Questions tagged [applied-mathematics]
the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)
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How does one justify funding for mathematics research?
G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...
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Examples of theorems misapplied to non-mathematical contexts
For something I'm writing -- I'm interested in examples of bad arguments which involve the application of mathematical theorems in non-mathematical contexts. E.G. folks who make theological arguments ...
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Deep learning / Deep neural nets for mathematician
I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".
Most of the papers/books that are often quoted in papers/...
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Mathematical conjectures on which applications depend
What are some examples of mathematical conjectures that applied mathematicians assume to be true in applications, despite it being unknown whether or not they are true?
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Is there a mathematical and information theoretic explanation for this cube packing phenomenon?
I saw this unintuitive result on dice packing:
A jumble of thousands of cubic dice, agitated by an oscillating
rotation, can rapidly become completely ordered, a result that is hard
to produce with ...
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Which high-degree derivatives play an essential role?
Q. Which high-degree derivatives play an essential role
in applications, or in theorems?
Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration),
and the ...
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Interesting mathematical topics arising from biology
I've heard that there's a relatively new field of science called mathematical biology.
It will certainly apply well known and less known mathematical techniques to the understanding of some biological ...
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What "real life" problems can be solved using billiards?
Recently I gave an interview to local media where I explained some basic open problems in billiard dynamics.
After a 45 min interview the reported asked me what "real life" problems can be ...
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Listing applications of the SVD
The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
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On Mathematical Analysis of MathSciNet & MathOverflow
This question has two original motivations: mathematical and social.
The mathematical motivation is mainly based on what I have seen about Zipf's law here and there. The Zipf's law simply states ...
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Examples of mathematics motivated by technological considerations
I would like examples of technological advances that were made possible only by the creation of new mathematics. I'm talking about technology that was desired in some period of history but for which ...
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Why is persistent cohomology so much faster than persistent homology
I refer to this paper: de Silva, Vin; Morozov, Dmitriy; Vejdemo-Johansson, Mikael. Dualities in persistent (co)homology. Inverse Problems 27 (2011), no. 12, 124003, 17 pp. (Journal link, arXiv link).
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How is differential geometry used in immediate industrial applications and what are some sources to learn about it?
Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...
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Do bubbles between plates approximate Voronoi diagrams?
For example, soap bubbles:
Image from UPenn:
"A 2-dimensional foam of wet soap bubbles squashed between glass plates, after 10 hours ...
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Differentiable functions with discontinuous derivatives
For years I've taught my honors calculus students about functions like (the continuous extension of) $x^2 \sin 1/x$, and for just as many years I've told them that they won't encounter functions like ...
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Persistence barcodes and spectral sequences
Persistent homology is a well-developed tool which allows topological analysis of large data sets. From a topological perspective, the input is a filtered complex, and the output is a sequence of ...
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Mathematics and cancer research
What are applications of mathematics in cancer research?
Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this ...
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Is there any paper which summarizes the mathematical foundation of deep learning?
Is there any paper which summarizes the mathematical foundation of deep learning?
Now, I am studying about the mathematical background of deep learning.
However, unfortunately I cannot know to what ...
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Importance of integral equations
Differential equations are at the heart of applied mathematics - they are used to great success in fields from physics to economics. Certainly, they are very useful in modelling a wide range of ...
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Recent uses of applied mathematics in pure mathematics
In this answer Yves de Cornulier mentioned a talk about the possible uses of persistent homology in geometric topology and group theory. Persistent homology is a tool from the area of topological data ...
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Is the field of q-series 'dead'? [closed]
I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
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Examples of research on how people perceive mathematical objects
What examples are there on research related to human perception and mathematical objects?
For example, the shape of a beer glass influences drinking habits,
since people are bad at integrating.
...
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Differential geometry applied to biology
This was originally a question posted here on MathSE. But I'll ask again here to see if I can get some different answers.
I'm looking for current areas of research which apply techniques from ...
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Physical interpretation of the Manifold Hypothesis
Motivation:
Most dimensionality reduction algorithms assume that the input data are sampled from a manifold $\mathcal{M}$ whose intrinsic dimension $d$ is much smaller than the ambient dimension $D$. ...
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What tools should I use for this problem?
Suppose we have $d$ cylindrical metal bars, with radius $l$, attached orthogonal to a support in random places:
Now we have to attach bars with radius $k$ EVENLY SPACED, with distance $p$ between ...
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Mathematicians learning from applications to other fields
Once upon a time a speaker at the weekly Applied Mathematics Colloquium at MIT (one of two weekly colloquia in the math department (but the other one is not called "pure")) said researchers ...
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Robotics, Cryptography, and Genetics applications of Grothendieck's work? [closed]
I was reading about the passing of Alexander Grothendieck, and something caught my interest:
Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal ...
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Relevant mathematics to the recent coronavirus outbreak
I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
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On the non-rigorous calculations of the trajectories in the moon landings
In a paragraph written by a person emphasizing that rigour is not everything in mathematics (I wish I had written down the details), it was stated that the moon landings would have been impossible ...
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Applications of commutative algebra
Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think ...
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Models for graphs representing real-life networks
I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks).
I will be thankful for answers ...
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How is Ricci flow related to computer graphics?
I recently came across the book Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications by Wei Zeng and Xianfeng David Gu. Because, I just saw the book on the ...
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2/3 power law in the plane
I've recently come across a particular problem whose solution turns out to be a probability distribution given by $f(x) = \alpha \|x\|^{-2/3}$ in the unit disk in $\mathbb{R}^2$ and zero elsewhere (I ...
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Is it fine to inquire about a paper that's been under review for around 9 months?
I have submitted a paper on applied probability in one of SIAM journals. The paper is under review for 9 months. I asked the editor 1 month ago about it, I was told that one review report has come and ...
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Malaysia Airlines Flight 370? [closed]
News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went.
From a naive intuitive point of view, if ...
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Are there any books/articles that apply abstract coordinate free differential geometry to basic thermodynamics?
The mathematical structure of thermodynamics by Peter Salamon (pdf) would be an example, but i would like a more abstract natural formulation of application of differential geometry or even geometric ...
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What are efficient pooling designs for RT-PCR tests?
I realize this is long, but hopefully I think it may be worth the reading for people interested in combinatorics and it might prove important to Covid-19 testing. Slightly reduced in edit.
The ...
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Is fuzzy mathematics useful in pure mathematics ?
Fuzzy sets and logic seem to be mostly used for applying to real-world situations, control-theory, game-theory, economics, statistics, data management, artificial intelligence, automated reasoning etc
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Orthogonal polynomial under linear transformation
Let $M_n(x) = x^n$ be the standard monomials. The binomial formula allows one to expand $M_n(ax+b)$ as a linear combination of $M_k(x)$, for $k \leq n$, giving
$$
M_n(ax+b) = (ax+b)^n = \sum_{k=0}^n \...
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How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?
I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...
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Moduli spaces in applied mathematics and condensed matter physics?
In this MO question it is stated that there is a relation between some aspects of condensed matter physics (namely the fractional quantum Hall effect) and the algebraic geometry of Hilbert schemes.
...
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random category theory
This question is in some sense dual to the one asked in Is there an introduction to probability theory from a structuralist/categorical perspective? since contrary to the OP who asks for references ...
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positions of a methane molecule with carbon atom at the origin
Let $\text{CH}_4$ be the molecule of Methane:
The four hydrogen atoms form vertices of a regular tetrahedron with the carbon atom in the center of the regular tetrahedron.
Here we regard all atoms to ...
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Question on pure mathematics helping climate change research
While I am a pure mathematics tenured professor, still at a relatively young age, and fairly passionate about my area of research, I cannot help but feel that it may be more useful to humanity if I ...
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Useful applications of applied category theory
Led by John Baez, applied category theory (e.g. [1]) seems to accumulate much popularity. As someone who has noticed the importance of category theory in pure mathematics (e.g. homotopy theory, tqfts, ...
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Explain seemingly non-random figures which arise from random Poisson points with normalization
Context Working with some biological datasets it was puzzling to see the patterns like Figure 2 (right) below. The first feeling was, that it corresponds to some biological effects like correlations ...
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Applications of Topological Complexity of configuration space
I'm starting to work on topological complexity of configuration spaces.
Articles say that this field has applications in robotic and control theory. One of the important articles belongs to Michael ...
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What are the top journals in applied mathematics and what are the differences between them? [closed]
This question is essentially an applied mathematics version of Which are the best mathematics journals, and what are the differences between them?
Unfortunately, unlike the above question I was not ...
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The function space defined by deep neural nets
Given a deep net graph and the activation functions on the hidden vertices do we have a description of the function space spanned by it? (even if for some specific architectures and activation ...
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Is there a way to define a Lie derivative of a connection?
I've been reading a little bit about the definition of symmetries on General Relativity, and they are related with the concept of Killing vector, i.e., vectors along which the Lie derivative of the ...
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