You might like this @visualpde.com simulation. It starts with a point source in a way equation, and you click to add obstacles. Press 'r' or click the second button from the bottom on the left to "restart" the simulation. Everything can be customized as you'd like.
visualpde.com/sim/?preset=...
"The institution built to nurture enquiry has increasingly become one that merely measures, audits and verifies it. We produce abundant evidence of learning, but not necessarily more learning itself."
Even before LLMs, this was increasingly problematic!
www.timeshighereducation.com/opinion/bure...
Right now, Professor Longhua Zhao from Case Western is giving a talk on fluid-structure interaction.
Please see below for information about joining the seminar.
A poster for the symposium described in the post. It lists the dates of 8-11 of September. It has a photo of the Durham castle, and a list of the invited speakers (which is also on the website linked in the post). It also has the application deadline of March 31st. The ICMS logo and Durham University logos are both displayed at the bottom.
Join us this September 8-11th for the Durham Symposium on Mathematical Approaches to Spatial Biology! Organized with @gcelora.bsky.social @valeriagiunta.bsky.social and Denis Patterson. This will be an exciting and interactive discussion-driven event!
sites.google.com/view/durham-...
Not exactly the same conclusion but in a similar vein to @lastpositivist.bsky.social's nice paper against peer review:
www.journals.uchicago.edu/doi/10.1093/...
I would much prefer Universities that were not laser-focused on credentialism, so that we could instead consider crazy ideas like "teaching."
I really am increasingly drawn to the idea that, outside of areas where professional accreditation matters, I think academics obsession with assessment is just a huge waste of time.
There is very little equitable assessment of mathematics that correlates at all to how mathematicians work.
Text which says: " You said: Uploaded image Can you transcribe the two paragraphs here into text I can copy and paste? ChatGPT said: Here is a clean transcription of the two paragraphs: Unlike the theory, models are restricted by technical considerations to a few components at a time, even in systems which are complex. Thus a satisfactory theory is usually a cluster of models. These models are related to each other in several ways: as coordinate alternative models for the same set of phenomena, they jointly produce robust theorems; as complementary models they can cope with different aspects of the same problem and give complementary as well as overlapping results; as hierarchically arranged “nested” models, each provides an interpretation of the sufficient parameters of the next higher level where they are taken as given. In Figure 3 we show schematically the relations among some of the models in the theory of community structure. The multiplicity of models is imposed by the contradictory demands of a complex, heterogeneous nature and a mind that can only cope with few variables at a time; by the contradictory desiderata of generality, realism, and precision; by the need to understand and also to control; even by the opposing esthetic standards which emphasize the stark simplicity and power of a general theorem as against the richness and the diversity of living nature. These conflicts are irreconcilable. Therefore, the alternative approaches even of contending schools are part of a larger mixed strategy. But the conflict is about method, not nature, for the individual models, while they are essential for understanding reality, should not be confused with that reality itself."
Related is the following passage from Levins, arguing for the need of diversity in schools of thought/paradigms in science:
www.jstor.org/stable/27836...
I like much of Feyerabend's writing about the scientific method. I disagree with a strong form of this, which might be "there is little value in formalizing good scientific practice," but the weaker form of no universally better methods is hard to argue with!
en.wikipedia.org/wiki/Against...
I haven't encountered this too much (that I can tell!) but it's also more than zero, and I have a similar reaction to Rose here. As she says... it's just very bizarre to do a philosophy degree if you don't actually want to think and work through ideas. What... what are you doing here?
At least there are a large collection of facts to put on the exams!
link.springer.com/article/10.1...
The fact that I could have genuine friends I knew only through plain text (no one had profile pics or avatars yet) felt like some kind of utopian dream at the time when I was an awkward kid irl. I think that dynamic is still one of the things that draws me to text-based social media over video/pics.
We are very grateful for funding from @icms-edinburgh.bsky.social, and for our excellent invited speakers @danieleavitabile.bsky.social, @zenahadjivasiliou.bsky.social, @cicelykrystyna.bsky.social, @pearce-maths.bsky.social, @kylewedgwood.bsky.social + those listed above not on Bluesky.
A poster for the symposium described in the post. It lists the dates of 8-11 of September. It has a photo of the Durham castle, and a list of the invited speakers (which is also on the website linked in the post). It also has the application deadline of March 31st. The ICMS logo and Durham University logos are both displayed at the bottom.
Join us this September 8-11th for the Durham Symposium on Mathematical Approaches to Spatial Biology! Organized with @gcelora.bsky.social @valeriagiunta.bsky.social and Denis Patterson. This will be an exciting and interactive discussion-driven event!
sites.google.com/view/durham-...
One (among many other) of the main applications of functional analysis is to extend these ideas to PDEs.
From the stability/dynamical systems perspective, the study of self-adjointness of an operator is often tied to questions like "does it have real eigenvalues? Can we say that the spectrum lies in the left-hand side of the complex plane (which implies a kind of stability)?"
That's a common thing to do! Linearizing a PDE around some steady state solution for example gives a linear operator which can be studied to understand stability. The same is true of n-dimensional systems of ODEs; linearizing gives a Jacobian matrix which determines stability.
For linear operators, the adjoint operator is typically easy to find, though I guess this depends on the function space/properties of the inner product. I don't know an example where it isn't algorithmic.
However, there are lots of approximations to a general operator by self-adjoint operators.
This was the motivation for the "reverse-order" from how I learned the topic.
You may also be interested in VisualPDE.com as a way to build intuition, especially about nonlinear PDE. This is rather a different, but complementary, approach to the analysis-focused way of approaching PDE.
My personal recommendations might be (roughly in reverse order of how advanced they are):
bookstore.ams.org/gsm-19-r
www.amazon.co.uk/Introductory...
www.amazon.co.uk/Principles-M...
(As a student I studied them in the reverse order; the last Chapter of the 3rd book is measure theory).
Next, a glorious combo of maths, metals, and microbial ecology. This one is supervised by Denis Patterson and @blindmath.bsky.social, also at Durham.
www.findaphd.com/phds/project...
Lots of PhD opportunities for UK + international students involving my lab. Topics relate to metals & microbiology.
First up: TonB-dependent receptors in commensal Neisseria in my lab at Durham, with @kjosts.bsky.social and @mattbashton.bsky.social.
www.findaphd.com/phds/project...
I've found Feyerabend to be very good at these pithy quotes that make you think. AFAIK his whole schtick was to say controversial things that made people think, and then to claim that this is what science is — a big dialogue requiring constant thinking and refinement of arguments.
Among other difficulties is that most biological things are nonequilibrium, where there is not (AFAIK) a universal definition of phases etc. Though there are lots of areas/subfields where people do use precise definitions of course; just not with the same generality as in equilibrium stat mech.
Possibly useful for @joshuabull.bsky.social @josh-moore.bsky.social. Josh will also give a seminar in February @darrenjw.bsky.social; it'd be good for you two to chat I think!
Some lecture notes on spatial and temporal modelling, illustrated using R - darrenjw.github.io/spatio-tempo... - #rstats #rspatial #quarto
We are recruiting several PhD students. If you are interested in conservation conflicts, population ecology, quantitative ecology, or biodiversity, check these projects out (links in the thread, feel free to reach out):
So it begins again here, like the germ of a continuous function...
OK, that thread was worth unraveling!
