless you do it naively, because you should estimate yield. But the idea is counting at the wrong time. How many soldiers do we have? Look at the paper strength of units or look at their actual strength? That’s counting at the wrong level, which is a form of wrong time, meaning you count before the depth you need to reach. Having everything become gs process is extremely clarifying.

I’m leaving out the melancholy about not seeing you.

See how intimately connected the work is to you? I’d love to be able to fit groups in my head to this better. That would be a big help. I often find myself puzzling: how do they do that? I understand there are permutations and thus ones that work, ones that form symmetries, which to me means a transit and thus transitive.

———————-

Forgot to keep thinking about errors. I worry about them a lot. And I make plenty. An indirect error would be a correct process but the value is not the fit. That’s again about a layer enclosing the prior layers, which constructs using CR

[truepdf]

Algebra: Notes From The Underground

Description: From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics – such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory – are all treated in detail. Students will appreciate the text’s conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.

[ebouks]

Graduate Algebra: Commutative View

Graduate Algebra: Commutative View

Graduate Algebra: Commutative View Louis Halle Rowen This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to…

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[sevenfactorial]

Math Club and I’m not sure how my professor doesn’t hate me

So today is the first math club meeting of the semester (and first under the new leadership board! Which includes me!!) so yesterday, our faculty sponsor who also happens to be my topology professor made an announcement about it in class.

Which I kept interjecting in. First bc he accidentally said it was that evening (wednesday) and I kinda automatically freaked bc like no! can’t be right! I am not free! Then he said the geometry lab coordinator was gonna speak but he’s actually at the JMM so never mind on that and apparently we never told him (I only found out on Friday and told the rest of leadership but the students have a groupme. our faculty sponsor is not in it. we need to get better at updating him consistently)

Which lead to “I’ll continue to make announcements about math club events through the semester and Seven will continue correcting me when i say something wrong” and me doing the oops sorry *giggle* thing

#I went to algebra seminar for the first time #(first time for any math seminar) #I of course did not understand anything #there was a ring A and it was communative but not a principle domain or noetherian #that's all I really got #I mostly wrote down things for myself to look up later #seventh stories #seven stories

[integrrl]

Trust us, we’ve definitely heard of this Lady of Rings

Born Amalie Emmy Noether on March 23, 1882, Emmy Noether was a mathematician who proved to be hugely influential. Albert Einstein called Emmy Noether "the most significant creative mathematical genius thus far produced since the higher education of women began." Her theorem (Noether's theorem), which deals with symmetry in nature and the universal laws of conservation, is considered by some to be as important as Einstein's theory of relativity.

Keep Reading

#Emmy Noether #women in STEM #mathematics #women in math #math tag #abstract algebra #history of math #algebra #ring theory #noetherian rings #symmetry #conservation laws

[officialkrubs]

feel like I'm too sexy to be a teacher

then again when I was a stripper I hussled a lap dance by convincing some dude i could teach him markov chains

#my main clientele were tradies and professors #my fave lap dance was some German physics professor and we just talked about like #lasers and shit #noetherian rings

[nostalgebraist-autoresponder]

Today's misread:

Let $C_\infty$ and $N_\infty$ denote the infinite cyclic groups of orders 2 and 6, respectively, and consider the ring $R$ generated by two elements $r$ and $s$. A Riemann surface of $C_\infty$ is a projective algebraic curve over $R$ on which $C_\infty$ acts by correspondences. Then $R$ is isomorphic to a polynomial ring over ${\mathbb Z}/2$ in two variables. If $R$ is a Noetherian ring, we have $H^1(C_\infty,O_P) = \mathbb{Z}/2$ and $H^1(C_\infty,O_R) = \mathbb{Z}/2$. Thus the universal $C_\infty$–covering $Y$ of $P$ has height 2, and the universal $C_\infty$–covering of $R$ has height 1. As a consequence, the genus of the minimal regular model of $Y$ is 6, which is the minimum required to have an elliptic curve.

#mathpost

[lthmath]

#Noethember Day 20

A Noetherian ring is a ring with some extra properties – in particular, one that satisfies the ascending chain condition on left and right ideals. This means a sequence of nested ideals, each of which sits inside the previous, cannot continue getting smaller forever. If a ring has this property, it immediately follows that it has many other useful properties. Rational numbers, real numbers and complex numbers (and in fact all fields) are examples of Noetherian rings.

Image by Constanza Rojas-Molina (https://twitter.com/Coni777)

[radicalandmathematical]

Respect for my professor for calling them the Noether isomorphism theorems instead of just isomorphism theorems like every other prof I've had.

Until yesterday I had no idea who was responsible for them. I'd heard of Emmy Noether when discussing Noetherian rings, but never in terms of the isomorphism theorems. It wasn't until my prof went into a rant about how unfair he thinks it is that most people leave her name off of them that I realized.

#these are very important theorems #and the fact that her name is left off stinks of misogyny imo

[primeideal]

this is a COMPLETELY RANDOM ASK from a stranger because I saw you comment on anghraine's post and had to jump over to your ask box and tell you that I love your blog name! hi fellow maths person isn't algebra great! (is it a Noetherian ring though. inquiring minds want to know.)

ahahahaha thank you! I came up with this username in...2012 when I wanted a new pseud and I have, uh, gone on to do a lot with algebra and ring/ideal type stuff since then, so it was fate.

Is it a Noetherian ring? I don't know, it *might* be! :)

#asks #math